APPLIED INDUSTRIAL ENERGY AND ENVIRONMENTAL MANAGEMENT

Z K Morvay D D Gvozdenac

Part III

FUNDAMENTALS FOR ANALYSIS AND CALCULATION OF ENERGY AND

ENVIRONMENTAL PERFORMANCE

1

Applied Industrial Energy and Environmental Management Zoran K Morvay and Dusan D Gvozdenac copy John Wiley amp Sons Ltd

Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-

PHYSICAL PROPERTIES AND OTHER

ENGINEERING DATA

SI UNITS

1 The System International (SI) This came into being in October 1960 and has ever since been recognized officially and adopted by

nearly every country although its actual use varies considerably It is based on seven principal units

one in each of seven different categories

Table 41 The SI Seven Principal Units

Category Name Abbreviation

Length Meter m

Mass Kilogram kg

Time Second s

Electric current Ampere A

Temperature Kelvin K

Amount of substance Mole mol

Luminous intensity Candela cd

From these basic units many other units are derived and named

2 Definitions of the Seven Basic SI Units

meter [m] Meter is a basic unit of length It is the distance light travels in a vacuum in 1299 792 458th

of a second

kilogram [kg] Kilogram is a basic unit of mass It is the mass of an international prototype in the form of a

platinum-iridium cylinder kept at Sevres in France It is now the only basic unit still defined in

terms of a material object and also the only one with a prefix [kilo] already in place

second [s] Second is a basic unit of time It is the length of time taken for 9 192 631 770 periods of

vibration of the cesium-133 atom

ampere [A]

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 2

Ampere is a basic unit of electric current It is that current which produces a specified force

between two parallel wires which are 1 meter apart in a vacuum

kelvin [K] Kelvin is a basic unit of temperature It is 127316th of the thermodynamic temperature of

the triple point of water

mole [mol] Mole is a basic unit of substance It is the amount of substance that contains as many

elementary units as there are atoms in 0012 kg of carbon-12

candela [cd] Candela is a basic unit of luminous intensity It is the intensity of a source of light of a

specified frequency which gives a specified amount of power in a given direction

3 Derived Units of the SI From the seven basic units of the SI other units are derived for a variety of purposes Only a few of

them are explained here as examples

farad [F] Farad is the SI unit of the capacitance of an electrical system that is its capacity to store

electricity

hertz [Hz] Hertz is a SI unit for the frequency of a periodic phenomenon One hertz indicates that one

cycle of the phenomenon occurs every second

joule [J] Joule is a SI unit of work or energy One joule is the amount of work done when an applied

force of 1 newton moves through a distance of 1 meter in the direction of the force

newton [N] Newton is a SI unit of force One newton is the force required to give a mass of 1 kilogram

an acceleration of 1 meter per second

ohm [Ω] Ohm is a SI unit of resistance of an electrical conductor

pascal [Pa] Pascal is a SI unit of pressure One pascal is the pressure generated by a force of 1 newton

acting on an area of 1 square meter

volt [V] Volt is a SI unit of electric potential One volt is the difference of potential between two

points of an electrical conductor when a current of 1 ampere flowing between those points

dissipates a power of 1 watt

watt [W] Watt is used to measure power or the rate of doing work One watt is a power of 1 joule per

second

4 The SI allows the sizes of units to be made bigger or smaller by the use of appropriate

prefixes

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 3

Table 42 Prefixes of Units yotta [Y] = 10+24

zetta [Z] = 10+21

exa [E] = 10+18

peta [P] = 10+15

tera [T] = 10+12

giga [G] = 10+9

mega [M] = 10+6

kilo [k] = 10+3

hecto [h] = 100

deca [da] = 10

deci [d] = 01

centi [c] = 001

milli [m] = 10-3

micro [micro] = 10-6

nano [n] = 10-9

pico [p] =10-12

femto [f] = 10-15

atto [a] = 10-18

zepto [z] = 10-21

yocto [y] = 10-24

1

5 SI unites and conversion factors For other systems of measurement these are as follows

Table 43 Conversion Factors

Name SI unit Conversion factors for most frequently used units of other

systems and non-system units

Acceleration linear ms2 1 ins2 = 00254 ms2

Area m2 1 ft2 = 00929 m2

1 in2 = 6451times10-4 m2

Density kgm3

1 tonm3 = 1 kgdm3 = 1 gcm3 = 103 kgm3

1 (kgf s2)m4 = 981 kgm3

1 lbft3 = 1602 kgm3

1 lbin3 = 2768times103 kgm3

Density of heat flux Wm2 1 kcalm2 = 1163 Wm2

Diffusion coefficient m2s 1 ft2s = 00929 m2s

Energy work quantity of heat J

1 kWh = 36times106 J

1 kcal = 41868 kJ = 41868times103 J

1 lbf timesft = 1356 J

1 lbf timesin = 0133 J

1 BTU = 10551 J

Enthalpy specific Jkg 1 kcalkg = 1 calg = 4190 Jkg

1 BTUlb = 2326 Jkg

Entropy specific J(kg K) 1 kcal(kg K) = 4190 J(kg K)

1 BTU(lb oF) = 4190 J(kg K)

Force (weight) N

1 kgf = 981 N

1 dyn = 10-5 N

1 sn = 103 N

1 lbf = 445 N

Frequency Hz

1 s-1 = 1 Hz

1 rps = 1 Hz

1 rpm = 160 Hz

Heat capacity specific J(kg K) 1 kcal(kg K) = 4190 J(kg K)

1 BTU(lb oF) = 4190 J(kg K)

Heat transfer coefficient individual

and overall W(m2 K)

1 kcal(kg K) 4190 J(kg K)

1 BTU(ft2 h oF) = 56 W(m2 K)

Length m

1 microm (micron) = 10-6 m

1 Aring =10-10 m

1 ft (lsquo) = 03048 m

1 in (lsquo) = 00254 m

Mass kg 1 ton (m3tric) = 1000 kg

1 lb = 0454 kg

Power W

1 (kgf m)s = 981 W

1 kcalh = 1163 W

1 (lbf ft)s = 1356 W

1 hp = 7353 W

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 4

Pressure Pa

1 bar = 105 Pa

1 mbar = 100 Pa

1 kgfcm2 = 1 at = 735 mm Hg = 981times104 Pa

1 atm = 760 mm Hg = 101325 Pa

1 kgfm2 = 981 Pa

1 mm H2O = 981 Pa

1 mmHg = 1333 Pa

1 lbfin2 = (psi) = 689476 Pa

1 lbfft2 = 4788 Pa

Rate of flow mass kgs 1 lbs = 0454 kgs

1 lbh = 126times10-4 kgs

Rate of flow volumetric m3s

1 lmin = 1667timesm3s

1 ft3s = 283times10-3 m3s

1 in3s = 164times10-6 m3s

Specific heat of phase transition Jkg 1 kcalkg = 4189 Jkg

1 BTUlb = 2326 Jkg

Surface tension Nm 1 kgfm = 981 Jm2 = 981 Nm

Thermal conductivity W(m K) 1 kcal(m h K) = 1163 W(m K)

1 BTU(ft h oF) = 173 W(m K)

Time s 1 h = 3600 s

1 min = 60 s

Temperature K

t [oC] = (t + 27315) [K]

t [oF] = 15273)32t(9

5 [K]

Velocity angular rads srad

30rpm1

srad2rps1

Velocity linear ms 1 fts = 03048 ms

Viscosity dynamic Pa s 1 P (poises)= 01 Pa s

1 cP (centipoises) = 19180 kgf sm2 = 10-3 Pa s

Viscosity kinematic m2s

1 S (stokes) = 1 cm2s = 10-4 m2s

1 ft2s = 0093 m2s

1 ft2h = 2581 m2s

Volume m3

1 l = 10-3 m3

1 ft3 = 283 dm3 = 00283 m3

1 in3 = 16387 cm3 = 1639times10-6 m3

Volume specific m3kg 1 m3ton = 10-3 m3kg

1 lkg = 1 cm3g = 10-3 m3kg

Note The values of the conversion factors are given with the sufficient accuracy for engineering calculations

A USEFUL DEFINITION FOR ENERGY ANALYSIS

6 The ton of oil equivalent (toe) is a unit for measuring energy It corresponds to 10 Gcal or

41868 GJ or 1163 MWh It is a rounded amount of energy that would be produced by burning one

metric ton of crude oil Since crude oil of different origin has different chemical properties and

therefore gives off varying amounts of heat when burnt the value is a matter of consensus to a certain

extent toe is A particularly useful unit for quantifying energy production or consumption for one

country or for the entire world

7 The most useful and practical definition of energy is that it is a measure of the capacity for

doing work Energy comes from many sources ndash sunlight wind water coal oil gas etc and it has

many types thermal electrical chemical nuclear etc

Specific energy is a measure of the amount of energy contained in a single quantity of some

substance It is also known as calorific value

The energy content can be expressed in any unit of energy BTU calories joules watt-hours etc

The preferred unit is joules with the appropriate range of prefixes for kilojoules [kJ] megajoules

[MJ] etc

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 5

The unit quantity may be either of mass (kg) or of volume (cubic meters) It depends on the nature

of the substance For solids it is usual to use unit mass and for gases to use unit volume (together

with a statement of pressure and temperature) For liquids either mass or volume can be used

The approximate Specific Energy values (NCV1 LCV

2) of some solid fuels are

Coal 23 to 35 MJkg

Wood 16 to 21 MJkg

Peat 23 MJkg

Charcoal 28 to 33 MJkg

Natural uranium ndash in light water reactor 443 000 MJkg

Enriched uranium (35 ) ndash in light water reactor 3 456 000 MJkg

Uranium - in fast breeder reactor 24 000 000 MJkg

The approximate Specific Energy values (NCV LCV) of some gas fuels are Coal gas 19 to 22 MJmsup3

Natural gas 37 MJmsup3

Acetylene 56 MJmsup3

Propane 93 MJmsup3

Butane 110 MJmsup3

All are based on particular pressure and temperature Gas heating value varies with the

geographical location

Standard metric gas conditions are 101325 kPa and 15 oC (dry)

Normal metric gas conditions 101325 kPa and 0 oC (dry)

The approximate specific energy values (LCV) of some liquid fuels are Gasoline 421 MJkg

Petroleum 398 MJkg

Diesel 418 MJkg

Heavy Fuel Oil 418 MJkg

Higher Heating Value (HHV) Gross Heating Value (GHV) Gross Calorific Value (GCV) and

Total Calorific Value (TCV) are different terms for the same value This can be defined as total heat

obtained from combustion of a specified amount of fuel and its stoichiometrically correct amount of

air both being at 1556 oC (60

oF) when combustion starts and the combustion products being cooled

to 1556 oC (60

oF) before heat release is measured

Lower Heating Value (LHV) Net Heating Value (NHV) Low Calorific Value (LCV) is lower

than Total Calorific Value for the value of latent heat of vaporization of water formed in combustion

Some typical values for the ratio of net to gross values are as follows

Fuel NetGross Ratio

Natural gas 090

Fuel oil 094

Coal 098

Nuclear energy is totally different in both the method of production and the scale of released

energy As a very rough guide the fission of a given mass of a suitable material (such as plutonium)

produces something of the order of 3 million times the energy obtained from the same mass of an

lsquoordinaryrsquo fuel such as coal

8 Density is mass of fluid in a unit volume [kgm3]

9 Dynamic viscosity is the tangential force per unit area required to move one horizontal plane

with respect to the other at unit velocity when maintained at a unit distance apart by the fluid It

appears as a result of cohesion and interaction between molecules

1 NCV ndash Net Calorific Value

2 LCV ndash Low Calorific Value (NCV = LCV)

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 6

Different fluids deform at different rates under the same shear forces Fluid with a high viscosity

such as syrup deforms more slowly than fluid with a low viscosity such as water

Newtonian fluids obey the linear relationship given by the Newtons law of viscositydx

dw

where is the shear stress and micro is the coefficient of dynamic viscosity

Viscosity is resistance of a fluid to flow This resistance acts against the motion of any solid

object through the fluid and also against motion of the fluid itself past stationary obstacles Viscosity

also acts internally on the fluid between slower and faster moving adjacent layers

All fluids (liquids and gases) exhibit viscosity to some degree Viscosity may be thought of as

fluid friction just as the friction between two solids resists the motion of one over the other but also

makes possible the acceleration of one relative to the other

The dynamic viscosities of some fluids are presented in Table 44 It is very important to know the

temperature of the fluid (and pressure)

Table 44 Dynamic Viscosity of Some Liquids and Gasses Liquid Gas

Gasoline Water Air (dry)

1013 bar

Carbon Dioxide

1013 bar

t (oC) Μ

[Pa s] t (oC)

μ

[Pa s] t (oC)

μ

[Pa s] t (oC)

μ

[Pa s]

20 0529times10-3 0 1780times10-3 0 0017times10-3 0 0014times10-3

40 0411times10-3 20 1004times10-3 100 0022times10-3 100 0018times10-3

60 0328times10-3 40 0653times10-3 200 0026times10-3 200 0023times10-3

100 0225times10-3 60 0470times10-3 300 0030times10-3 300 0026times10-3

80 0355times10-3 400 0033times10-3 400 0030times10-3

100 0283times10-3 500 0036times10-3 500 0033times10-3

10 Kinematic viscosity is the ratio of absolute viscosity to density For either dynamic or

kinematic viscosity to be meaningful a reference temperature must be quoted

11 Thermal conductivity is a measurement of the ability of a material to conduct heat It is

defined using the Fouriers law of conduction which relates the rate of heat transfer by conduction to

the temperature gradient

dx

dTAkq (41)

where k is the thermal conductivity Using the Fouriers law we can define the thermal conductivity

as the rate of heat transfer through a unit thickness of material per unit area and per unit temperature

difference A good conductor of heat has a high value of thermal conductivity

The temperature variations of the thermal conductivities of some materials are presented in Table

5

Table 45 Thermal Conductivity of Some Materials ndash k [W(m K)]

t (oC)

Solid Liquid Gas

Copper Aluminum Gasoline Water Air (dry)

1013 bar

Steam

(saturated)

-100 407 -

0 386 221 00244 001760

100 379 - 01005 00680 00321 002372

200 373 229 00670 00393 003547

300 - 222 00558 00460 006270

500 - - 00574

700 - - 00671

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 7

12 Specific heat is the amount of heat that is required to raise the temperature of the unit mass of

a substance by one degree In a constant pressure process

Tcmq p (42)

cp is specific heat at constant pressure

Values of cp [kJ(kg K)] for various materials (at 20 oC) are shown in Table 46

Table 46 Specific Heat at Constant Pressure of Some Materials

SOLID cp

kJ(kg K) LIQUID

cp

kJ(kg K) GAS

cp

kJ(kg K)

Aluminum (pure) 0903 Water 418 Air 1010

Copper (pure) 0385 Ethyl Alcohol 229 Nitrogen 1047

Gold 0129 Gasoline 206 Sulfur Dioxide 0633

Silicon 1382 Oil 185 Carbon Dioxide 0837

13 Coefficient of thermal expansion is defined as the change in the density of a substance as a

function of temperature at constant pressure It is expressed as follows

pT

1 (43)

For ideal gases TRp

there is T

1

14 Thermal diffusivity is measure of heat propagation through a medium and may be defined by

the ratio of heat conducted through a material to the heat stored in the material The thermal

diffusivity is defined as

pc

ka (44)

The larger the thermal diffusivity is the faster the propagation of heat into the material If the

thermal diffusivity is small it means that a large part of heat is absorbed by the material and only a

small portion is conducted through it Some typical values of thermal diffusivity are given in Table

47 (0 oC 1013 bar)

Table 47 Thermal Diffusivity of Some Materials

SOLID a

m2s LIQUID

a

m2s GAS

a

m2s

Aluminum 93166times10-6 Water 0131times10-6 Air 18777times10-6

Copper 114085times10-6 Ethyl Alcohol 0100times10-6 Nitrogen 18703times10-6

Gold 12479times10-6 Gasoline 0075times10-6 Sulfur Dioxide 4711times10-6

Polystyrene 0611times10-6 Oil 0154times10-6 Carbon Dioxide 9097times10-6

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 8

PHYSICAL PROPERTIES

15 Physical Properties of Selected Gases

Table 48 Physical Properties of Selected Gases (10 bar 0 oC)

Material Density

Molar

Mass

Gas

Const

Boiling

Point cp cpcv 106 timesmicro K Pr

kgm3 gmol J(kg K) ordmC J(kg K) - Pa s W(m K) -

Air (dry) 1293 2895 287 -195 1010 14 173 00245 071

Argon [Ar] 1782 3994 2085 -1858 532 165 209 00173 064

Carbon Dioxide

[CO2] 1976 4401 189 - 837 13 137 00137 084

Carbon Monoxide

[CO] 125 2801 297 1047 14 166 00226 077

Helium [He] 0178 4002 2079 -2689 5274 166 188 0144 069

Hydrogen [H2] 00898 2016 4125 -2529 14266 1407 842 0163 074

Nitrogen [N2] 1251 2802 2967 -1958 1047 14 17 00228 078

Oxygen [O2] 1429 32 2599 -1829 913 14 203 0024 077

Normal composition of clean dry atmospheric air near the sea level

Nitrogen (N2) =78084 Oxygen (O2) = 20948 Argon (Ar) = 0934 Carbon Dioxide (CO2) =0031

Neon (Ne) Helium (He) Krypton (Kr) Hydrogen (H2) Xenon (Xe) Methane (CH4) Nitrogen Oxide (N2O) Ozone (O3)

Sulfur Dioxide (NO2) Ammonia (NH3) Carbon Monoxide (CO) and Iodine (I2) =traces of each gas for a total of 0003

Formulae for the calculation of average constant-pressure specific heat ndash cp [kJkg] of various gases in

the range from 0 to 2000 oC are presented in Table 49

Table 49 Average Specific Heat at Constant Pressure of some Gases

Gas

Average Specific Heat at Constant Pressure

])C[t()Kkg(kJ[c ot

op

(Range 0 to 2000 oC)

Maxim

um

Error

Hydrogen (H2) 01+143810E +t 04-200328E +t08-356131E - t10-342031E + t13-108329E- = 234 006

Nitrogen (clean)

(N2) 00103937E t 06-857115E t07-173326E t10-106900E - t14-207571E = 234 009

Oxygen (O2) 01-907389E t 04-144682E t08-150961E t11-443486E - t14-123574E = 234 012

Carbon Monoxide

(CO) 00103823E t 05-124096E t07-176241E t10-120740E - t14-251706E 234 011

Carbon Dioxide

(CO2) 01-820310E t 04-516236E t07-298914E - t10-104359E t14-156925E- = 234 006

Water Vapor (H2O) 00185773E t 04-135306E t07-267351E t10-142139E - t14-235461E= 234 004

Sulfur Dioxide

(SO2) 01-606803E t 04-321094E t07-201319E - t11-653115E t15-804281E- = 234 012

Air 00100361E t 05-218551E t07-142841E t11-968901E - t14-199627E = 234 009

Nitrogen (form Air)

(N2) 00102694E t 05-142726E t07-131381E t11-797576E - t14-148364E = 234 014

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 9

16 Physical Properties of Selected Liquids

Table 410 Physical Properties of Selected Liquids

Liquid t [oC] ρ [kgm3] cp [kJkg

K)]

k [W(m

K)]

micro times 103 [Pa

s]

β times 105

[1K] a [m2s]

Acetone 20

50

791

756

216

225

0170

0163

0331

-

143

-

Gasoline

20

40

60

100

751

735

717

681

206

215

224

246

01165

-

-

01005

0529

0411

0328

0225

125

-

-

-

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol

0

20

50

806

789

-

229

245

281

0185

0183

0178

178

119

0695

Ethylene

Glycol

20

40

60

80

100

1113

1099

1085

1070

1056

2382

2474

2562

2650

2742

0258

-

-

-

0269

1990

913

495

302

199

Glycerin

20

50

100

200

1260

1244

1200

1090

235

250

279

334

-

0283

0289

-

1480

180

13

022

53

-

-

-

Methyl Alcohol

0

20

50

810

792

765

243

247

256

0241

0212

-

0818

0585

0400

Petroleum

20

50

100

200

819

801

766

785

200

214

238

289

-

01114

01042

00891

149

0956

0545

0262

100

-

-

-

Oil (lubricant)

25

50

75

100

920

905

896

880

1850

1943

2041

2136

0130

0128

0125

0123

190

429

156

572

Oil

(transformer)

25

50

75

100

860

845

835

820

1918

2043

2169

2294

0123

0122

0120

0117

2420

990

477

302

17 Thermodynamic and Transport Properties of Water and Steam

a Some of thermodynamic properties of water are

H2O = Chemical formula

M = 18016 [kgkmol] (Molecular Mass)

tc = 37415 [oC] (Critical Temperature)

Tc = 647286 [K] (Absolute Critical Temperature)

pc = 22089 [bar] (Critical Pressure)

c = 3170 [kgm3] (Critical Density)

tm = 001 [oC] (Melting Temperature at 101325 bar)

rm = 332432 [kJkg] (Heat of Melting at 101325 bar)

tb = 1000 [oC] (Boiling Temperature at 101325 bar)

rb = 22570 [kJkg] (Heat of Evaporation at 101325 bar)

R = 462507 [J(kg K)] (Gas Constant)

Enthalpies and entropies of boiling water and saturated steam versus temperature and

pressure (001 lt p lt 20 bar 7 lt t lt 212 oC)

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 10

a Saturated steam and boiling water temperature versus pressure3

112

31-42-

5-36-5

109963430 ln(p)][102794824 ln(p)][2397684

ln(p)][102118802 ln(p)][101786280

ln(p)][101285144 ln(p)][1005-5518190E t

(45)

Error is in the range 007

b Saturated steam and boiling water pressure versus temperature

5098158] -t 107261845 t102974345 - t101096061

t103381446 - t107363934 t10316exp[-7789p

2-24-36-

4-95-126-15

(46)

Error is in the range of 005

c Enthalpy of boiling water versus temperature

1-

2-53-74-9

10359463 t 417927

t10723854 - t10706612 t10833022h (47)

d Enthalpy of saturated steam versus temperature

250044 t 187334

t10103177 - t10151237 t10332313 - h 2-33-64-8

(48)

e Entropy of boiling water versus pressure

130250 ln(p)10315672

(ln(p))10167802 (ln(p))10145398 (ln(p))10973390s

2-

2-33-44-5

(49)

f Entropy of saturated steam versus pressure

736130 ln(p)10336497 - (ln(p)10760363 (ln(p)10-538843s -12-43-4 (41

0)

Water properties (temperatures from 0 to 300 oC)

(From 0 to 100 oC at 1013 bar and for higher temperatures for boiling pressure)

g Density [kgm3]

22-23-

3-54-75-106-13

10999945 t 10410381 t10726539 -

t10428877 t10208168 - t10556465 t10-644703

(411

)

3 ln - natural logarithm

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 11

h Specific heat at constant pressure cp [J(kg K)]

30-21-

3-34-65-86-11p

10421629 t 10370637 - t10109452

t10142353 -t10976851 t10317259 - t10400424c

(412

)

i Thermal conductivity [W(m K)]

11-23-

3-64-95-116-112

10549688 t 10285413 t10210253 -

t10672554 t10740918 - t10187737 - t1036594410

(413

)

j Thermal diffusivity a [m2s]

pca (414)

k Dynamic viscosity [Pa s]

748230 t 10322128 - t10218237

t10103401 - t10272328 t1077Exp(-291810

2-22-

3-64-95-126

(415)

l Kinematic viscosity [m2s]

(416)

m Coefficient of volume expansion [1K]

1-1-23-35-

4-85-106-134

10684475 -t 10163711 t10182013 -t10158931

t10746034 - t10170218 t10-12877310

(417

)

Some important properties for heat transfer calculations are presented in Table 48 It is obvious

that they depend on temperature much more than on pressure Because of that for almost all industrial

calculations the influence of pressure can be ignored

Table 411 Water Density Specific Heat Thermal Conductivity and Dynamic Viscosity versus

Temperature and Pressure

]mkg[ 3 )]Kkg(J[cp )]Km(W[ ]sPa[106

]bar[p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o

0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 1295

20 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 1001

30 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 803

40 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 657

50 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 554

60 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 475

70 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 12

80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 360

90 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287

150 9221 9273 4275 4237 0693 0699 188 190

200 8707 8776 4455 4396 0672 0679 138 140

250 8059 8161 4781 4681 0624 0636 112 115

300 7154 7346 5661 5275 0542 0558 91 94

350 6006 8206 0452 75

360 547 12560 0412 69

Saturated steam properties (0 lt t lt 210 oC or 0006 bar lt p lt 1908 bar)

n Density of saturated steam

00203297 + p0554983 +p000557908 - p8000014411= 23 (418)

o Specific heat at constant pressure of saturated steam

186459 +t 0784614 + t000461955 + t93000009956 =c 23p (419)

p Thermal conductivity of saturated steam

0404835 -t 00474611 +t8000026173 - t3939000000064=10 232 (420)

q Dynamic viscosity of saturated steam

81587 +t 00375325 + t281000000762=10 26 (421)

Superheated steam properties (250 lt t lt 550 oC or 1961 bar lt p lt 5884 bar)

Table 412 Superheated Steam

]mkg[ 3 )]Kkg(J[cp )]Km(W[102

]sPa[10 6

p[bar] 1961 3923 5884 1961 3923 5884 1961 3923 5884 1961 3923 5884

t [oC]

220 9588 2935 373 168

230 9285 2784 383 174

240 9025 2633 393 177

250 8787 1962 2554 3647 403 453 181 183

280 2937 4438 532 198

290 2808 4028 505 202

300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205

350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225

400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246

450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268

500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289

550 1606 2353 784 312

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 13

18 Physical Properties of Selected Solid Materials

Table 413 Properties of Selected Solids at 25 oC

Substance

kgm3 pc

[kJ(kg K)]

Asphalt 2120 167

Brick (common) 1800 084

Carbon (diamond) 3250 051

Carbon (graphite) 2000ndash2500 061

Coal 1200ndash1500 126

Concrete 2200 088

Glass (plate) 2500 080

Glass (wool) 200 066

Granite 2750 089

Ice (0 oC) 917 204

Paper 700 120

Plexiglas 1180 144

Polystyrene 920 230

Polyvinyl chloride 1380 096

Rubber (soft) 1100 167

Salt (rock) 2100ndash2500 092

Sand (dry) 1500 080

Silicon 2330 070

Snow (firm) 560 210

Wood (hard oak) 720 126

Wood (soft pine) 510 138

Wool 100 172

Table 414 Properties of Selected Metals at 25 oC

Metals

kgm3

pc

[kJ(kg

K)] Aluminum 2700 090

Copper (commercial) 8300 042

Brass (60-40) 8400 038

Gold 19300 013

Iron (cast) 7272 042

Iron (Steel 304 St) 7820 046

Lead 11340 013

Magnesium (2 Mn) 1778 100

Nickel (10 Cr) 8666 044

Silver (999 Ag) 10524 024

Sodium 971 121

Tin 7304 022

Tungsten 19300 013

Zinc 7144 039

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 14

Table 415 Thermal Expansion Coefficients and

Thermal Conductivity of Solids

Material

Thermal

Expansion

Coefficient

(times10-6ordmC)

Thermal

Conductivity

(WmmiddotK)

Aluminum 230 237

Aluminum Alloy 230 ndash

Brass 191 ndash 212 ndash

Brass Noval 211 ndash

Brass Red (80 Cu

20 Zn) 191 ndash

Brick 500 ndash 700 ndash

Bronze Regular 180 ndash 210 ndash

Bronze Manganese 200 ndash

Concrete 700 ndash 140 ndash

Copper 166 ndash 176 410

Copper Alloy 170 ndash

Glass 500 ndash 110 ndash

Gold ndash 317

Iron ndash 802

Iron (Cast) 990 ndash 120 ndash

Iron (Wrought) 120 -

Lead ndash 353

Magnesium 252 156

Magnesium Alloy 261 ndash 288 ndash

Monel (67 Ni 30

Cu) 140 ndash

Nickel 130 907

Nylon Polyamide 750 ndash 100 ndash

Platinum ndash 716

Rubber 130 ndash 200 ndash

Silicon ndash 148

Silver ndash 429

Solder Tin-Lead ndash 300 ndash 498

Steel 100 ndash 180 ndash

Tin ndash 666

Titanium ndash 219

Titanium Alloy 800 ndash 100 ndash

Tungsten 430 174

Zinc 302 116

Table 416 Density Melting and Boiling Points of

Solids

Material

Density

[times1000

kgm3]

Melting

Point

[oC]

Boiling

Point

[oC]

Aluminum 271 6603 2519

Aluminum Alloy 264 ndash

28

5650 ndash

6600 ndash

Brass 84 ndash

875 9300 ndash

Brass Noval 84 ndash ndash

Brass Red (80 Cu 20

Zn) 875 1000 ndash

Brick (Compression) 18 ndash

24 ndash- ndash

Bronze Regular 78 ndash

88 1050 ndash

Bronze Manganese 83 ndash ndash

Carbon 225 4492 3642

Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash

24 ndash ndash

Copper 894 1085 2562

Copper Alloy 823 9250 ndash

Cork 015 ndash

02 ndash ndash

Glass 24 ndash

28 ndash ndash

Gold 1932 1064 2856

Iron (Cast) 787 1538 2861

Iron (Wrought) 7 ndash 74 ndash ndash-

Magnesium [Mg] 74 ndash

78 ndash ndash

Magnesium Alloy 113 3275 1749

Monel (67 Ni 30 Cu) 174 6500 1090

Nickel [Ni] 177 1246 2061

Nylon Polyamide 884 1330 ndash

Platinum 889 1455 2913

Rubber 11 - -

Silver 214 1768 3825

Solder Tin-Lead 096 ndash

13 ndash ndash

Steel 233 1382 ndash

Stone Granite

(Compression) 1049 9618 2162

Stone

Limestone (Compression)

817 ndash

1134 2150 ndash

Stone Marble

(Compression) 785 1425 ndash

Tin 26 ndash ndash

Titanium 2 ndash29 ndash ndash

Titanium Alloy 26 ndash

29 ndash ndash

Wood Ash (Bending) 26 ndash ndash

Wood Douglas Fir

(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287

Wood Southern Pine

(Bending) 451 ndash ndash

Zinc 193 3422 5555

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 3

Table 42 Prefixes of Units yotta [Y] = 10+24

zetta [Z] = 10+21

exa [E] = 10+18

peta [P] = 10+15

tera [T] = 10+12

giga [G] = 10+9

mega [M] = 10+6

kilo [k] = 10+3

hecto [h] = 100

deca [da] = 10

deci [d] = 01

centi [c] = 001

milli [m] = 10-3

micro [micro] = 10-6

nano [n] = 10-9

pico [p] =10-12

femto [f] = 10-15

atto [a] = 10-18

zepto [z] = 10-21

yocto [y] = 10-24

1

5 SI unites and conversion factors For other systems of measurement these are as follows

Table 43 Conversion Factors

Name SI unit Conversion factors for most frequently used units of other

systems and non-system units

Acceleration linear ms2 1 ins2 = 00254 ms2

Area m2 1 ft2 = 00929 m2

1 in2 = 6451times10-4 m2

Density kgm3

1 tonm3 = 1 kgdm3 = 1 gcm3 = 103 kgm3

1 (kgf s2)m4 = 981 kgm3

1 lbft3 = 1602 kgm3

1 lbin3 = 2768times103 kgm3

Density of heat flux Wm2 1 kcalm2 = 1163 Wm2

Diffusion coefficient m2s 1 ft2s = 00929 m2s

Energy work quantity of heat J

1 kWh = 36times106 J

1 kcal = 41868 kJ = 41868times103 J

1 lbf timesft = 1356 J

1 lbf timesin = 0133 J

1 BTU = 10551 J

Enthalpy specific Jkg 1 kcalkg = 1 calg = 4190 Jkg

1 BTUlb = 2326 Jkg

Entropy specific J(kg K) 1 kcal(kg K) = 4190 J(kg K)

1 BTU(lb oF) = 4190 J(kg K)

Force (weight) N

1 kgf = 981 N

1 dyn = 10-5 N

1 sn = 103 N

1 lbf = 445 N

Frequency Hz

1 s-1 = 1 Hz

1 rps = 1 Hz

1 rpm = 160 Hz

Heat capacity specific J(kg K) 1 kcal(kg K) = 4190 J(kg K)

1 BTU(lb oF) = 4190 J(kg K)

Heat transfer coefficient individual

and overall W(m2 K)

1 kcal(kg K) 4190 J(kg K)

1 BTU(ft2 h oF) = 56 W(m2 K)

Length m

1 microm (micron) = 10-6 m

1 Aring =10-10 m

1 ft (lsquo) = 03048 m

1 in (lsquo) = 00254 m

Mass kg 1 ton (m3tric) = 1000 kg

1 lb = 0454 kg

Power W

1 (kgf m)s = 981 W

1 kcalh = 1163 W

1 (lbf ft)s = 1356 W

1 hp = 7353 W

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 4

Pressure Pa

1 bar = 105 Pa

1 mbar = 100 Pa

1 kgfcm2 = 1 at = 735 mm Hg = 981times104 Pa

1 atm = 760 mm Hg = 101325 Pa

1 kgfm2 = 981 Pa

1 mm H2O = 981 Pa

1 mmHg = 1333 Pa

1 lbfin2 = (psi) = 689476 Pa

1 lbfft2 = 4788 Pa

Rate of flow mass kgs 1 lbs = 0454 kgs

1 lbh = 126times10-4 kgs

Rate of flow volumetric m3s

1 lmin = 1667timesm3s

1 ft3s = 283times10-3 m3s

1 in3s = 164times10-6 m3s

Specific heat of phase transition Jkg 1 kcalkg = 4189 Jkg

1 BTUlb = 2326 Jkg

Surface tension Nm 1 kgfm = 981 Jm2 = 981 Nm

Thermal conductivity W(m K) 1 kcal(m h K) = 1163 W(m K)

1 BTU(ft h oF) = 173 W(m K)

Time s 1 h = 3600 s

1 min = 60 s

Temperature K

t [oC] = (t + 27315) [K]

t [oF] = 15273)32t(9

5 [K]

Velocity angular rads srad

30rpm1

srad2rps1

Velocity linear ms 1 fts = 03048 ms

Viscosity dynamic Pa s 1 P (poises)= 01 Pa s

1 cP (centipoises) = 19180 kgf sm2 = 10-3 Pa s

Viscosity kinematic m2s

1 S (stokes) = 1 cm2s = 10-4 m2s

1 ft2s = 0093 m2s

1 ft2h = 2581 m2s

Volume m3

1 l = 10-3 m3

1 ft3 = 283 dm3 = 00283 m3

1 in3 = 16387 cm3 = 1639times10-6 m3

Volume specific m3kg 1 m3ton = 10-3 m3kg

1 lkg = 1 cm3g = 10-3 m3kg

Note The values of the conversion factors are given with the sufficient accuracy for engineering calculations

A USEFUL DEFINITION FOR ENERGY ANALYSIS

6 The ton of oil equivalent (toe) is a unit for measuring energy It corresponds to 10 Gcal or

41868 GJ or 1163 MWh It is a rounded amount of energy that would be produced by burning one

metric ton of crude oil Since crude oil of different origin has different chemical properties and

therefore gives off varying amounts of heat when burnt the value is a matter of consensus to a certain

extent toe is A particularly useful unit for quantifying energy production or consumption for one

country or for the entire world

7 The most useful and practical definition of energy is that it is a measure of the capacity for

doing work Energy comes from many sources ndash sunlight wind water coal oil gas etc and it has

many types thermal electrical chemical nuclear etc

Specific energy is a measure of the amount of energy contained in a single quantity of some

substance It is also known as calorific value

The energy content can be expressed in any unit of energy BTU calories joules watt-hours etc

The preferred unit is joules with the appropriate range of prefixes for kilojoules [kJ] megajoules

[MJ] etc

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 5

The unit quantity may be either of mass (kg) or of volume (cubic meters) It depends on the nature

of the substance For solids it is usual to use unit mass and for gases to use unit volume (together

with a statement of pressure and temperature) For liquids either mass or volume can be used

The approximate Specific Energy values (NCV1 LCV

2) of some solid fuels are

Coal 23 to 35 MJkg

Wood 16 to 21 MJkg

Peat 23 MJkg

Charcoal 28 to 33 MJkg

Natural uranium ndash in light water reactor 443 000 MJkg

Enriched uranium (35 ) ndash in light water reactor 3 456 000 MJkg

Uranium - in fast breeder reactor 24 000 000 MJkg

The approximate Specific Energy values (NCV LCV) of some gas fuels are Coal gas 19 to 22 MJmsup3

Natural gas 37 MJmsup3

Acetylene 56 MJmsup3

Propane 93 MJmsup3

Butane 110 MJmsup3

All are based on particular pressure and temperature Gas heating value varies with the

geographical location

Standard metric gas conditions are 101325 kPa and 15 oC (dry)

Normal metric gas conditions 101325 kPa and 0 oC (dry)

The approximate specific energy values (LCV) of some liquid fuels are Gasoline 421 MJkg

Petroleum 398 MJkg

Diesel 418 MJkg

Heavy Fuel Oil 418 MJkg

Higher Heating Value (HHV) Gross Heating Value (GHV) Gross Calorific Value (GCV) and

Total Calorific Value (TCV) are different terms for the same value This can be defined as total heat

obtained from combustion of a specified amount of fuel and its stoichiometrically correct amount of

air both being at 1556 oC (60

oF) when combustion starts and the combustion products being cooled

to 1556 oC (60

oF) before heat release is measured

Lower Heating Value (LHV) Net Heating Value (NHV) Low Calorific Value (LCV) is lower

than Total Calorific Value for the value of latent heat of vaporization of water formed in combustion

Some typical values for the ratio of net to gross values are as follows

Fuel NetGross Ratio

Natural gas 090

Fuel oil 094

Coal 098

Nuclear energy is totally different in both the method of production and the scale of released

energy As a very rough guide the fission of a given mass of a suitable material (such as plutonium)

produces something of the order of 3 million times the energy obtained from the same mass of an

lsquoordinaryrsquo fuel such as coal

8 Density is mass of fluid in a unit volume [kgm3]

9 Dynamic viscosity is the tangential force per unit area required to move one horizontal plane

with respect to the other at unit velocity when maintained at a unit distance apart by the fluid It

appears as a result of cohesion and interaction between molecules

1 NCV ndash Net Calorific Value

2 LCV ndash Low Calorific Value (NCV = LCV)

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 6

Different fluids deform at different rates under the same shear forces Fluid with a high viscosity

such as syrup deforms more slowly than fluid with a low viscosity such as water

Newtonian fluids obey the linear relationship given by the Newtons law of viscositydx

dw

where is the shear stress and micro is the coefficient of dynamic viscosity

Viscosity is resistance of a fluid to flow This resistance acts against the motion of any solid

object through the fluid and also against motion of the fluid itself past stationary obstacles Viscosity

also acts internally on the fluid between slower and faster moving adjacent layers

All fluids (liquids and gases) exhibit viscosity to some degree Viscosity may be thought of as

fluid friction just as the friction between two solids resists the motion of one over the other but also

makes possible the acceleration of one relative to the other

The dynamic viscosities of some fluids are presented in Table 44 It is very important to know the

temperature of the fluid (and pressure)

Table 44 Dynamic Viscosity of Some Liquids and Gasses Liquid Gas

Gasoline Water Air (dry)

1013 bar

Carbon Dioxide

1013 bar

t (oC) Μ

[Pa s] t (oC)

μ

[Pa s] t (oC)

μ

[Pa s] t (oC)

μ

[Pa s]

20 0529times10-3 0 1780times10-3 0 0017times10-3 0 0014times10-3

40 0411times10-3 20 1004times10-3 100 0022times10-3 100 0018times10-3

60 0328times10-3 40 0653times10-3 200 0026times10-3 200 0023times10-3

100 0225times10-3 60 0470times10-3 300 0030times10-3 300 0026times10-3

80 0355times10-3 400 0033times10-3 400 0030times10-3

100 0283times10-3 500 0036times10-3 500 0033times10-3

10 Kinematic viscosity is the ratio of absolute viscosity to density For either dynamic or

kinematic viscosity to be meaningful a reference temperature must be quoted

11 Thermal conductivity is a measurement of the ability of a material to conduct heat It is

defined using the Fouriers law of conduction which relates the rate of heat transfer by conduction to

the temperature gradient

dx

dTAkq (41)

where k is the thermal conductivity Using the Fouriers law we can define the thermal conductivity

as the rate of heat transfer through a unit thickness of material per unit area and per unit temperature

difference A good conductor of heat has a high value of thermal conductivity

The temperature variations of the thermal conductivities of some materials are presented in Table

5

Table 45 Thermal Conductivity of Some Materials ndash k [W(m K)]

t (oC)

Solid Liquid Gas

Copper Aluminum Gasoline Water Air (dry)

1013 bar

Steam

(saturated)

-100 407 -

0 386 221 00244 001760

100 379 - 01005 00680 00321 002372

200 373 229 00670 00393 003547

300 - 222 00558 00460 006270

500 - - 00574

700 - - 00671

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 7

12 Specific heat is the amount of heat that is required to raise the temperature of the unit mass of

a substance by one degree In a constant pressure process

Tcmq p (42)

cp is specific heat at constant pressure

Values of cp [kJ(kg K)] for various materials (at 20 oC) are shown in Table 46

Table 46 Specific Heat at Constant Pressure of Some Materials

SOLID cp

kJ(kg K) LIQUID

cp

kJ(kg K) GAS

cp

kJ(kg K)

Aluminum (pure) 0903 Water 418 Air 1010

Copper (pure) 0385 Ethyl Alcohol 229 Nitrogen 1047

Gold 0129 Gasoline 206 Sulfur Dioxide 0633

Silicon 1382 Oil 185 Carbon Dioxide 0837

13 Coefficient of thermal expansion is defined as the change in the density of a substance as a

function of temperature at constant pressure It is expressed as follows

pT

1 (43)

For ideal gases TRp

there is T

1

14 Thermal diffusivity is measure of heat propagation through a medium and may be defined by

the ratio of heat conducted through a material to the heat stored in the material The thermal

diffusivity is defined as

pc

ka (44)

The larger the thermal diffusivity is the faster the propagation of heat into the material If the

thermal diffusivity is small it means that a large part of heat is absorbed by the material and only a

small portion is conducted through it Some typical values of thermal diffusivity are given in Table

47 (0 oC 1013 bar)

Table 47 Thermal Diffusivity of Some Materials

SOLID a

m2s LIQUID

a

m2s GAS

a

m2s

Aluminum 93166times10-6 Water 0131times10-6 Air 18777times10-6

Copper 114085times10-6 Ethyl Alcohol 0100times10-6 Nitrogen 18703times10-6

Gold 12479times10-6 Gasoline 0075times10-6 Sulfur Dioxide 4711times10-6

Polystyrene 0611times10-6 Oil 0154times10-6 Carbon Dioxide 9097times10-6

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 8

PHYSICAL PROPERTIES

15 Physical Properties of Selected Gases

Table 48 Physical Properties of Selected Gases (10 bar 0 oC)

Material Density

Molar

Mass

Gas

Const

Boiling

Point cp cpcv 106 timesmicro K Pr

kgm3 gmol J(kg K) ordmC J(kg K) - Pa s W(m K) -

Air (dry) 1293 2895 287 -195 1010 14 173 00245 071

Argon [Ar] 1782 3994 2085 -1858 532 165 209 00173 064

Carbon Dioxide

[CO2] 1976 4401 189 - 837 13 137 00137 084

Carbon Monoxide

[CO] 125 2801 297 1047 14 166 00226 077

Helium [He] 0178 4002 2079 -2689 5274 166 188 0144 069

Hydrogen [H2] 00898 2016 4125 -2529 14266 1407 842 0163 074

Nitrogen [N2] 1251 2802 2967 -1958 1047 14 17 00228 078

Oxygen [O2] 1429 32 2599 -1829 913 14 203 0024 077

Normal composition of clean dry atmospheric air near the sea level

Nitrogen (N2) =78084 Oxygen (O2) = 20948 Argon (Ar) = 0934 Carbon Dioxide (CO2) =0031

Neon (Ne) Helium (He) Krypton (Kr) Hydrogen (H2) Xenon (Xe) Methane (CH4) Nitrogen Oxide (N2O) Ozone (O3)

Sulfur Dioxide (NO2) Ammonia (NH3) Carbon Monoxide (CO) and Iodine (I2) =traces of each gas for a total of 0003

Formulae for the calculation of average constant-pressure specific heat ndash cp [kJkg] of various gases in

the range from 0 to 2000 oC are presented in Table 49

Table 49 Average Specific Heat at Constant Pressure of some Gases

Gas

Average Specific Heat at Constant Pressure

])C[t()Kkg(kJ[c ot

op

(Range 0 to 2000 oC)

Maxim

um

Error

Hydrogen (H2) 01+143810E +t 04-200328E +t08-356131E - t10-342031E + t13-108329E- = 234 006

Nitrogen (clean)

(N2) 00103937E t 06-857115E t07-173326E t10-106900E - t14-207571E = 234 009

Oxygen (O2) 01-907389E t 04-144682E t08-150961E t11-443486E - t14-123574E = 234 012

Carbon Monoxide

(CO) 00103823E t 05-124096E t07-176241E t10-120740E - t14-251706E 234 011

Carbon Dioxide

(CO2) 01-820310E t 04-516236E t07-298914E - t10-104359E t14-156925E- = 234 006

Water Vapor (H2O) 00185773E t 04-135306E t07-267351E t10-142139E - t14-235461E= 234 004

Sulfur Dioxide

(SO2) 01-606803E t 04-321094E t07-201319E - t11-653115E t15-804281E- = 234 012

Air 00100361E t 05-218551E t07-142841E t11-968901E - t14-199627E = 234 009

Nitrogen (form Air)

(N2) 00102694E t 05-142726E t07-131381E t11-797576E - t14-148364E = 234 014

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 9

16 Physical Properties of Selected Liquids

Table 410 Physical Properties of Selected Liquids

Liquid t [oC] ρ [kgm3] cp [kJkg

K)]

k [W(m

K)]

micro times 103 [Pa

s]

β times 105

[1K] a [m2s]

Acetone 20

50

791

756

216

225

0170

0163

0331

-

143

-

Gasoline

20

40

60

100

751

735

717

681

206

215

224

246

01165

-

-

01005

0529

0411

0328

0225

125

-

-

-

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol

0

20

50

806

789

-

229

245

281

0185

0183

0178

178

119

0695

Ethylene

Glycol

20

40

60

80

100

1113

1099

1085

1070

1056

2382

2474

2562

2650

2742

0258

-

-

-

0269

1990

913

495

302

199

Glycerin

20

50

100

200

1260

1244

1200

1090

235

250

279

334

-

0283

0289

-

1480

180

13

022

53

-

-

-

Methyl Alcohol

0

20

50

810

792

765

243

247

256

0241

0212

-

0818

0585

0400

Petroleum

20

50

100

200

819

801

766

785

200

214

238

289

-

01114

01042

00891

149

0956

0545

0262

100

-

-

-

Oil (lubricant)

25

50

75

100

920

905

896

880

1850

1943

2041

2136

0130

0128

0125

0123

190

429

156

572

Oil

(transformer)

25

50

75

100

860

845

835

820

1918

2043

2169

2294

0123

0122

0120

0117

2420

990

477

302

17 Thermodynamic and Transport Properties of Water and Steam

a Some of thermodynamic properties of water are

H2O = Chemical formula

M = 18016 [kgkmol] (Molecular Mass)

tc = 37415 [oC] (Critical Temperature)

Tc = 647286 [K] (Absolute Critical Temperature)

pc = 22089 [bar] (Critical Pressure)

c = 3170 [kgm3] (Critical Density)

tm = 001 [oC] (Melting Temperature at 101325 bar)

rm = 332432 [kJkg] (Heat of Melting at 101325 bar)

tb = 1000 [oC] (Boiling Temperature at 101325 bar)

rb = 22570 [kJkg] (Heat of Evaporation at 101325 bar)

R = 462507 [J(kg K)] (Gas Constant)

Enthalpies and entropies of boiling water and saturated steam versus temperature and

pressure (001 lt p lt 20 bar 7 lt t lt 212 oC)

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 10

a Saturated steam and boiling water temperature versus pressure3

112

31-42-

5-36-5

109963430 ln(p)][102794824 ln(p)][2397684

ln(p)][102118802 ln(p)][101786280

ln(p)][101285144 ln(p)][1005-5518190E t

(45)

Error is in the range 007

b Saturated steam and boiling water pressure versus temperature

5098158] -t 107261845 t102974345 - t101096061

t103381446 - t107363934 t10316exp[-7789p

2-24-36-

4-95-126-15

(46)

Error is in the range of 005

c Enthalpy of boiling water versus temperature

1-

2-53-74-9

10359463 t 417927

t10723854 - t10706612 t10833022h (47)

d Enthalpy of saturated steam versus temperature

250044 t 187334

t10103177 - t10151237 t10332313 - h 2-33-64-8

(48)

e Entropy of boiling water versus pressure

130250 ln(p)10315672

(ln(p))10167802 (ln(p))10145398 (ln(p))10973390s

2-

2-33-44-5

(49)

f Entropy of saturated steam versus pressure

736130 ln(p)10336497 - (ln(p)10760363 (ln(p)10-538843s -12-43-4 (41

0)

Water properties (temperatures from 0 to 300 oC)

(From 0 to 100 oC at 1013 bar and for higher temperatures for boiling pressure)

g Density [kgm3]

22-23-

3-54-75-106-13

10999945 t 10410381 t10726539 -

t10428877 t10208168 - t10556465 t10-644703

(411

)

3 ln - natural logarithm

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 11

h Specific heat at constant pressure cp [J(kg K)]

30-21-

3-34-65-86-11p

10421629 t 10370637 - t10109452

t10142353 -t10976851 t10317259 - t10400424c

(412

)

i Thermal conductivity [W(m K)]

11-23-

3-64-95-116-112

10549688 t 10285413 t10210253 -

t10672554 t10740918 - t10187737 - t1036594410

(413

)

j Thermal diffusivity a [m2s]

pca (414)

k Dynamic viscosity [Pa s]

748230 t 10322128 - t10218237

t10103401 - t10272328 t1077Exp(-291810

2-22-

3-64-95-126

(415)

l Kinematic viscosity [m2s]

(416)

m Coefficient of volume expansion [1K]

1-1-23-35-

4-85-106-134

10684475 -t 10163711 t10182013 -t10158931

t10746034 - t10170218 t10-12877310

(417

)

Some important properties for heat transfer calculations are presented in Table 48 It is obvious

that they depend on temperature much more than on pressure Because of that for almost all industrial

calculations the influence of pressure can be ignored

Table 411 Water Density Specific Heat Thermal Conductivity and Dynamic Viscosity versus

Temperature and Pressure

]mkg[ 3 )]Kkg(J[cp )]Km(W[ ]sPa[106

]bar[p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o

0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 1295

20 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 1001

30 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 803

40 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 657

50 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 554

60 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 475

70 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 12

80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 360

90 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287

150 9221 9273 4275 4237 0693 0699 188 190

200 8707 8776 4455 4396 0672 0679 138 140

250 8059 8161 4781 4681 0624 0636 112 115

300 7154 7346 5661 5275 0542 0558 91 94

350 6006 8206 0452 75

360 547 12560 0412 69

Saturated steam properties (0 lt t lt 210 oC or 0006 bar lt p lt 1908 bar)

n Density of saturated steam

00203297 + p0554983 +p000557908 - p8000014411= 23 (418)

o Specific heat at constant pressure of saturated steam

186459 +t 0784614 + t000461955 + t93000009956 =c 23p (419)

p Thermal conductivity of saturated steam

0404835 -t 00474611 +t8000026173 - t3939000000064=10 232 (420)

q Dynamic viscosity of saturated steam

81587 +t 00375325 + t281000000762=10 26 (421)

Superheated steam properties (250 lt t lt 550 oC or 1961 bar lt p lt 5884 bar)

Table 412 Superheated Steam

]mkg[ 3 )]Kkg(J[cp )]Km(W[102

]sPa[10 6

p[bar] 1961 3923 5884 1961 3923 5884 1961 3923 5884 1961 3923 5884

t [oC]

220 9588 2935 373 168

230 9285 2784 383 174

240 9025 2633 393 177

250 8787 1962 2554 3647 403 453 181 183

280 2937 4438 532 198

290 2808 4028 505 202

300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205

350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225

400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246

450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268

500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289

550 1606 2353 784 312

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 13

18 Physical Properties of Selected Solid Materials

Table 413 Properties of Selected Solids at 25 oC

Substance

kgm3 pc

[kJ(kg K)]

Asphalt 2120 167

Brick (common) 1800 084

Carbon (diamond) 3250 051

Carbon (graphite) 2000ndash2500 061

Coal 1200ndash1500 126

Concrete 2200 088

Glass (plate) 2500 080

Glass (wool) 200 066

Granite 2750 089

Ice (0 oC) 917 204

Paper 700 120

Plexiglas 1180 144

Polystyrene 920 230

Polyvinyl chloride 1380 096

Rubber (soft) 1100 167

Salt (rock) 2100ndash2500 092

Sand (dry) 1500 080

Silicon 2330 070

Snow (firm) 560 210

Wood (hard oak) 720 126

Wood (soft pine) 510 138

Wool 100 172

Table 414 Properties of Selected Metals at 25 oC

Metals

kgm3

pc

[kJ(kg

K)] Aluminum 2700 090

Copper (commercial) 8300 042

Brass (60-40) 8400 038

Gold 19300 013

Iron (cast) 7272 042

Iron (Steel 304 St) 7820 046

Lead 11340 013

Magnesium (2 Mn) 1778 100

Nickel (10 Cr) 8666 044

Silver (999 Ag) 10524 024

Sodium 971 121

Tin 7304 022

Tungsten 19300 013

Zinc 7144 039

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 14

Table 415 Thermal Expansion Coefficients and

Thermal Conductivity of Solids

Material

Thermal

Expansion

Coefficient

(times10-6ordmC)

Thermal

Conductivity

(WmmiddotK)

Aluminum 230 237

Aluminum Alloy 230 ndash

Brass 191 ndash 212 ndash

Brass Noval 211 ndash

Brass Red (80 Cu

20 Zn) 191 ndash

Brick 500 ndash 700 ndash

Bronze Regular 180 ndash 210 ndash

Bronze Manganese 200 ndash

Concrete 700 ndash 140 ndash

Copper 166 ndash 176 410

Copper Alloy 170 ndash

Glass 500 ndash 110 ndash

Gold ndash 317

Iron ndash 802

Iron (Cast) 990 ndash 120 ndash

Iron (Wrought) 120 -

Lead ndash 353

Magnesium 252 156

Magnesium Alloy 261 ndash 288 ndash

Monel (67 Ni 30

Cu) 140 ndash

Nickel 130 907

Nylon Polyamide 750 ndash 100 ndash

Platinum ndash 716

Rubber 130 ndash 200 ndash

Silicon ndash 148

Silver ndash 429

Solder Tin-Lead ndash 300 ndash 498

Steel 100 ndash 180 ndash

Tin ndash 666

Titanium ndash 219

Titanium Alloy 800 ndash 100 ndash

Tungsten 430 174

Zinc 302 116

Table 416 Density Melting and Boiling Points of

Solids

Material

Density

[times1000

kgm3]

Melting

Point

[oC]

Boiling

Point

[oC]

Aluminum 271 6603 2519

Aluminum Alloy 264 ndash

28

5650 ndash

6600 ndash

Brass 84 ndash

875 9300 ndash

Brass Noval 84 ndash ndash

Brass Red (80 Cu 20

Zn) 875 1000 ndash

Brick (Compression) 18 ndash

24 ndash- ndash

Bronze Regular 78 ndash

88 1050 ndash

Bronze Manganese 83 ndash ndash

Carbon 225 4492 3642

Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash

24 ndash ndash

Copper 894 1085 2562

Copper Alloy 823 9250 ndash

Cork 015 ndash

02 ndash ndash

Glass 24 ndash

28 ndash ndash

Gold 1932 1064 2856

Iron (Cast) 787 1538 2861

Iron (Wrought) 7 ndash 74 ndash ndash-

Magnesium [Mg] 74 ndash

78 ndash ndash

Magnesium Alloy 113 3275 1749

Monel (67 Ni 30 Cu) 174 6500 1090

Nickel [Ni] 177 1246 2061

Nylon Polyamide 884 1330 ndash

Platinum 889 1455 2913

Rubber 11 - -

Silver 214 1768 3825

Solder Tin-Lead 096 ndash

13 ndash ndash

Steel 233 1382 ndash

Stone Granite

(Compression) 1049 9618 2162

Stone

Limestone (Compression)

817 ndash

1134 2150 ndash

Stone Marble

(Compression) 785 1425 ndash

Tin 26 ndash ndash

Titanium 2 ndash29 ndash ndash

Titanium Alloy 26 ndash

29 ndash ndash

Wood Ash (Bending) 26 ndash ndash

Wood Douglas Fir

(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287

Wood Southern Pine

(Bending) 451 ndash ndash

Zinc 193 3422 5555

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 4

Pressure Pa

1 bar = 105 Pa

1 mbar = 100 Pa

1 kgfcm2 = 1 at = 735 mm Hg = 981times104 Pa

1 atm = 760 mm Hg = 101325 Pa

1 kgfm2 = 981 Pa

1 mm H2O = 981 Pa

1 mmHg = 1333 Pa

1 lbfin2 = (psi) = 689476 Pa

1 lbfft2 = 4788 Pa

Rate of flow mass kgs 1 lbs = 0454 kgs

1 lbh = 126times10-4 kgs

Rate of flow volumetric m3s

1 lmin = 1667timesm3s

1 ft3s = 283times10-3 m3s

1 in3s = 164times10-6 m3s

Specific heat of phase transition Jkg 1 kcalkg = 4189 Jkg

1 BTUlb = 2326 Jkg

Surface tension Nm 1 kgfm = 981 Jm2 = 981 Nm

Thermal conductivity W(m K) 1 kcal(m h K) = 1163 W(m K)

1 BTU(ft h oF) = 173 W(m K)

Time s 1 h = 3600 s

1 min = 60 s

Temperature K

t [oC] = (t + 27315) [K]

t [oF] = 15273)32t(9

5 [K]

Velocity angular rads srad

30rpm1

srad2rps1

Velocity linear ms 1 fts = 03048 ms

Viscosity dynamic Pa s 1 P (poises)= 01 Pa s

1 cP (centipoises) = 19180 kgf sm2 = 10-3 Pa s

Viscosity kinematic m2s

1 S (stokes) = 1 cm2s = 10-4 m2s

1 ft2s = 0093 m2s

1 ft2h = 2581 m2s

Volume m3

1 l = 10-3 m3

1 ft3 = 283 dm3 = 00283 m3

1 in3 = 16387 cm3 = 1639times10-6 m3

Volume specific m3kg 1 m3ton = 10-3 m3kg

1 lkg = 1 cm3g = 10-3 m3kg

Note The values of the conversion factors are given with the sufficient accuracy for engineering calculations

A USEFUL DEFINITION FOR ENERGY ANALYSIS

6 The ton of oil equivalent (toe) is a unit for measuring energy It corresponds to 10 Gcal or

41868 GJ or 1163 MWh It is a rounded amount of energy that would be produced by burning one

metric ton of crude oil Since crude oil of different origin has different chemical properties and

therefore gives off varying amounts of heat when burnt the value is a matter of consensus to a certain

extent toe is A particularly useful unit for quantifying energy production or consumption for one

country or for the entire world

7 The most useful and practical definition of energy is that it is a measure of the capacity for

doing work Energy comes from many sources ndash sunlight wind water coal oil gas etc and it has

many types thermal electrical chemical nuclear etc

Specific energy is a measure of the amount of energy contained in a single quantity of some

substance It is also known as calorific value

The energy content can be expressed in any unit of energy BTU calories joules watt-hours etc

The preferred unit is joules with the appropriate range of prefixes for kilojoules [kJ] megajoules

[MJ] etc

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 5

The unit quantity may be either of mass (kg) or of volume (cubic meters) It depends on the nature

of the substance For solids it is usual to use unit mass and for gases to use unit volume (together

with a statement of pressure and temperature) For liquids either mass or volume can be used

The approximate Specific Energy values (NCV1 LCV

2) of some solid fuels are

Coal 23 to 35 MJkg

Wood 16 to 21 MJkg

Peat 23 MJkg

Charcoal 28 to 33 MJkg

Natural uranium ndash in light water reactor 443 000 MJkg

Enriched uranium (35 ) ndash in light water reactor 3 456 000 MJkg

Uranium - in fast breeder reactor 24 000 000 MJkg

The approximate Specific Energy values (NCV LCV) of some gas fuels are Coal gas 19 to 22 MJmsup3

Natural gas 37 MJmsup3

Acetylene 56 MJmsup3

Propane 93 MJmsup3

Butane 110 MJmsup3

All are based on particular pressure and temperature Gas heating value varies with the

geographical location

Standard metric gas conditions are 101325 kPa and 15 oC (dry)

Normal metric gas conditions 101325 kPa and 0 oC (dry)

The approximate specific energy values (LCV) of some liquid fuels are Gasoline 421 MJkg

Petroleum 398 MJkg

Diesel 418 MJkg

Heavy Fuel Oil 418 MJkg

Higher Heating Value (HHV) Gross Heating Value (GHV) Gross Calorific Value (GCV) and

Total Calorific Value (TCV) are different terms for the same value This can be defined as total heat

obtained from combustion of a specified amount of fuel and its stoichiometrically correct amount of

air both being at 1556 oC (60

oF) when combustion starts and the combustion products being cooled

to 1556 oC (60

oF) before heat release is measured

Lower Heating Value (LHV) Net Heating Value (NHV) Low Calorific Value (LCV) is lower

than Total Calorific Value for the value of latent heat of vaporization of water formed in combustion

Some typical values for the ratio of net to gross values are as follows

Fuel NetGross Ratio

Natural gas 090

Fuel oil 094

Coal 098

Nuclear energy is totally different in both the method of production and the scale of released

energy As a very rough guide the fission of a given mass of a suitable material (such as plutonium)

produces something of the order of 3 million times the energy obtained from the same mass of an

lsquoordinaryrsquo fuel such as coal

8 Density is mass of fluid in a unit volume [kgm3]

9 Dynamic viscosity is the tangential force per unit area required to move one horizontal plane

with respect to the other at unit velocity when maintained at a unit distance apart by the fluid It

appears as a result of cohesion and interaction between molecules

1 NCV ndash Net Calorific Value

2 LCV ndash Low Calorific Value (NCV = LCV)

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 6

Different fluids deform at different rates under the same shear forces Fluid with a high viscosity

such as syrup deforms more slowly than fluid with a low viscosity such as water

Newtonian fluids obey the linear relationship given by the Newtons law of viscositydx

dw

where is the shear stress and micro is the coefficient of dynamic viscosity

Viscosity is resistance of a fluid to flow This resistance acts against the motion of any solid

object through the fluid and also against motion of the fluid itself past stationary obstacles Viscosity

also acts internally on the fluid between slower and faster moving adjacent layers

All fluids (liquids and gases) exhibit viscosity to some degree Viscosity may be thought of as

fluid friction just as the friction between two solids resists the motion of one over the other but also

makes possible the acceleration of one relative to the other

The dynamic viscosities of some fluids are presented in Table 44 It is very important to know the

temperature of the fluid (and pressure)

Table 44 Dynamic Viscosity of Some Liquids and Gasses Liquid Gas

Gasoline Water Air (dry)

1013 bar

Carbon Dioxide

1013 bar

t (oC) Μ

[Pa s] t (oC)

μ

[Pa s] t (oC)

μ

[Pa s] t (oC)

μ

[Pa s]

20 0529times10-3 0 1780times10-3 0 0017times10-3 0 0014times10-3

40 0411times10-3 20 1004times10-3 100 0022times10-3 100 0018times10-3

60 0328times10-3 40 0653times10-3 200 0026times10-3 200 0023times10-3

100 0225times10-3 60 0470times10-3 300 0030times10-3 300 0026times10-3

80 0355times10-3 400 0033times10-3 400 0030times10-3

100 0283times10-3 500 0036times10-3 500 0033times10-3

10 Kinematic viscosity is the ratio of absolute viscosity to density For either dynamic or

kinematic viscosity to be meaningful a reference temperature must be quoted

11 Thermal conductivity is a measurement of the ability of a material to conduct heat It is

defined using the Fouriers law of conduction which relates the rate of heat transfer by conduction to

the temperature gradient

dx

dTAkq (41)

where k is the thermal conductivity Using the Fouriers law we can define the thermal conductivity

as the rate of heat transfer through a unit thickness of material per unit area and per unit temperature

difference A good conductor of heat has a high value of thermal conductivity

The temperature variations of the thermal conductivities of some materials are presented in Table

5

Table 45 Thermal Conductivity of Some Materials ndash k [W(m K)]

t (oC)

Solid Liquid Gas

Copper Aluminum Gasoline Water Air (dry)

1013 bar

Steam

(saturated)

-100 407 -

0 386 221 00244 001760

100 379 - 01005 00680 00321 002372

200 373 229 00670 00393 003547

300 - 222 00558 00460 006270

500 - - 00574

700 - - 00671

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 7

12 Specific heat is the amount of heat that is required to raise the temperature of the unit mass of

a substance by one degree In a constant pressure process

Tcmq p (42)

cp is specific heat at constant pressure

Values of cp [kJ(kg K)] for various materials (at 20 oC) are shown in Table 46

Table 46 Specific Heat at Constant Pressure of Some Materials

SOLID cp

kJ(kg K) LIQUID

cp

kJ(kg K) GAS

cp

kJ(kg K)

Aluminum (pure) 0903 Water 418 Air 1010

Copper (pure) 0385 Ethyl Alcohol 229 Nitrogen 1047

Gold 0129 Gasoline 206 Sulfur Dioxide 0633

Silicon 1382 Oil 185 Carbon Dioxide 0837

13 Coefficient of thermal expansion is defined as the change in the density of a substance as a

function of temperature at constant pressure It is expressed as follows

pT

1 (43)

For ideal gases TRp

there is T

1

14 Thermal diffusivity is measure of heat propagation through a medium and may be defined by

the ratio of heat conducted through a material to the heat stored in the material The thermal

diffusivity is defined as

pc

ka (44)

The larger the thermal diffusivity is the faster the propagation of heat into the material If the

thermal diffusivity is small it means that a large part of heat is absorbed by the material and only a

small portion is conducted through it Some typical values of thermal diffusivity are given in Table

47 (0 oC 1013 bar)

Table 47 Thermal Diffusivity of Some Materials

SOLID a

m2s LIQUID

a

m2s GAS

a

m2s

Aluminum 93166times10-6 Water 0131times10-6 Air 18777times10-6

Copper 114085times10-6 Ethyl Alcohol 0100times10-6 Nitrogen 18703times10-6

Gold 12479times10-6 Gasoline 0075times10-6 Sulfur Dioxide 4711times10-6

Polystyrene 0611times10-6 Oil 0154times10-6 Carbon Dioxide 9097times10-6

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 8

PHYSICAL PROPERTIES

15 Physical Properties of Selected Gases

Table 48 Physical Properties of Selected Gases (10 bar 0 oC)

Material Density

Molar

Mass

Gas

Const

Boiling

Point cp cpcv 106 timesmicro K Pr

kgm3 gmol J(kg K) ordmC J(kg K) - Pa s W(m K) -

Air (dry) 1293 2895 287 -195 1010 14 173 00245 071

Argon [Ar] 1782 3994 2085 -1858 532 165 209 00173 064

Carbon Dioxide

[CO2] 1976 4401 189 - 837 13 137 00137 084

Carbon Monoxide

[CO] 125 2801 297 1047 14 166 00226 077

Helium [He] 0178 4002 2079 -2689 5274 166 188 0144 069

Hydrogen [H2] 00898 2016 4125 -2529 14266 1407 842 0163 074

Nitrogen [N2] 1251 2802 2967 -1958 1047 14 17 00228 078

Oxygen [O2] 1429 32 2599 -1829 913 14 203 0024 077

Normal composition of clean dry atmospheric air near the sea level

Nitrogen (N2) =78084 Oxygen (O2) = 20948 Argon (Ar) = 0934 Carbon Dioxide (CO2) =0031

Neon (Ne) Helium (He) Krypton (Kr) Hydrogen (H2) Xenon (Xe) Methane (CH4) Nitrogen Oxide (N2O) Ozone (O3)

Sulfur Dioxide (NO2) Ammonia (NH3) Carbon Monoxide (CO) and Iodine (I2) =traces of each gas for a total of 0003

Formulae for the calculation of average constant-pressure specific heat ndash cp [kJkg] of various gases in

the range from 0 to 2000 oC are presented in Table 49

Table 49 Average Specific Heat at Constant Pressure of some Gases

Gas

Average Specific Heat at Constant Pressure

])C[t()Kkg(kJ[c ot

op

(Range 0 to 2000 oC)

Maxim

um

Error

Hydrogen (H2) 01+143810E +t 04-200328E +t08-356131E - t10-342031E + t13-108329E- = 234 006

Nitrogen (clean)

(N2) 00103937E t 06-857115E t07-173326E t10-106900E - t14-207571E = 234 009

Oxygen (O2) 01-907389E t 04-144682E t08-150961E t11-443486E - t14-123574E = 234 012

Carbon Monoxide

(CO) 00103823E t 05-124096E t07-176241E t10-120740E - t14-251706E 234 011

Carbon Dioxide

(CO2) 01-820310E t 04-516236E t07-298914E - t10-104359E t14-156925E- = 234 006

Water Vapor (H2O) 00185773E t 04-135306E t07-267351E t10-142139E - t14-235461E= 234 004

Sulfur Dioxide

(SO2) 01-606803E t 04-321094E t07-201319E - t11-653115E t15-804281E- = 234 012

Air 00100361E t 05-218551E t07-142841E t11-968901E - t14-199627E = 234 009

Nitrogen (form Air)

(N2) 00102694E t 05-142726E t07-131381E t11-797576E - t14-148364E = 234 014

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 9

16 Physical Properties of Selected Liquids

Table 410 Physical Properties of Selected Liquids

Liquid t [oC] ρ [kgm3] cp [kJkg

K)]

k [W(m

K)]

micro times 103 [Pa

s]

β times 105

[1K] a [m2s]

Acetone 20

50

791

756

216

225

0170

0163

0331

-

143

-

Gasoline

20

40

60

100

751

735

717

681

206

215

224

246

01165

-

-

01005

0529

0411

0328

0225

125

-

-

-

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol

0

20

50

806

789

-

229

245

281

0185

0183

0178

178

119

0695

Ethylene

Glycol

20

40

60

80

100

1113

1099

1085

1070

1056

2382

2474

2562

2650

2742

0258

-

-

-

0269

1990

913

495

302

199

Glycerin

20

50

100

200

1260

1244

1200

1090

235

250

279

334

-

0283

0289

-

1480

180

13

022

53

-

-

-

Methyl Alcohol

0

20

50

810

792

765

243

247

256

0241

0212

-

0818

0585

0400

Petroleum

20

50

100

200

819

801

766

785

200

214

238

289

-

01114

01042

00891

149

0956

0545

0262

100

-

-

-

Oil (lubricant)

25

50

75

100

920

905

896

880

1850

1943

2041

2136

0130

0128

0125

0123

190

429

156

572

Oil

(transformer)

25

50

75

100

860

845

835

820

1918

2043

2169

2294

0123

0122

0120

0117

2420

990

477

302

17 Thermodynamic and Transport Properties of Water and Steam

a Some of thermodynamic properties of water are

H2O = Chemical formula

M = 18016 [kgkmol] (Molecular Mass)

tc = 37415 [oC] (Critical Temperature)

Tc = 647286 [K] (Absolute Critical Temperature)

pc = 22089 [bar] (Critical Pressure)

c = 3170 [kgm3] (Critical Density)

tm = 001 [oC] (Melting Temperature at 101325 bar)

rm = 332432 [kJkg] (Heat of Melting at 101325 bar)

tb = 1000 [oC] (Boiling Temperature at 101325 bar)

rb = 22570 [kJkg] (Heat of Evaporation at 101325 bar)

R = 462507 [J(kg K)] (Gas Constant)

Enthalpies and entropies of boiling water and saturated steam versus temperature and

pressure (001 lt p lt 20 bar 7 lt t lt 212 oC)

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 10

a Saturated steam and boiling water temperature versus pressure3

112

31-42-

5-36-5

109963430 ln(p)][102794824 ln(p)][2397684

ln(p)][102118802 ln(p)][101786280

ln(p)][101285144 ln(p)][1005-5518190E t

(45)

Error is in the range 007

b Saturated steam and boiling water pressure versus temperature

5098158] -t 107261845 t102974345 - t101096061

t103381446 - t107363934 t10316exp[-7789p

2-24-36-

4-95-126-15

(46)

Error is in the range of 005

c Enthalpy of boiling water versus temperature

1-

2-53-74-9

10359463 t 417927

t10723854 - t10706612 t10833022h (47)

d Enthalpy of saturated steam versus temperature

250044 t 187334

t10103177 - t10151237 t10332313 - h 2-33-64-8

(48)

e Entropy of boiling water versus pressure

130250 ln(p)10315672

(ln(p))10167802 (ln(p))10145398 (ln(p))10973390s

2-

2-33-44-5

(49)

f Entropy of saturated steam versus pressure

736130 ln(p)10336497 - (ln(p)10760363 (ln(p)10-538843s -12-43-4 (41

0)

Water properties (temperatures from 0 to 300 oC)

(From 0 to 100 oC at 1013 bar and for higher temperatures for boiling pressure)

g Density [kgm3]

22-23-

3-54-75-106-13

10999945 t 10410381 t10726539 -

t10428877 t10208168 - t10556465 t10-644703

(411

)

3 ln - natural logarithm

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 11

h Specific heat at constant pressure cp [J(kg K)]

30-21-

3-34-65-86-11p

10421629 t 10370637 - t10109452

t10142353 -t10976851 t10317259 - t10400424c

(412

)

i Thermal conductivity [W(m K)]

11-23-

3-64-95-116-112

10549688 t 10285413 t10210253 -

t10672554 t10740918 - t10187737 - t1036594410

(413

)

j Thermal diffusivity a [m2s]

pca (414)

k Dynamic viscosity [Pa s]

748230 t 10322128 - t10218237

t10103401 - t10272328 t1077Exp(-291810

2-22-

3-64-95-126

(415)

l Kinematic viscosity [m2s]

(416)

m Coefficient of volume expansion [1K]

1-1-23-35-

4-85-106-134

10684475 -t 10163711 t10182013 -t10158931

t10746034 - t10170218 t10-12877310

(417

)

Some important properties for heat transfer calculations are presented in Table 48 It is obvious

that they depend on temperature much more than on pressure Because of that for almost all industrial

calculations the influence of pressure can be ignored

Table 411 Water Density Specific Heat Thermal Conductivity and Dynamic Viscosity versus

Temperature and Pressure

]mkg[ 3 )]Kkg(J[cp )]Km(W[ ]sPa[106

]bar[p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o

0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 1295

20 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 1001

30 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 803

40 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 657

50 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 554

60 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 475

70 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 12

80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 360

90 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287

150 9221 9273 4275 4237 0693 0699 188 190

200 8707 8776 4455 4396 0672 0679 138 140

250 8059 8161 4781 4681 0624 0636 112 115

300 7154 7346 5661 5275 0542 0558 91 94

350 6006 8206 0452 75

360 547 12560 0412 69

Saturated steam properties (0 lt t lt 210 oC or 0006 bar lt p lt 1908 bar)

n Density of saturated steam

00203297 + p0554983 +p000557908 - p8000014411= 23 (418)

o Specific heat at constant pressure of saturated steam

186459 +t 0784614 + t000461955 + t93000009956 =c 23p (419)

p Thermal conductivity of saturated steam

0404835 -t 00474611 +t8000026173 - t3939000000064=10 232 (420)

q Dynamic viscosity of saturated steam

81587 +t 00375325 + t281000000762=10 26 (421)

Superheated steam properties (250 lt t lt 550 oC or 1961 bar lt p lt 5884 bar)

Table 412 Superheated Steam

]mkg[ 3 )]Kkg(J[cp )]Km(W[102

]sPa[10 6

p[bar] 1961 3923 5884 1961 3923 5884 1961 3923 5884 1961 3923 5884

t [oC]

220 9588 2935 373 168

230 9285 2784 383 174

240 9025 2633 393 177

250 8787 1962 2554 3647 403 453 181 183

280 2937 4438 532 198

290 2808 4028 505 202

300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205

350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225

400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246

450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268

500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289

550 1606 2353 784 312

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 13

18 Physical Properties of Selected Solid Materials

Table 413 Properties of Selected Solids at 25 oC

Substance

kgm3 pc

[kJ(kg K)]

Asphalt 2120 167

Brick (common) 1800 084

Carbon (diamond) 3250 051

Carbon (graphite) 2000ndash2500 061

Coal 1200ndash1500 126

Concrete 2200 088

Glass (plate) 2500 080

Glass (wool) 200 066

Granite 2750 089

Ice (0 oC) 917 204

Paper 700 120

Plexiglas 1180 144

Polystyrene 920 230

Polyvinyl chloride 1380 096

Rubber (soft) 1100 167

Salt (rock) 2100ndash2500 092

Sand (dry) 1500 080

Silicon 2330 070

Snow (firm) 560 210

Wood (hard oak) 720 126

Wood (soft pine) 510 138

Wool 100 172

Table 414 Properties of Selected Metals at 25 oC

Metals

kgm3

pc

[kJ(kg

K)] Aluminum 2700 090

Copper (commercial) 8300 042

Brass (60-40) 8400 038

Gold 19300 013

Iron (cast) 7272 042

Iron (Steel 304 St) 7820 046

Lead 11340 013

Magnesium (2 Mn) 1778 100

Nickel (10 Cr) 8666 044

Silver (999 Ag) 10524 024

Sodium 971 121

Tin 7304 022

Tungsten 19300 013

Zinc 7144 039

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 14

Table 415 Thermal Expansion Coefficients and

Thermal Conductivity of Solids

Material

Thermal

Expansion

Coefficient

(times10-6ordmC)

Thermal

Conductivity

(WmmiddotK)

Aluminum 230 237

Aluminum Alloy 230 ndash

Brass 191 ndash 212 ndash

Brass Noval 211 ndash

Brass Red (80 Cu

20 Zn) 191 ndash

Brick 500 ndash 700 ndash

Bronze Regular 180 ndash 210 ndash

Bronze Manganese 200 ndash

Concrete 700 ndash 140 ndash

Copper 166 ndash 176 410

Copper Alloy 170 ndash

Glass 500 ndash 110 ndash

Gold ndash 317

Iron ndash 802

Iron (Cast) 990 ndash 120 ndash

Iron (Wrought) 120 -

Lead ndash 353

Magnesium 252 156

Magnesium Alloy 261 ndash 288 ndash

Monel (67 Ni 30

Cu) 140 ndash

Nickel 130 907

Nylon Polyamide 750 ndash 100 ndash

Platinum ndash 716

Rubber 130 ndash 200 ndash

Silicon ndash 148

Silver ndash 429

Solder Tin-Lead ndash 300 ndash 498

Steel 100 ndash 180 ndash

Tin ndash 666

Titanium ndash 219

Titanium Alloy 800 ndash 100 ndash

Tungsten 430 174

Zinc 302 116

Table 416 Density Melting and Boiling Points of

Solids

Material

Density

[times1000

kgm3]

Melting

Point

[oC]

Boiling

Point

[oC]

Aluminum 271 6603 2519

Aluminum Alloy 264 ndash

28

5650 ndash

6600 ndash

Brass 84 ndash

875 9300 ndash

Brass Noval 84 ndash ndash

Brass Red (80 Cu 20

Zn) 875 1000 ndash

Brick (Compression) 18 ndash

24 ndash- ndash

Bronze Regular 78 ndash

88 1050 ndash

Bronze Manganese 83 ndash ndash

Carbon 225 4492 3642

Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash

24 ndash ndash

Copper 894 1085 2562

Copper Alloy 823 9250 ndash

Cork 015 ndash

02 ndash ndash

Glass 24 ndash

28 ndash ndash

Gold 1932 1064 2856

Iron (Cast) 787 1538 2861

Iron (Wrought) 7 ndash 74 ndash ndash-

Magnesium [Mg] 74 ndash

78 ndash ndash

Magnesium Alloy 113 3275 1749

Monel (67 Ni 30 Cu) 174 6500 1090

Nickel [Ni] 177 1246 2061

Nylon Polyamide 884 1330 ndash

Platinum 889 1455 2913

Rubber 11 - -

Silver 214 1768 3825

Solder Tin-Lead 096 ndash

13 ndash ndash

Steel 233 1382 ndash

Stone Granite

(Compression) 1049 9618 2162

Stone

Limestone (Compression)

817 ndash

1134 2150 ndash

Stone Marble

(Compression) 785 1425 ndash

Tin 26 ndash ndash

Titanium 2 ndash29 ndash ndash

Titanium Alloy 26 ndash

29 ndash ndash

Wood Ash (Bending) 26 ndash ndash

Wood Douglas Fir

(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287

Wood Southern Pine

(Bending) 451 ndash ndash

Zinc 193 3422 5555

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 5

The unit quantity may be either of mass (kg) or of volume (cubic meters) It depends on the nature

of the substance For solids it is usual to use unit mass and for gases to use unit volume (together

with a statement of pressure and temperature) For liquids either mass or volume can be used

The approximate Specific Energy values (NCV1 LCV

2) of some solid fuels are

Coal 23 to 35 MJkg

Wood 16 to 21 MJkg

Peat 23 MJkg

Charcoal 28 to 33 MJkg

Natural uranium ndash in light water reactor 443 000 MJkg

Enriched uranium (35 ) ndash in light water reactor 3 456 000 MJkg

Uranium - in fast breeder reactor 24 000 000 MJkg

The approximate Specific Energy values (NCV LCV) of some gas fuels are Coal gas 19 to 22 MJmsup3

Natural gas 37 MJmsup3

Acetylene 56 MJmsup3

Propane 93 MJmsup3

Butane 110 MJmsup3

All are based on particular pressure and temperature Gas heating value varies with the

geographical location

Standard metric gas conditions are 101325 kPa and 15 oC (dry)

Normal metric gas conditions 101325 kPa and 0 oC (dry)

The approximate specific energy values (LCV) of some liquid fuels are Gasoline 421 MJkg

Petroleum 398 MJkg

Diesel 418 MJkg

Heavy Fuel Oil 418 MJkg

Higher Heating Value (HHV) Gross Heating Value (GHV) Gross Calorific Value (GCV) and

Total Calorific Value (TCV) are different terms for the same value This can be defined as total heat

obtained from combustion of a specified amount of fuel and its stoichiometrically correct amount of

air both being at 1556 oC (60

oF) when combustion starts and the combustion products being cooled

to 1556 oC (60

oF) before heat release is measured

Lower Heating Value (LHV) Net Heating Value (NHV) Low Calorific Value (LCV) is lower

than Total Calorific Value for the value of latent heat of vaporization of water formed in combustion

Some typical values for the ratio of net to gross values are as follows

Fuel NetGross Ratio

Natural gas 090

Fuel oil 094

Coal 098

Nuclear energy is totally different in both the method of production and the scale of released

energy As a very rough guide the fission of a given mass of a suitable material (such as plutonium)

produces something of the order of 3 million times the energy obtained from the same mass of an

lsquoordinaryrsquo fuel such as coal

8 Density is mass of fluid in a unit volume [kgm3]

9 Dynamic viscosity is the tangential force per unit area required to move one horizontal plane

with respect to the other at unit velocity when maintained at a unit distance apart by the fluid It

appears as a result of cohesion and interaction between molecules

1 NCV ndash Net Calorific Value

2 LCV ndash Low Calorific Value (NCV = LCV)

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 6

Different fluids deform at different rates under the same shear forces Fluid with a high viscosity

such as syrup deforms more slowly than fluid with a low viscosity such as water

Newtonian fluids obey the linear relationship given by the Newtons law of viscositydx

dw

where is the shear stress and micro is the coefficient of dynamic viscosity

Viscosity is resistance of a fluid to flow This resistance acts against the motion of any solid

object through the fluid and also against motion of the fluid itself past stationary obstacles Viscosity

also acts internally on the fluid between slower and faster moving adjacent layers

All fluids (liquids and gases) exhibit viscosity to some degree Viscosity may be thought of as

fluid friction just as the friction between two solids resists the motion of one over the other but also

makes possible the acceleration of one relative to the other

The dynamic viscosities of some fluids are presented in Table 44 It is very important to know the

temperature of the fluid (and pressure)

Table 44 Dynamic Viscosity of Some Liquids and Gasses Liquid Gas

Gasoline Water Air (dry)

1013 bar

Carbon Dioxide

1013 bar

t (oC) Μ

[Pa s] t (oC)

μ

[Pa s] t (oC)

μ

[Pa s] t (oC)

μ

[Pa s]

20 0529times10-3 0 1780times10-3 0 0017times10-3 0 0014times10-3

40 0411times10-3 20 1004times10-3 100 0022times10-3 100 0018times10-3

60 0328times10-3 40 0653times10-3 200 0026times10-3 200 0023times10-3

100 0225times10-3 60 0470times10-3 300 0030times10-3 300 0026times10-3

80 0355times10-3 400 0033times10-3 400 0030times10-3

100 0283times10-3 500 0036times10-3 500 0033times10-3

10 Kinematic viscosity is the ratio of absolute viscosity to density For either dynamic or

kinematic viscosity to be meaningful a reference temperature must be quoted

11 Thermal conductivity is a measurement of the ability of a material to conduct heat It is

defined using the Fouriers law of conduction which relates the rate of heat transfer by conduction to

the temperature gradient

dx

dTAkq (41)

where k is the thermal conductivity Using the Fouriers law we can define the thermal conductivity

as the rate of heat transfer through a unit thickness of material per unit area and per unit temperature

difference A good conductor of heat has a high value of thermal conductivity

The temperature variations of the thermal conductivities of some materials are presented in Table

5

Table 45 Thermal Conductivity of Some Materials ndash k [W(m K)]

t (oC)

Solid Liquid Gas

Copper Aluminum Gasoline Water Air (dry)

1013 bar

Steam

(saturated)

-100 407 -

0 386 221 00244 001760

100 379 - 01005 00680 00321 002372

200 373 229 00670 00393 003547

300 - 222 00558 00460 006270

500 - - 00574

700 - - 00671

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 7

12 Specific heat is the amount of heat that is required to raise the temperature of the unit mass of

a substance by one degree In a constant pressure process

Tcmq p (42)

cp is specific heat at constant pressure

Values of cp [kJ(kg K)] for various materials (at 20 oC) are shown in Table 46

Table 46 Specific Heat at Constant Pressure of Some Materials

SOLID cp

kJ(kg K) LIQUID

cp

kJ(kg K) GAS

cp

kJ(kg K)

Aluminum (pure) 0903 Water 418 Air 1010

Copper (pure) 0385 Ethyl Alcohol 229 Nitrogen 1047

Gold 0129 Gasoline 206 Sulfur Dioxide 0633

Silicon 1382 Oil 185 Carbon Dioxide 0837

13 Coefficient of thermal expansion is defined as the change in the density of a substance as a

function of temperature at constant pressure It is expressed as follows

pT

1 (43)

For ideal gases TRp

there is T

1

14 Thermal diffusivity is measure of heat propagation through a medium and may be defined by

the ratio of heat conducted through a material to the heat stored in the material The thermal

diffusivity is defined as

pc

ka (44)

The larger the thermal diffusivity is the faster the propagation of heat into the material If the

thermal diffusivity is small it means that a large part of heat is absorbed by the material and only a

small portion is conducted through it Some typical values of thermal diffusivity are given in Table

47 (0 oC 1013 bar)

Table 47 Thermal Diffusivity of Some Materials

SOLID a

m2s LIQUID

a

m2s GAS

a

m2s

Aluminum 93166times10-6 Water 0131times10-6 Air 18777times10-6

Copper 114085times10-6 Ethyl Alcohol 0100times10-6 Nitrogen 18703times10-6

Gold 12479times10-6 Gasoline 0075times10-6 Sulfur Dioxide 4711times10-6

Polystyrene 0611times10-6 Oil 0154times10-6 Carbon Dioxide 9097times10-6

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 8

PHYSICAL PROPERTIES

15 Physical Properties of Selected Gases

Table 48 Physical Properties of Selected Gases (10 bar 0 oC)

Material Density

Molar

Mass

Gas

Const

Boiling

Point cp cpcv 106 timesmicro K Pr

kgm3 gmol J(kg K) ordmC J(kg K) - Pa s W(m K) -

Air (dry) 1293 2895 287 -195 1010 14 173 00245 071

Argon [Ar] 1782 3994 2085 -1858 532 165 209 00173 064

Carbon Dioxide

[CO2] 1976 4401 189 - 837 13 137 00137 084

Carbon Monoxide

[CO] 125 2801 297 1047 14 166 00226 077

Helium [He] 0178 4002 2079 -2689 5274 166 188 0144 069

Hydrogen [H2] 00898 2016 4125 -2529 14266 1407 842 0163 074

Nitrogen [N2] 1251 2802 2967 -1958 1047 14 17 00228 078

Oxygen [O2] 1429 32 2599 -1829 913 14 203 0024 077

Normal composition of clean dry atmospheric air near the sea level

Nitrogen (N2) =78084 Oxygen (O2) = 20948 Argon (Ar) = 0934 Carbon Dioxide (CO2) =0031

Neon (Ne) Helium (He) Krypton (Kr) Hydrogen (H2) Xenon (Xe) Methane (CH4) Nitrogen Oxide (N2O) Ozone (O3)

Sulfur Dioxide (NO2) Ammonia (NH3) Carbon Monoxide (CO) and Iodine (I2) =traces of each gas for a total of 0003

Formulae for the calculation of average constant-pressure specific heat ndash cp [kJkg] of various gases in

the range from 0 to 2000 oC are presented in Table 49

Table 49 Average Specific Heat at Constant Pressure of some Gases

Gas

Average Specific Heat at Constant Pressure

])C[t()Kkg(kJ[c ot

op

(Range 0 to 2000 oC)

Maxim

um

Error

Hydrogen (H2) 01+143810E +t 04-200328E +t08-356131E - t10-342031E + t13-108329E- = 234 006

Nitrogen (clean)

(N2) 00103937E t 06-857115E t07-173326E t10-106900E - t14-207571E = 234 009

Oxygen (O2) 01-907389E t 04-144682E t08-150961E t11-443486E - t14-123574E = 234 012

Carbon Monoxide

(CO) 00103823E t 05-124096E t07-176241E t10-120740E - t14-251706E 234 011

Carbon Dioxide

(CO2) 01-820310E t 04-516236E t07-298914E - t10-104359E t14-156925E- = 234 006

Water Vapor (H2O) 00185773E t 04-135306E t07-267351E t10-142139E - t14-235461E= 234 004

Sulfur Dioxide

(SO2) 01-606803E t 04-321094E t07-201319E - t11-653115E t15-804281E- = 234 012

Air 00100361E t 05-218551E t07-142841E t11-968901E - t14-199627E = 234 009

Nitrogen (form Air)

(N2) 00102694E t 05-142726E t07-131381E t11-797576E - t14-148364E = 234 014

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 9

16 Physical Properties of Selected Liquids

Table 410 Physical Properties of Selected Liquids

Liquid t [oC] ρ [kgm3] cp [kJkg

K)]

k [W(m

K)]

micro times 103 [Pa

s]

β times 105

[1K] a [m2s]

Acetone 20

50

791

756

216

225

0170

0163

0331

-

143

-

Gasoline

20

40

60

100

751

735

717

681

206

215

224

246

01165

-

-

01005

0529

0411

0328

0225

125

-

-

-

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol

0

20

50

806

789

-

229

245

281

0185

0183

0178

178

119

0695

Ethylene

Glycol

20

40

60

80

100

1113

1099

1085

1070

1056

2382

2474

2562

2650

2742

0258

-

-

-

0269

1990

913

495

302

199

Glycerin

20

50

100

200

1260

1244

1200

1090

235

250

279

334

-

0283

0289

-

1480

180

13

022

53

-

-

-

Methyl Alcohol

0

20

50

810

792

765

243

247

256

0241

0212

-

0818

0585

0400

Petroleum

20

50

100

200

819

801

766

785

200

214

238

289

-

01114

01042

00891

149

0956

0545

0262

100

-

-

-

Oil (lubricant)

25

50

75

100

920

905

896

880

1850

1943

2041

2136

0130

0128

0125

0123

190

429

156

572

Oil

(transformer)

25

50

75

100

860

845

835

820

1918

2043

2169

2294

0123

0122

0120

0117

2420

990

477

302

17 Thermodynamic and Transport Properties of Water and Steam

a Some of thermodynamic properties of water are

H2O = Chemical formula

M = 18016 [kgkmol] (Molecular Mass)

tc = 37415 [oC] (Critical Temperature)

Tc = 647286 [K] (Absolute Critical Temperature)

pc = 22089 [bar] (Critical Pressure)

c = 3170 [kgm3] (Critical Density)

tm = 001 [oC] (Melting Temperature at 101325 bar)

rm = 332432 [kJkg] (Heat of Melting at 101325 bar)

tb = 1000 [oC] (Boiling Temperature at 101325 bar)

rb = 22570 [kJkg] (Heat of Evaporation at 101325 bar)

R = 462507 [J(kg K)] (Gas Constant)

Enthalpies and entropies of boiling water and saturated steam versus temperature and

pressure (001 lt p lt 20 bar 7 lt t lt 212 oC)

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 10

a Saturated steam and boiling water temperature versus pressure3

112

31-42-

5-36-5

109963430 ln(p)][102794824 ln(p)][2397684

ln(p)][102118802 ln(p)][101786280

ln(p)][101285144 ln(p)][1005-5518190E t

(45)

Error is in the range 007

b Saturated steam and boiling water pressure versus temperature

5098158] -t 107261845 t102974345 - t101096061

t103381446 - t107363934 t10316exp[-7789p

2-24-36-

4-95-126-15

(46)

Error is in the range of 005

c Enthalpy of boiling water versus temperature

1-

2-53-74-9

10359463 t 417927

t10723854 - t10706612 t10833022h (47)

d Enthalpy of saturated steam versus temperature

250044 t 187334

t10103177 - t10151237 t10332313 - h 2-33-64-8

(48)

e Entropy of boiling water versus pressure

130250 ln(p)10315672

(ln(p))10167802 (ln(p))10145398 (ln(p))10973390s

2-

2-33-44-5

(49)

f Entropy of saturated steam versus pressure

736130 ln(p)10336497 - (ln(p)10760363 (ln(p)10-538843s -12-43-4 (41

0)

Water properties (temperatures from 0 to 300 oC)

(From 0 to 100 oC at 1013 bar and for higher temperatures for boiling pressure)

g Density [kgm3]

22-23-

3-54-75-106-13

10999945 t 10410381 t10726539 -

t10428877 t10208168 - t10556465 t10-644703

(411

)

3 ln - natural logarithm

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 11

h Specific heat at constant pressure cp [J(kg K)]

30-21-

3-34-65-86-11p

10421629 t 10370637 - t10109452

t10142353 -t10976851 t10317259 - t10400424c

(412

)

i Thermal conductivity [W(m K)]

11-23-

3-64-95-116-112

10549688 t 10285413 t10210253 -

t10672554 t10740918 - t10187737 - t1036594410

(413

)

j Thermal diffusivity a [m2s]

pca (414)

k Dynamic viscosity [Pa s]

748230 t 10322128 - t10218237

t10103401 - t10272328 t1077Exp(-291810

2-22-

3-64-95-126

(415)

l Kinematic viscosity [m2s]

(416)

m Coefficient of volume expansion [1K]

1-1-23-35-

4-85-106-134

10684475 -t 10163711 t10182013 -t10158931

t10746034 - t10170218 t10-12877310

(417

)

Some important properties for heat transfer calculations are presented in Table 48 It is obvious

that they depend on temperature much more than on pressure Because of that for almost all industrial

calculations the influence of pressure can be ignored

Table 411 Water Density Specific Heat Thermal Conductivity and Dynamic Viscosity versus

Temperature and Pressure

]mkg[ 3 )]Kkg(J[cp )]Km(W[ ]sPa[106

]bar[p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o

0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 1295

20 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 1001

30 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 803

40 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 657

50 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 554

60 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 475

70 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 12

80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 360

90 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287

150 9221 9273 4275 4237 0693 0699 188 190

200 8707 8776 4455 4396 0672 0679 138 140

250 8059 8161 4781 4681 0624 0636 112 115

300 7154 7346 5661 5275 0542 0558 91 94

350 6006 8206 0452 75

360 547 12560 0412 69

Saturated steam properties (0 lt t lt 210 oC or 0006 bar lt p lt 1908 bar)

n Density of saturated steam

00203297 + p0554983 +p000557908 - p8000014411= 23 (418)

o Specific heat at constant pressure of saturated steam

186459 +t 0784614 + t000461955 + t93000009956 =c 23p (419)

p Thermal conductivity of saturated steam

0404835 -t 00474611 +t8000026173 - t3939000000064=10 232 (420)

q Dynamic viscosity of saturated steam

81587 +t 00375325 + t281000000762=10 26 (421)

Superheated steam properties (250 lt t lt 550 oC or 1961 bar lt p lt 5884 bar)

Table 412 Superheated Steam

]mkg[ 3 )]Kkg(J[cp )]Km(W[102

]sPa[10 6

p[bar] 1961 3923 5884 1961 3923 5884 1961 3923 5884 1961 3923 5884

t [oC]

220 9588 2935 373 168

230 9285 2784 383 174

240 9025 2633 393 177

250 8787 1962 2554 3647 403 453 181 183

280 2937 4438 532 198

290 2808 4028 505 202

300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205

350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225

400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246

450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268

500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289

550 1606 2353 784 312

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 13

18 Physical Properties of Selected Solid Materials

Table 413 Properties of Selected Solids at 25 oC

Substance

kgm3 pc

[kJ(kg K)]

Asphalt 2120 167

Brick (common) 1800 084

Carbon (diamond) 3250 051

Carbon (graphite) 2000ndash2500 061

Coal 1200ndash1500 126

Concrete 2200 088

Glass (plate) 2500 080

Glass (wool) 200 066

Granite 2750 089

Ice (0 oC) 917 204

Paper 700 120

Plexiglas 1180 144

Polystyrene 920 230

Polyvinyl chloride 1380 096

Rubber (soft) 1100 167

Salt (rock) 2100ndash2500 092

Sand (dry) 1500 080

Silicon 2330 070

Snow (firm) 560 210

Wood (hard oak) 720 126

Wood (soft pine) 510 138

Wool 100 172

Table 414 Properties of Selected Metals at 25 oC

Metals

kgm3

pc

[kJ(kg

K)] Aluminum 2700 090

Copper (commercial) 8300 042

Brass (60-40) 8400 038

Gold 19300 013

Iron (cast) 7272 042

Iron (Steel 304 St) 7820 046

Lead 11340 013

Magnesium (2 Mn) 1778 100

Nickel (10 Cr) 8666 044

Silver (999 Ag) 10524 024

Sodium 971 121

Tin 7304 022

Tungsten 19300 013

Zinc 7144 039

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 14

Table 415 Thermal Expansion Coefficients and

Thermal Conductivity of Solids

Material

Thermal

Expansion

Coefficient

(times10-6ordmC)

Thermal

Conductivity

(WmmiddotK)

Aluminum 230 237

Aluminum Alloy 230 ndash

Brass 191 ndash 212 ndash

Brass Noval 211 ndash

Brass Red (80 Cu

20 Zn) 191 ndash

Brick 500 ndash 700 ndash

Bronze Regular 180 ndash 210 ndash

Bronze Manganese 200 ndash

Concrete 700 ndash 140 ndash

Copper 166 ndash 176 410

Copper Alloy 170 ndash

Glass 500 ndash 110 ndash

Gold ndash 317

Iron ndash 802

Iron (Cast) 990 ndash 120 ndash

Iron (Wrought) 120 -

Lead ndash 353

Magnesium 252 156

Magnesium Alloy 261 ndash 288 ndash

Monel (67 Ni 30

Cu) 140 ndash

Nickel 130 907

Nylon Polyamide 750 ndash 100 ndash

Platinum ndash 716

Rubber 130 ndash 200 ndash

Silicon ndash 148

Silver ndash 429

Solder Tin-Lead ndash 300 ndash 498

Steel 100 ndash 180 ndash

Tin ndash 666

Titanium ndash 219

Titanium Alloy 800 ndash 100 ndash

Tungsten 430 174

Zinc 302 116

Table 416 Density Melting and Boiling Points of

Solids

Material

Density

[times1000

kgm3]

Melting

Point

[oC]

Boiling

Point

[oC]

Aluminum 271 6603 2519

Aluminum Alloy 264 ndash

28

5650 ndash

6600 ndash

Brass 84 ndash

875 9300 ndash

Brass Noval 84 ndash ndash

Brass Red (80 Cu 20

Zn) 875 1000 ndash

Brick (Compression) 18 ndash

24 ndash- ndash

Bronze Regular 78 ndash

88 1050 ndash

Bronze Manganese 83 ndash ndash

Carbon 225 4492 3642

Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash

24 ndash ndash

Copper 894 1085 2562

Copper Alloy 823 9250 ndash

Cork 015 ndash

02 ndash ndash

Glass 24 ndash

28 ndash ndash

Gold 1932 1064 2856

Iron (Cast) 787 1538 2861

Iron (Wrought) 7 ndash 74 ndash ndash-

Magnesium [Mg] 74 ndash

78 ndash ndash

Magnesium Alloy 113 3275 1749

Monel (67 Ni 30 Cu) 174 6500 1090

Nickel [Ni] 177 1246 2061

Nylon Polyamide 884 1330 ndash

Platinum 889 1455 2913

Rubber 11 - -

Silver 214 1768 3825

Solder Tin-Lead 096 ndash

13 ndash ndash

Steel 233 1382 ndash

Stone Granite

(Compression) 1049 9618 2162

Stone

Limestone (Compression)

817 ndash

1134 2150 ndash

Stone Marble

(Compression) 785 1425 ndash

Tin 26 ndash ndash

Titanium 2 ndash29 ndash ndash

Titanium Alloy 26 ndash

29 ndash ndash

Wood Ash (Bending) 26 ndash ndash

Wood Douglas Fir

(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287

Wood Southern Pine

(Bending) 451 ndash ndash

Zinc 193 3422 5555

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 6

Different fluids deform at different rates under the same shear forces Fluid with a high viscosity

such as syrup deforms more slowly than fluid with a low viscosity such as water

Newtonian fluids obey the linear relationship given by the Newtons law of viscositydx

dw

where is the shear stress and micro is the coefficient of dynamic viscosity

Viscosity is resistance of a fluid to flow This resistance acts against the motion of any solid

object through the fluid and also against motion of the fluid itself past stationary obstacles Viscosity

also acts internally on the fluid between slower and faster moving adjacent layers

All fluids (liquids and gases) exhibit viscosity to some degree Viscosity may be thought of as

fluid friction just as the friction between two solids resists the motion of one over the other but also

makes possible the acceleration of one relative to the other

The dynamic viscosities of some fluids are presented in Table 44 It is very important to know the

temperature of the fluid (and pressure)

Table 44 Dynamic Viscosity of Some Liquids and Gasses Liquid Gas

Gasoline Water Air (dry)

1013 bar

Carbon Dioxide

1013 bar

t (oC) Μ

[Pa s] t (oC)

μ

[Pa s] t (oC)

μ

[Pa s] t (oC)

μ

[Pa s]

20 0529times10-3 0 1780times10-3 0 0017times10-3 0 0014times10-3

40 0411times10-3 20 1004times10-3 100 0022times10-3 100 0018times10-3

60 0328times10-3 40 0653times10-3 200 0026times10-3 200 0023times10-3

100 0225times10-3 60 0470times10-3 300 0030times10-3 300 0026times10-3

80 0355times10-3 400 0033times10-3 400 0030times10-3

100 0283times10-3 500 0036times10-3 500 0033times10-3

10 Kinematic viscosity is the ratio of absolute viscosity to density For either dynamic or

kinematic viscosity to be meaningful a reference temperature must be quoted

11 Thermal conductivity is a measurement of the ability of a material to conduct heat It is

defined using the Fouriers law of conduction which relates the rate of heat transfer by conduction to

the temperature gradient

dx

dTAkq (41)

where k is the thermal conductivity Using the Fouriers law we can define the thermal conductivity

as the rate of heat transfer through a unit thickness of material per unit area and per unit temperature

difference A good conductor of heat has a high value of thermal conductivity

The temperature variations of the thermal conductivities of some materials are presented in Table

5

Table 45 Thermal Conductivity of Some Materials ndash k [W(m K)]

t (oC)

Solid Liquid Gas

Copper Aluminum Gasoline Water Air (dry)

1013 bar

Steam

(saturated)

-100 407 -

0 386 221 00244 001760

100 379 - 01005 00680 00321 002372

200 373 229 00670 00393 003547

300 - 222 00558 00460 006270

500 - - 00574

700 - - 00671

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 7

12 Specific heat is the amount of heat that is required to raise the temperature of the unit mass of

a substance by one degree In a constant pressure process

Tcmq p (42)

cp is specific heat at constant pressure

Values of cp [kJ(kg K)] for various materials (at 20 oC) are shown in Table 46

Table 46 Specific Heat at Constant Pressure of Some Materials

SOLID cp

kJ(kg K) LIQUID

cp

kJ(kg K) GAS

cp

kJ(kg K)

Aluminum (pure) 0903 Water 418 Air 1010

Copper (pure) 0385 Ethyl Alcohol 229 Nitrogen 1047

Gold 0129 Gasoline 206 Sulfur Dioxide 0633

Silicon 1382 Oil 185 Carbon Dioxide 0837

13 Coefficient of thermal expansion is defined as the change in the density of a substance as a

function of temperature at constant pressure It is expressed as follows

pT

1 (43)

For ideal gases TRp

there is T

1

14 Thermal diffusivity is measure of heat propagation through a medium and may be defined by

the ratio of heat conducted through a material to the heat stored in the material The thermal

diffusivity is defined as

pc

ka (44)

The larger the thermal diffusivity is the faster the propagation of heat into the material If the

thermal diffusivity is small it means that a large part of heat is absorbed by the material and only a

small portion is conducted through it Some typical values of thermal diffusivity are given in Table

47 (0 oC 1013 bar)

Table 47 Thermal Diffusivity of Some Materials

SOLID a

m2s LIQUID

a

m2s GAS

a

m2s

Aluminum 93166times10-6 Water 0131times10-6 Air 18777times10-6

Copper 114085times10-6 Ethyl Alcohol 0100times10-6 Nitrogen 18703times10-6

Gold 12479times10-6 Gasoline 0075times10-6 Sulfur Dioxide 4711times10-6

Polystyrene 0611times10-6 Oil 0154times10-6 Carbon Dioxide 9097times10-6

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 8

PHYSICAL PROPERTIES

15 Physical Properties of Selected Gases

Table 48 Physical Properties of Selected Gases (10 bar 0 oC)

Material Density

Molar

Mass

Gas

Const

Boiling

Point cp cpcv 106 timesmicro K Pr

kgm3 gmol J(kg K) ordmC J(kg K) - Pa s W(m K) -

Air (dry) 1293 2895 287 -195 1010 14 173 00245 071

Argon [Ar] 1782 3994 2085 -1858 532 165 209 00173 064

Carbon Dioxide

[CO2] 1976 4401 189 - 837 13 137 00137 084

Carbon Monoxide

[CO] 125 2801 297 1047 14 166 00226 077

Helium [He] 0178 4002 2079 -2689 5274 166 188 0144 069

Hydrogen [H2] 00898 2016 4125 -2529 14266 1407 842 0163 074

Nitrogen [N2] 1251 2802 2967 -1958 1047 14 17 00228 078

Oxygen [O2] 1429 32 2599 -1829 913 14 203 0024 077

Normal composition of clean dry atmospheric air near the sea level

Nitrogen (N2) =78084 Oxygen (O2) = 20948 Argon (Ar) = 0934 Carbon Dioxide (CO2) =0031

Neon (Ne) Helium (He) Krypton (Kr) Hydrogen (H2) Xenon (Xe) Methane (CH4) Nitrogen Oxide (N2O) Ozone (O3)

Sulfur Dioxide (NO2) Ammonia (NH3) Carbon Monoxide (CO) and Iodine (I2) =traces of each gas for a total of 0003

Formulae for the calculation of average constant-pressure specific heat ndash cp [kJkg] of various gases in

the range from 0 to 2000 oC are presented in Table 49

Table 49 Average Specific Heat at Constant Pressure of some Gases

Gas

Average Specific Heat at Constant Pressure

])C[t()Kkg(kJ[c ot

op

(Range 0 to 2000 oC)

Maxim

um

Error

Hydrogen (H2) 01+143810E +t 04-200328E +t08-356131E - t10-342031E + t13-108329E- = 234 006

Nitrogen (clean)

(N2) 00103937E t 06-857115E t07-173326E t10-106900E - t14-207571E = 234 009

Oxygen (O2) 01-907389E t 04-144682E t08-150961E t11-443486E - t14-123574E = 234 012

Carbon Monoxide

(CO) 00103823E t 05-124096E t07-176241E t10-120740E - t14-251706E 234 011

Carbon Dioxide

(CO2) 01-820310E t 04-516236E t07-298914E - t10-104359E t14-156925E- = 234 006

Water Vapor (H2O) 00185773E t 04-135306E t07-267351E t10-142139E - t14-235461E= 234 004

Sulfur Dioxide

(SO2) 01-606803E t 04-321094E t07-201319E - t11-653115E t15-804281E- = 234 012

Air 00100361E t 05-218551E t07-142841E t11-968901E - t14-199627E = 234 009

Nitrogen (form Air)

(N2) 00102694E t 05-142726E t07-131381E t11-797576E - t14-148364E = 234 014

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 9

16 Physical Properties of Selected Liquids

Table 410 Physical Properties of Selected Liquids

Liquid t [oC] ρ [kgm3] cp [kJkg

K)]

k [W(m

K)]

micro times 103 [Pa

s]

β times 105

[1K] a [m2s]

Acetone 20

50

791

756

216

225

0170

0163

0331

-

143

-

Gasoline

20

40

60

100

751

735

717

681

206

215

224

246

01165

-

-

01005

0529

0411

0328

0225

125

-

-

-

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol

0

20

50

806

789

-

229

245

281

0185

0183

0178

178

119

0695

Ethylene

Glycol

20

40

60

80

100

1113

1099

1085

1070

1056

2382

2474

2562

2650

2742

0258

-

-

-

0269

1990

913

495

302

199

Glycerin

20

50

100

200

1260

1244

1200

1090

235

250

279

334

-

0283

0289

-

1480

180

13

022

53

-

-

-

Methyl Alcohol

0

20

50

810

792

765

243

247

256

0241

0212

-

0818

0585

0400

Petroleum

20

50

100

200

819

801

766

785

200

214

238

289

-

01114

01042

00891

149

0956

0545

0262

100

-

-

-

Oil (lubricant)

25

50

75

100

920

905

896

880

1850

1943

2041

2136

0130

0128

0125

0123

190

429

156

572

Oil

(transformer)

25

50

75

100

860

845

835

820

1918

2043

2169

2294

0123

0122

0120

0117

2420

990

477

302

17 Thermodynamic and Transport Properties of Water and Steam

a Some of thermodynamic properties of water are

H2O = Chemical formula

M = 18016 [kgkmol] (Molecular Mass)

tc = 37415 [oC] (Critical Temperature)

Tc = 647286 [K] (Absolute Critical Temperature)

pc = 22089 [bar] (Critical Pressure)

c = 3170 [kgm3] (Critical Density)

tm = 001 [oC] (Melting Temperature at 101325 bar)

rm = 332432 [kJkg] (Heat of Melting at 101325 bar)

tb = 1000 [oC] (Boiling Temperature at 101325 bar)

rb = 22570 [kJkg] (Heat of Evaporation at 101325 bar)

R = 462507 [J(kg K)] (Gas Constant)

Enthalpies and entropies of boiling water and saturated steam versus temperature and

pressure (001 lt p lt 20 bar 7 lt t lt 212 oC)

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 10

a Saturated steam and boiling water temperature versus pressure3

112

31-42-

5-36-5

109963430 ln(p)][102794824 ln(p)][2397684

ln(p)][102118802 ln(p)][101786280

ln(p)][101285144 ln(p)][1005-5518190E t

(45)

Error is in the range 007

b Saturated steam and boiling water pressure versus temperature

5098158] -t 107261845 t102974345 - t101096061

t103381446 - t107363934 t10316exp[-7789p

2-24-36-

4-95-126-15

(46)

Error is in the range of 005

c Enthalpy of boiling water versus temperature

1-

2-53-74-9

10359463 t 417927

t10723854 - t10706612 t10833022h (47)

d Enthalpy of saturated steam versus temperature

250044 t 187334

t10103177 - t10151237 t10332313 - h 2-33-64-8

(48)

e Entropy of boiling water versus pressure

130250 ln(p)10315672

(ln(p))10167802 (ln(p))10145398 (ln(p))10973390s

2-

2-33-44-5

(49)

f Entropy of saturated steam versus pressure

736130 ln(p)10336497 - (ln(p)10760363 (ln(p)10-538843s -12-43-4 (41

0)

Water properties (temperatures from 0 to 300 oC)

(From 0 to 100 oC at 1013 bar and for higher temperatures for boiling pressure)

g Density [kgm3]

22-23-

3-54-75-106-13

10999945 t 10410381 t10726539 -

t10428877 t10208168 - t10556465 t10-644703

(411

)

3 ln - natural logarithm

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 11

h Specific heat at constant pressure cp [J(kg K)]

30-21-

3-34-65-86-11p

10421629 t 10370637 - t10109452

t10142353 -t10976851 t10317259 - t10400424c

(412

)

i Thermal conductivity [W(m K)]

11-23-

3-64-95-116-112

10549688 t 10285413 t10210253 -

t10672554 t10740918 - t10187737 - t1036594410

(413

)

j Thermal diffusivity a [m2s]

pca (414)

k Dynamic viscosity [Pa s]

748230 t 10322128 - t10218237

t10103401 - t10272328 t1077Exp(-291810

2-22-

3-64-95-126

(415)

l Kinematic viscosity [m2s]

(416)

m Coefficient of volume expansion [1K]

1-1-23-35-

4-85-106-134

10684475 -t 10163711 t10182013 -t10158931

t10746034 - t10170218 t10-12877310

(417

)

Some important properties for heat transfer calculations are presented in Table 48 It is obvious

that they depend on temperature much more than on pressure Because of that for almost all industrial

calculations the influence of pressure can be ignored

Table 411 Water Density Specific Heat Thermal Conductivity and Dynamic Viscosity versus

Temperature and Pressure

]mkg[ 3 )]Kkg(J[cp )]Km(W[ ]sPa[106

]bar[p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o

0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 1295

20 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 1001

30 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 803

40 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 657

50 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 554

60 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 475

70 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 12

80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 360

90 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287

150 9221 9273 4275 4237 0693 0699 188 190

200 8707 8776 4455 4396 0672 0679 138 140

250 8059 8161 4781 4681 0624 0636 112 115

300 7154 7346 5661 5275 0542 0558 91 94

350 6006 8206 0452 75

360 547 12560 0412 69

Saturated steam properties (0 lt t lt 210 oC or 0006 bar lt p lt 1908 bar)

n Density of saturated steam

00203297 + p0554983 +p000557908 - p8000014411= 23 (418)

o Specific heat at constant pressure of saturated steam

186459 +t 0784614 + t000461955 + t93000009956 =c 23p (419)

p Thermal conductivity of saturated steam

0404835 -t 00474611 +t8000026173 - t3939000000064=10 232 (420)

q Dynamic viscosity of saturated steam

81587 +t 00375325 + t281000000762=10 26 (421)

Superheated steam properties (250 lt t lt 550 oC or 1961 bar lt p lt 5884 bar)

Table 412 Superheated Steam

]mkg[ 3 )]Kkg(J[cp )]Km(W[102

]sPa[10 6

p[bar] 1961 3923 5884 1961 3923 5884 1961 3923 5884 1961 3923 5884

t [oC]

220 9588 2935 373 168

230 9285 2784 383 174

240 9025 2633 393 177

250 8787 1962 2554 3647 403 453 181 183

280 2937 4438 532 198

290 2808 4028 505 202

300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205

350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225

400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246

450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268

500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289

550 1606 2353 784 312

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 13

18 Physical Properties of Selected Solid Materials

Table 413 Properties of Selected Solids at 25 oC

Substance

kgm3 pc

[kJ(kg K)]

Asphalt 2120 167

Brick (common) 1800 084

Carbon (diamond) 3250 051

Carbon (graphite) 2000ndash2500 061

Coal 1200ndash1500 126

Concrete 2200 088

Glass (plate) 2500 080

Glass (wool) 200 066

Granite 2750 089

Ice (0 oC) 917 204

Paper 700 120

Plexiglas 1180 144

Polystyrene 920 230

Polyvinyl chloride 1380 096

Rubber (soft) 1100 167

Salt (rock) 2100ndash2500 092

Sand (dry) 1500 080

Silicon 2330 070

Snow (firm) 560 210

Wood (hard oak) 720 126

Wood (soft pine) 510 138

Wool 100 172

Table 414 Properties of Selected Metals at 25 oC

Metals

kgm3

pc

[kJ(kg

K)] Aluminum 2700 090

Copper (commercial) 8300 042

Brass (60-40) 8400 038

Gold 19300 013

Iron (cast) 7272 042

Iron (Steel 304 St) 7820 046

Lead 11340 013

Magnesium (2 Mn) 1778 100

Nickel (10 Cr) 8666 044

Silver (999 Ag) 10524 024

Sodium 971 121

Tin 7304 022

Tungsten 19300 013

Zinc 7144 039

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 14

Table 415 Thermal Expansion Coefficients and

Thermal Conductivity of Solids

Material

Thermal

Expansion

Coefficient

(times10-6ordmC)

Thermal

Conductivity

(WmmiddotK)

Aluminum 230 237

Aluminum Alloy 230 ndash

Brass 191 ndash 212 ndash

Brass Noval 211 ndash

Brass Red (80 Cu

20 Zn) 191 ndash

Brick 500 ndash 700 ndash

Bronze Regular 180 ndash 210 ndash

Bronze Manganese 200 ndash

Concrete 700 ndash 140 ndash

Copper 166 ndash 176 410

Copper Alloy 170 ndash

Glass 500 ndash 110 ndash

Gold ndash 317

Iron ndash 802

Iron (Cast) 990 ndash 120 ndash

Iron (Wrought) 120 -

Lead ndash 353

Magnesium 252 156

Magnesium Alloy 261 ndash 288 ndash

Monel (67 Ni 30

Cu) 140 ndash

Nickel 130 907

Nylon Polyamide 750 ndash 100 ndash

Platinum ndash 716

Rubber 130 ndash 200 ndash

Silicon ndash 148

Silver ndash 429

Solder Tin-Lead ndash 300 ndash 498

Steel 100 ndash 180 ndash

Tin ndash 666

Titanium ndash 219

Titanium Alloy 800 ndash 100 ndash

Tungsten 430 174

Zinc 302 116

Table 416 Density Melting and Boiling Points of

Solids

Material

Density

[times1000

kgm3]

Melting

Point

[oC]

Boiling

Point

[oC]

Aluminum 271 6603 2519

Aluminum Alloy 264 ndash

28

5650 ndash

6600 ndash

Brass 84 ndash

875 9300 ndash

Brass Noval 84 ndash ndash

Brass Red (80 Cu 20

Zn) 875 1000 ndash

Brick (Compression) 18 ndash

24 ndash- ndash

Bronze Regular 78 ndash

88 1050 ndash

Bronze Manganese 83 ndash ndash

Carbon 225 4492 3642

Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash

24 ndash ndash

Copper 894 1085 2562

Copper Alloy 823 9250 ndash

Cork 015 ndash

02 ndash ndash

Glass 24 ndash

28 ndash ndash

Gold 1932 1064 2856

Iron (Cast) 787 1538 2861

Iron (Wrought) 7 ndash 74 ndash ndash-

Magnesium [Mg] 74 ndash

78 ndash ndash

Magnesium Alloy 113 3275 1749

Monel (67 Ni 30 Cu) 174 6500 1090

Nickel [Ni] 177 1246 2061

Nylon Polyamide 884 1330 ndash

Platinum 889 1455 2913

Rubber 11 - -

Silver 214 1768 3825

Solder Tin-Lead 096 ndash

13 ndash ndash

Steel 233 1382 ndash

Stone Granite

(Compression) 1049 9618 2162

Stone

Limestone (Compression)

817 ndash

1134 2150 ndash

Stone Marble

(Compression) 785 1425 ndash

Tin 26 ndash ndash

Titanium 2 ndash29 ndash ndash

Titanium Alloy 26 ndash

29 ndash ndash

Wood Ash (Bending) 26 ndash ndash

Wood Douglas Fir

(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287

Wood Southern Pine

(Bending) 451 ndash ndash

Zinc 193 3422 5555

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 7

12 Specific heat is the amount of heat that is required to raise the temperature of the unit mass of

a substance by one degree In a constant pressure process

Tcmq p (42)

cp is specific heat at constant pressure

Values of cp [kJ(kg K)] for various materials (at 20 oC) are shown in Table 46

Table 46 Specific Heat at Constant Pressure of Some Materials

SOLID cp

kJ(kg K) LIQUID

cp

kJ(kg K) GAS

cp

kJ(kg K)

Aluminum (pure) 0903 Water 418 Air 1010

Copper (pure) 0385 Ethyl Alcohol 229 Nitrogen 1047

Gold 0129 Gasoline 206 Sulfur Dioxide 0633

Silicon 1382 Oil 185 Carbon Dioxide 0837

13 Coefficient of thermal expansion is defined as the change in the density of a substance as a

function of temperature at constant pressure It is expressed as follows

pT

1 (43)

For ideal gases TRp

there is T

1

14 Thermal diffusivity is measure of heat propagation through a medium and may be defined by

the ratio of heat conducted through a material to the heat stored in the material The thermal

diffusivity is defined as

pc

ka (44)

The larger the thermal diffusivity is the faster the propagation of heat into the material If the

thermal diffusivity is small it means that a large part of heat is absorbed by the material and only a

small portion is conducted through it Some typical values of thermal diffusivity are given in Table

47 (0 oC 1013 bar)

Table 47 Thermal Diffusivity of Some Materials

SOLID a

m2s LIQUID

a

m2s GAS

a

m2s

Aluminum 93166times10-6 Water 0131times10-6 Air 18777times10-6

Copper 114085times10-6 Ethyl Alcohol 0100times10-6 Nitrogen 18703times10-6

Gold 12479times10-6 Gasoline 0075times10-6 Sulfur Dioxide 4711times10-6

Polystyrene 0611times10-6 Oil 0154times10-6 Carbon Dioxide 9097times10-6

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 8

PHYSICAL PROPERTIES

15 Physical Properties of Selected Gases

Table 48 Physical Properties of Selected Gases (10 bar 0 oC)

Material Density

Molar

Mass

Gas

Const

Boiling

Point cp cpcv 106 timesmicro K Pr

kgm3 gmol J(kg K) ordmC J(kg K) - Pa s W(m K) -

Air (dry) 1293 2895 287 -195 1010 14 173 00245 071

Argon [Ar] 1782 3994 2085 -1858 532 165 209 00173 064

Carbon Dioxide

[CO2] 1976 4401 189 - 837 13 137 00137 084

Carbon Monoxide

[CO] 125 2801 297 1047 14 166 00226 077

Helium [He] 0178 4002 2079 -2689 5274 166 188 0144 069

Hydrogen [H2] 00898 2016 4125 -2529 14266 1407 842 0163 074

Nitrogen [N2] 1251 2802 2967 -1958 1047 14 17 00228 078

Oxygen [O2] 1429 32 2599 -1829 913 14 203 0024 077

Normal composition of clean dry atmospheric air near the sea level

Nitrogen (N2) =78084 Oxygen (O2) = 20948 Argon (Ar) = 0934 Carbon Dioxide (CO2) =0031

Neon (Ne) Helium (He) Krypton (Kr) Hydrogen (H2) Xenon (Xe) Methane (CH4) Nitrogen Oxide (N2O) Ozone (O3)

Sulfur Dioxide (NO2) Ammonia (NH3) Carbon Monoxide (CO) and Iodine (I2) =traces of each gas for a total of 0003

Formulae for the calculation of average constant-pressure specific heat ndash cp [kJkg] of various gases in

the range from 0 to 2000 oC are presented in Table 49

Table 49 Average Specific Heat at Constant Pressure of some Gases

Gas

Average Specific Heat at Constant Pressure

])C[t()Kkg(kJ[c ot

op

(Range 0 to 2000 oC)

Maxim

um

Error

Hydrogen (H2) 01+143810E +t 04-200328E +t08-356131E - t10-342031E + t13-108329E- = 234 006

Nitrogen (clean)

(N2) 00103937E t 06-857115E t07-173326E t10-106900E - t14-207571E = 234 009

Oxygen (O2) 01-907389E t 04-144682E t08-150961E t11-443486E - t14-123574E = 234 012

Carbon Monoxide

(CO) 00103823E t 05-124096E t07-176241E t10-120740E - t14-251706E 234 011

Carbon Dioxide

(CO2) 01-820310E t 04-516236E t07-298914E - t10-104359E t14-156925E- = 234 006

Water Vapor (H2O) 00185773E t 04-135306E t07-267351E t10-142139E - t14-235461E= 234 004

Sulfur Dioxide

(SO2) 01-606803E t 04-321094E t07-201319E - t11-653115E t15-804281E- = 234 012

Air 00100361E t 05-218551E t07-142841E t11-968901E - t14-199627E = 234 009

Nitrogen (form Air)

(N2) 00102694E t 05-142726E t07-131381E t11-797576E - t14-148364E = 234 014

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 9

16 Physical Properties of Selected Liquids

Table 410 Physical Properties of Selected Liquids

Liquid t [oC] ρ [kgm3] cp [kJkg

K)]

k [W(m

K)]

micro times 103 [Pa

s]

β times 105

[1K] a [m2s]

Acetone 20

50

791

756

216

225

0170

0163

0331

-

143

-

Gasoline

20

40

60

100

751

735

717

681

206

215

224

246

01165

-

-

01005

0529

0411

0328

0225

125

-

-

-

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol

0

20

50

806

789

-

229

245

281

0185

0183

0178

178

119

0695

Ethylene

Glycol

20

40

60

80

100

1113

1099

1085

1070

1056

2382

2474

2562

2650

2742

0258

-

-

-

0269

1990

913

495

302

199

Glycerin

20

50

100

200

1260

1244

1200

1090

235

250

279

334

-

0283

0289

-

1480

180

13

022

53

-

-

-

Methyl Alcohol

0

20

50

810

792

765

243

247

256

0241

0212

-

0818

0585

0400

Petroleum

20

50

100

200

819

801

766

785

200

214

238

289

-

01114

01042

00891

149

0956

0545

0262

100

-

-

-

Oil (lubricant)

25

50

75

100

920

905

896

880

1850

1943

2041

2136

0130

0128

0125

0123

190

429

156

572

Oil

(transformer)

25

50

75

100

860

845

835

820

1918

2043

2169

2294

0123

0122

0120

0117

2420

990

477

302

17 Thermodynamic and Transport Properties of Water and Steam

a Some of thermodynamic properties of water are

H2O = Chemical formula

M = 18016 [kgkmol] (Molecular Mass)

tc = 37415 [oC] (Critical Temperature)

Tc = 647286 [K] (Absolute Critical Temperature)

pc = 22089 [bar] (Critical Pressure)

c = 3170 [kgm3] (Critical Density)

tm = 001 [oC] (Melting Temperature at 101325 bar)

rm = 332432 [kJkg] (Heat of Melting at 101325 bar)

tb = 1000 [oC] (Boiling Temperature at 101325 bar)

rb = 22570 [kJkg] (Heat of Evaporation at 101325 bar)

R = 462507 [J(kg K)] (Gas Constant)

Enthalpies and entropies of boiling water and saturated steam versus temperature and

pressure (001 lt p lt 20 bar 7 lt t lt 212 oC)

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 10

a Saturated steam and boiling water temperature versus pressure3

112

31-42-

5-36-5

109963430 ln(p)][102794824 ln(p)][2397684

ln(p)][102118802 ln(p)][101786280

ln(p)][101285144 ln(p)][1005-5518190E t

(45)

Error is in the range 007

b Saturated steam and boiling water pressure versus temperature

5098158] -t 107261845 t102974345 - t101096061

t103381446 - t107363934 t10316exp[-7789p

2-24-36-

4-95-126-15

(46)

Error is in the range of 005

c Enthalpy of boiling water versus temperature

1-

2-53-74-9

10359463 t 417927

t10723854 - t10706612 t10833022h (47)

d Enthalpy of saturated steam versus temperature

250044 t 187334

t10103177 - t10151237 t10332313 - h 2-33-64-8

(48)

e Entropy of boiling water versus pressure

130250 ln(p)10315672

(ln(p))10167802 (ln(p))10145398 (ln(p))10973390s

2-

2-33-44-5

(49)

f Entropy of saturated steam versus pressure

736130 ln(p)10336497 - (ln(p)10760363 (ln(p)10-538843s -12-43-4 (41

0)

Water properties (temperatures from 0 to 300 oC)

(From 0 to 100 oC at 1013 bar and for higher temperatures for boiling pressure)

g Density [kgm3]

22-23-

3-54-75-106-13

10999945 t 10410381 t10726539 -

t10428877 t10208168 - t10556465 t10-644703

(411

)

3 ln - natural logarithm

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 11

h Specific heat at constant pressure cp [J(kg K)]

30-21-

3-34-65-86-11p

10421629 t 10370637 - t10109452

t10142353 -t10976851 t10317259 - t10400424c

(412

)

i Thermal conductivity [W(m K)]

11-23-

3-64-95-116-112

10549688 t 10285413 t10210253 -

t10672554 t10740918 - t10187737 - t1036594410

(413

)

j Thermal diffusivity a [m2s]

pca (414)

k Dynamic viscosity [Pa s]

748230 t 10322128 - t10218237

t10103401 - t10272328 t1077Exp(-291810

2-22-

3-64-95-126

(415)

l Kinematic viscosity [m2s]

(416)

m Coefficient of volume expansion [1K]

1-1-23-35-

4-85-106-134

10684475 -t 10163711 t10182013 -t10158931

t10746034 - t10170218 t10-12877310

(417

)

Some important properties for heat transfer calculations are presented in Table 48 It is obvious

that they depend on temperature much more than on pressure Because of that for almost all industrial

calculations the influence of pressure can be ignored

Table 411 Water Density Specific Heat Thermal Conductivity and Dynamic Viscosity versus

Temperature and Pressure

]mkg[ 3 )]Kkg(J[cp )]Km(W[ ]sPa[106

]bar[p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o

0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 1295

20 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 1001

30 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 803

40 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 657

50 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 554

60 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 475

70 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 12

80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 360

90 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287

150 9221 9273 4275 4237 0693 0699 188 190

200 8707 8776 4455 4396 0672 0679 138 140

250 8059 8161 4781 4681 0624 0636 112 115

300 7154 7346 5661 5275 0542 0558 91 94

350 6006 8206 0452 75

360 547 12560 0412 69

Saturated steam properties (0 lt t lt 210 oC or 0006 bar lt p lt 1908 bar)

n Density of saturated steam

00203297 + p0554983 +p000557908 - p8000014411= 23 (418)

o Specific heat at constant pressure of saturated steam

186459 +t 0784614 + t000461955 + t93000009956 =c 23p (419)

p Thermal conductivity of saturated steam

0404835 -t 00474611 +t8000026173 - t3939000000064=10 232 (420)

q Dynamic viscosity of saturated steam

81587 +t 00375325 + t281000000762=10 26 (421)

Superheated steam properties (250 lt t lt 550 oC or 1961 bar lt p lt 5884 bar)

Table 412 Superheated Steam

]mkg[ 3 )]Kkg(J[cp )]Km(W[102

]sPa[10 6

p[bar] 1961 3923 5884 1961 3923 5884 1961 3923 5884 1961 3923 5884

t [oC]

220 9588 2935 373 168

230 9285 2784 383 174

240 9025 2633 393 177

250 8787 1962 2554 3647 403 453 181 183

280 2937 4438 532 198

290 2808 4028 505 202

300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205

350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225

400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246

450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268

500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289

550 1606 2353 784 312

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 13

18 Physical Properties of Selected Solid Materials

Table 413 Properties of Selected Solids at 25 oC

Substance

kgm3 pc

[kJ(kg K)]

Asphalt 2120 167

Brick (common) 1800 084

Carbon (diamond) 3250 051

Carbon (graphite) 2000ndash2500 061

Coal 1200ndash1500 126

Concrete 2200 088

Glass (plate) 2500 080

Glass (wool) 200 066

Granite 2750 089

Ice (0 oC) 917 204

Paper 700 120

Plexiglas 1180 144

Polystyrene 920 230

Polyvinyl chloride 1380 096

Rubber (soft) 1100 167

Salt (rock) 2100ndash2500 092

Sand (dry) 1500 080

Silicon 2330 070

Snow (firm) 560 210

Wood (hard oak) 720 126

Wood (soft pine) 510 138

Wool 100 172

Table 414 Properties of Selected Metals at 25 oC

Metals

kgm3

pc

[kJ(kg

K)] Aluminum 2700 090

Copper (commercial) 8300 042

Brass (60-40) 8400 038

Gold 19300 013

Iron (cast) 7272 042

Iron (Steel 304 St) 7820 046

Lead 11340 013

Magnesium (2 Mn) 1778 100

Nickel (10 Cr) 8666 044

Silver (999 Ag) 10524 024

Sodium 971 121

Tin 7304 022

Tungsten 19300 013

Zinc 7144 039

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 14

Table 415 Thermal Expansion Coefficients and

Thermal Conductivity of Solids

Material

Thermal

Expansion

Coefficient

(times10-6ordmC)

Thermal

Conductivity

(WmmiddotK)

Aluminum 230 237

Aluminum Alloy 230 ndash

Brass 191 ndash 212 ndash

Brass Noval 211 ndash

Brass Red (80 Cu

20 Zn) 191 ndash

Brick 500 ndash 700 ndash

Bronze Regular 180 ndash 210 ndash

Bronze Manganese 200 ndash

Concrete 700 ndash 140 ndash

Copper 166 ndash 176 410

Copper Alloy 170 ndash

Glass 500 ndash 110 ndash

Gold ndash 317

Iron ndash 802

Iron (Cast) 990 ndash 120 ndash

Iron (Wrought) 120 -

Lead ndash 353

Magnesium 252 156

Magnesium Alloy 261 ndash 288 ndash

Monel (67 Ni 30

Cu) 140 ndash

Nickel 130 907

Nylon Polyamide 750 ndash 100 ndash

Platinum ndash 716

Rubber 130 ndash 200 ndash

Silicon ndash 148

Silver ndash 429

Solder Tin-Lead ndash 300 ndash 498

Steel 100 ndash 180 ndash

Tin ndash 666

Titanium ndash 219

Titanium Alloy 800 ndash 100 ndash

Tungsten 430 174

Zinc 302 116

Table 416 Density Melting and Boiling Points of

Solids

Material

Density

[times1000

kgm3]

Melting

Point

[oC]

Boiling

Point

[oC]

Aluminum 271 6603 2519

Aluminum Alloy 264 ndash

28

5650 ndash

6600 ndash

Brass 84 ndash

875 9300 ndash

Brass Noval 84 ndash ndash

Brass Red (80 Cu 20

Zn) 875 1000 ndash

Brick (Compression) 18 ndash

24 ndash- ndash

Bronze Regular 78 ndash

88 1050 ndash

Bronze Manganese 83 ndash ndash

Carbon 225 4492 3642

Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash

24 ndash ndash

Copper 894 1085 2562

Copper Alloy 823 9250 ndash

Cork 015 ndash

02 ndash ndash

Glass 24 ndash

28 ndash ndash

Gold 1932 1064 2856

Iron (Cast) 787 1538 2861

Iron (Wrought) 7 ndash 74 ndash ndash-

Magnesium [Mg] 74 ndash

78 ndash ndash

Magnesium Alloy 113 3275 1749

Monel (67 Ni 30 Cu) 174 6500 1090

Nickel [Ni] 177 1246 2061

Nylon Polyamide 884 1330 ndash

Platinum 889 1455 2913

Rubber 11 - -

Silver 214 1768 3825

Solder Tin-Lead 096 ndash

13 ndash ndash

Steel 233 1382 ndash

Stone Granite

(Compression) 1049 9618 2162

Stone

Limestone (Compression)

817 ndash

1134 2150 ndash

Stone Marble

(Compression) 785 1425 ndash

Tin 26 ndash ndash

Titanium 2 ndash29 ndash ndash

Titanium Alloy 26 ndash

29 ndash ndash

Wood Ash (Bending) 26 ndash ndash

Wood Douglas Fir

(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287

Wood Southern Pine

(Bending) 451 ndash ndash

Zinc 193 3422 5555

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 8

PHYSICAL PROPERTIES

15 Physical Properties of Selected Gases

Table 48 Physical Properties of Selected Gases (10 bar 0 oC)

Material Density

Molar

Mass

Gas

Const

Boiling

Point cp cpcv 106 timesmicro K Pr

kgm3 gmol J(kg K) ordmC J(kg K) - Pa s W(m K) -

Air (dry) 1293 2895 287 -195 1010 14 173 00245 071

Argon [Ar] 1782 3994 2085 -1858 532 165 209 00173 064

Carbon Dioxide

[CO2] 1976 4401 189 - 837 13 137 00137 084

Carbon Monoxide

[CO] 125 2801 297 1047 14 166 00226 077

Helium [He] 0178 4002 2079 -2689 5274 166 188 0144 069

Hydrogen [H2] 00898 2016 4125 -2529 14266 1407 842 0163 074

Nitrogen [N2] 1251 2802 2967 -1958 1047 14 17 00228 078

Oxygen [O2] 1429 32 2599 -1829 913 14 203 0024 077

Normal composition of clean dry atmospheric air near the sea level

Nitrogen (N2) =78084 Oxygen (O2) = 20948 Argon (Ar) = 0934 Carbon Dioxide (CO2) =0031

Neon (Ne) Helium (He) Krypton (Kr) Hydrogen (H2) Xenon (Xe) Methane (CH4) Nitrogen Oxide (N2O) Ozone (O3)

Sulfur Dioxide (NO2) Ammonia (NH3) Carbon Monoxide (CO) and Iodine (I2) =traces of each gas for a total of 0003

Formulae for the calculation of average constant-pressure specific heat ndash cp [kJkg] of various gases in

the range from 0 to 2000 oC are presented in Table 49

Table 49 Average Specific Heat at Constant Pressure of some Gases

Gas

Average Specific Heat at Constant Pressure

])C[t()Kkg(kJ[c ot

op

(Range 0 to 2000 oC)

Maxim

um

Error

Hydrogen (H2) 01+143810E +t 04-200328E +t08-356131E - t10-342031E + t13-108329E- = 234 006

Nitrogen (clean)

(N2) 00103937E t 06-857115E t07-173326E t10-106900E - t14-207571E = 234 009

Oxygen (O2) 01-907389E t 04-144682E t08-150961E t11-443486E - t14-123574E = 234 012

Carbon Monoxide

(CO) 00103823E t 05-124096E t07-176241E t10-120740E - t14-251706E 234 011

Carbon Dioxide

(CO2) 01-820310E t 04-516236E t07-298914E - t10-104359E t14-156925E- = 234 006

Water Vapor (H2O) 00185773E t 04-135306E t07-267351E t10-142139E - t14-235461E= 234 004

Sulfur Dioxide

(SO2) 01-606803E t 04-321094E t07-201319E - t11-653115E t15-804281E- = 234 012

Air 00100361E t 05-218551E t07-142841E t11-968901E - t14-199627E = 234 009

Nitrogen (form Air)

(N2) 00102694E t 05-142726E t07-131381E t11-797576E - t14-148364E = 234 014

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 9

16 Physical Properties of Selected Liquids

Table 410 Physical Properties of Selected Liquids

Liquid t [oC] ρ [kgm3] cp [kJkg

K)]

k [W(m

K)]

micro times 103 [Pa

s]

β times 105

[1K] a [m2s]

Acetone 20

50

791

756

216

225

0170

0163

0331

-

143

-

Gasoline

20

40

60

100

751

735

717

681

206

215

224

246

01165

-

-

01005

0529

0411

0328

0225

125

-

-

-

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol

0

20

50

806

789

-

229

245

281

0185

0183

0178

178

119

0695

Ethylene

Glycol

20

40

60

80

100

1113

1099

1085

1070

1056

2382

2474

2562

2650

2742

0258

-

-

-

0269

1990

913

495

302

199

Glycerin

20

50

100

200

1260

1244

1200

1090

235

250

279

334

-

0283

0289

-

1480

180

13

022

53

-

-

-

Methyl Alcohol

0

20

50

810

792

765

243

247

256

0241

0212

-

0818

0585

0400

Petroleum

20

50

100

200

819

801

766

785

200

214

238

289

-

01114

01042

00891

149

0956

0545

0262

100

-

-

-

Oil (lubricant)

25

50

75

100

920

905

896

880

1850

1943

2041

2136

0130

0128

0125

0123

190

429

156

572

Oil

(transformer)

25

50

75

100

860

845

835

820

1918

2043

2169

2294

0123

0122

0120

0117

2420

990

477

302

17 Thermodynamic and Transport Properties of Water and Steam

a Some of thermodynamic properties of water are

H2O = Chemical formula

M = 18016 [kgkmol] (Molecular Mass)

tc = 37415 [oC] (Critical Temperature)

Tc = 647286 [K] (Absolute Critical Temperature)

pc = 22089 [bar] (Critical Pressure)

c = 3170 [kgm3] (Critical Density)

tm = 001 [oC] (Melting Temperature at 101325 bar)

rm = 332432 [kJkg] (Heat of Melting at 101325 bar)

tb = 1000 [oC] (Boiling Temperature at 101325 bar)

rb = 22570 [kJkg] (Heat of Evaporation at 101325 bar)

R = 462507 [J(kg K)] (Gas Constant)

Enthalpies and entropies of boiling water and saturated steam versus temperature and

pressure (001 lt p lt 20 bar 7 lt t lt 212 oC)

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 10

a Saturated steam and boiling water temperature versus pressure3

112

31-42-

5-36-5

109963430 ln(p)][102794824 ln(p)][2397684

ln(p)][102118802 ln(p)][101786280

ln(p)][101285144 ln(p)][1005-5518190E t

(45)

Error is in the range 007

b Saturated steam and boiling water pressure versus temperature

5098158] -t 107261845 t102974345 - t101096061

t103381446 - t107363934 t10316exp[-7789p

2-24-36-

4-95-126-15

(46)

Error is in the range of 005

c Enthalpy of boiling water versus temperature

1-

2-53-74-9

10359463 t 417927

t10723854 - t10706612 t10833022h (47)

d Enthalpy of saturated steam versus temperature

250044 t 187334

t10103177 - t10151237 t10332313 - h 2-33-64-8

(48)

e Entropy of boiling water versus pressure

130250 ln(p)10315672

(ln(p))10167802 (ln(p))10145398 (ln(p))10973390s

2-

2-33-44-5

(49)

f Entropy of saturated steam versus pressure

736130 ln(p)10336497 - (ln(p)10760363 (ln(p)10-538843s -12-43-4 (41

0)

Water properties (temperatures from 0 to 300 oC)

(From 0 to 100 oC at 1013 bar and for higher temperatures for boiling pressure)

g Density [kgm3]

22-23-

3-54-75-106-13

10999945 t 10410381 t10726539 -

t10428877 t10208168 - t10556465 t10-644703

(411

)

3 ln - natural logarithm

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 11

h Specific heat at constant pressure cp [J(kg K)]

30-21-

3-34-65-86-11p

10421629 t 10370637 - t10109452

t10142353 -t10976851 t10317259 - t10400424c

(412

)

i Thermal conductivity [W(m K)]

11-23-

3-64-95-116-112

10549688 t 10285413 t10210253 -

t10672554 t10740918 - t10187737 - t1036594410

(413

)

j Thermal diffusivity a [m2s]

pca (414)

k Dynamic viscosity [Pa s]

748230 t 10322128 - t10218237

t10103401 - t10272328 t1077Exp(-291810

2-22-

3-64-95-126

(415)

l Kinematic viscosity [m2s]

(416)

m Coefficient of volume expansion [1K]

1-1-23-35-

4-85-106-134

10684475 -t 10163711 t10182013 -t10158931

t10746034 - t10170218 t10-12877310

(417

)

Some important properties for heat transfer calculations are presented in Table 48 It is obvious

that they depend on temperature much more than on pressure Because of that for almost all industrial

calculations the influence of pressure can be ignored

Table 411 Water Density Specific Heat Thermal Conductivity and Dynamic Viscosity versus

Temperature and Pressure

]mkg[ 3 )]Kkg(J[cp )]Km(W[ ]sPa[106

]bar[p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o

0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 1295

20 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 1001

30 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 803

40 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 657

50 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 554

60 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 475

70 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 12

80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 360

90 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287

150 9221 9273 4275 4237 0693 0699 188 190

200 8707 8776 4455 4396 0672 0679 138 140

250 8059 8161 4781 4681 0624 0636 112 115

300 7154 7346 5661 5275 0542 0558 91 94

350 6006 8206 0452 75

360 547 12560 0412 69

Saturated steam properties (0 lt t lt 210 oC or 0006 bar lt p lt 1908 bar)

n Density of saturated steam

00203297 + p0554983 +p000557908 - p8000014411= 23 (418)

o Specific heat at constant pressure of saturated steam

186459 +t 0784614 + t000461955 + t93000009956 =c 23p (419)

p Thermal conductivity of saturated steam

0404835 -t 00474611 +t8000026173 - t3939000000064=10 232 (420)

q Dynamic viscosity of saturated steam

81587 +t 00375325 + t281000000762=10 26 (421)

Superheated steam properties (250 lt t lt 550 oC or 1961 bar lt p lt 5884 bar)

Table 412 Superheated Steam

]mkg[ 3 )]Kkg(J[cp )]Km(W[102

]sPa[10 6

p[bar] 1961 3923 5884 1961 3923 5884 1961 3923 5884 1961 3923 5884

t [oC]

220 9588 2935 373 168

230 9285 2784 383 174

240 9025 2633 393 177

250 8787 1962 2554 3647 403 453 181 183

280 2937 4438 532 198

290 2808 4028 505 202

300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205

350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225

400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246

450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268

500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289

550 1606 2353 784 312

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 13

18 Physical Properties of Selected Solid Materials

Table 413 Properties of Selected Solids at 25 oC

Substance

kgm3 pc

[kJ(kg K)]

Asphalt 2120 167

Brick (common) 1800 084

Carbon (diamond) 3250 051

Carbon (graphite) 2000ndash2500 061

Coal 1200ndash1500 126

Concrete 2200 088

Glass (plate) 2500 080

Glass (wool) 200 066

Granite 2750 089

Ice (0 oC) 917 204

Paper 700 120

Plexiglas 1180 144

Polystyrene 920 230

Polyvinyl chloride 1380 096

Rubber (soft) 1100 167

Salt (rock) 2100ndash2500 092

Sand (dry) 1500 080

Silicon 2330 070

Snow (firm) 560 210

Wood (hard oak) 720 126

Wood (soft pine) 510 138

Wool 100 172

Table 414 Properties of Selected Metals at 25 oC

Metals

kgm3

pc

[kJ(kg

K)] Aluminum 2700 090

Copper (commercial) 8300 042

Brass (60-40) 8400 038

Gold 19300 013

Iron (cast) 7272 042

Iron (Steel 304 St) 7820 046

Lead 11340 013

Magnesium (2 Mn) 1778 100

Nickel (10 Cr) 8666 044

Silver (999 Ag) 10524 024

Sodium 971 121

Tin 7304 022

Tungsten 19300 013

Zinc 7144 039

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 14

Table 415 Thermal Expansion Coefficients and

Thermal Conductivity of Solids

Material

Thermal

Expansion

Coefficient

(times10-6ordmC)

Thermal

Conductivity

(WmmiddotK)

Aluminum 230 237

Aluminum Alloy 230 ndash

Brass 191 ndash 212 ndash

Brass Noval 211 ndash

Brass Red (80 Cu

20 Zn) 191 ndash

Brick 500 ndash 700 ndash

Bronze Regular 180 ndash 210 ndash

Bronze Manganese 200 ndash

Concrete 700 ndash 140 ndash

Copper 166 ndash 176 410

Copper Alloy 170 ndash

Glass 500 ndash 110 ndash

Gold ndash 317

Iron ndash 802

Iron (Cast) 990 ndash 120 ndash

Iron (Wrought) 120 -

Lead ndash 353

Magnesium 252 156

Magnesium Alloy 261 ndash 288 ndash

Monel (67 Ni 30

Cu) 140 ndash

Nickel 130 907

Nylon Polyamide 750 ndash 100 ndash

Platinum ndash 716

Rubber 130 ndash 200 ndash

Silicon ndash 148

Silver ndash 429

Solder Tin-Lead ndash 300 ndash 498

Steel 100 ndash 180 ndash

Tin ndash 666

Titanium ndash 219

Titanium Alloy 800 ndash 100 ndash

Tungsten 430 174

Zinc 302 116

Table 416 Density Melting and Boiling Points of

Solids

Material

Density

[times1000

kgm3]

Melting

Point

[oC]

Boiling

Point

[oC]

Aluminum 271 6603 2519

Aluminum Alloy 264 ndash

28

5650 ndash

6600 ndash

Brass 84 ndash

875 9300 ndash

Brass Noval 84 ndash ndash

Brass Red (80 Cu 20

Zn) 875 1000 ndash

Brick (Compression) 18 ndash

24 ndash- ndash

Bronze Regular 78 ndash

88 1050 ndash

Bronze Manganese 83 ndash ndash

Carbon 225 4492 3642

Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash

24 ndash ndash

Copper 894 1085 2562

Copper Alloy 823 9250 ndash

Cork 015 ndash

02 ndash ndash

Glass 24 ndash

28 ndash ndash

Gold 1932 1064 2856

Iron (Cast) 787 1538 2861

Iron (Wrought) 7 ndash 74 ndash ndash-

Magnesium [Mg] 74 ndash

78 ndash ndash

Magnesium Alloy 113 3275 1749

Monel (67 Ni 30 Cu) 174 6500 1090

Nickel [Ni] 177 1246 2061

Nylon Polyamide 884 1330 ndash

Platinum 889 1455 2913

Rubber 11 - -

Silver 214 1768 3825

Solder Tin-Lead 096 ndash

13 ndash ndash

Steel 233 1382 ndash

Stone Granite

(Compression) 1049 9618 2162

Stone

Limestone (Compression)

817 ndash

1134 2150 ndash

Stone Marble

(Compression) 785 1425 ndash

Tin 26 ndash ndash

Titanium 2 ndash29 ndash ndash

Titanium Alloy 26 ndash

29 ndash ndash

Wood Ash (Bending) 26 ndash ndash

Wood Douglas Fir

(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287

Wood Southern Pine

(Bending) 451 ndash ndash

Zinc 193 3422 5555

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 9

16 Physical Properties of Selected Liquids

Table 410 Physical Properties of Selected Liquids

Liquid t [oC] ρ [kgm3] cp [kJkg

K)]

k [W(m

K)]

micro times 103 [Pa

s]

β times 105

[1K] a [m2s]

Acetone 20

50

791

756

216

225

0170

0163

0331

-

143

-

Gasoline

20

40

60

100

751

735

717

681

206

215

224

246

01165

-

-

01005

0529

0411

0328

0225

125

-

-

-

Benzene 20 879 1738 0154 065 124

Ethyl Alcohol

0

20

50

806

789

-

229

245

281

0185

0183

0178

178

119

0695

Ethylene

Glycol

20

40

60

80

100

1113

1099

1085

1070

1056

2382

2474

2562

2650

2742

0258

-

-

-

0269

1990

913

495

302

199

Glycerin

20

50

100

200

1260

1244

1200

1090

235

250

279

334

-

0283

0289

-

1480

180

13

022

53

-

-

-

Methyl Alcohol

0

20

50

810

792

765

243

247

256

0241

0212

-

0818

0585

0400

Petroleum

20

50

100

200

819

801

766

785

200

214

238

289

-

01114

01042

00891

149

0956

0545

0262

100

-

-

-

Oil (lubricant)

25

50

75

100

920

905

896

880

1850

1943

2041

2136

0130

0128

0125

0123

190

429

156

572

Oil

(transformer)

25

50

75

100

860

845

835

820

1918

2043

2169

2294

0123

0122

0120

0117

2420

990

477

302

17 Thermodynamic and Transport Properties of Water and Steam

a Some of thermodynamic properties of water are

H2O = Chemical formula

M = 18016 [kgkmol] (Molecular Mass)

tc = 37415 [oC] (Critical Temperature)

Tc = 647286 [K] (Absolute Critical Temperature)

pc = 22089 [bar] (Critical Pressure)

c = 3170 [kgm3] (Critical Density)

tm = 001 [oC] (Melting Temperature at 101325 bar)

rm = 332432 [kJkg] (Heat of Melting at 101325 bar)

tb = 1000 [oC] (Boiling Temperature at 101325 bar)

rb = 22570 [kJkg] (Heat of Evaporation at 101325 bar)

R = 462507 [J(kg K)] (Gas Constant)

Enthalpies and entropies of boiling water and saturated steam versus temperature and

pressure (001 lt p lt 20 bar 7 lt t lt 212 oC)

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 10

a Saturated steam and boiling water temperature versus pressure3

112

31-42-

5-36-5

109963430 ln(p)][102794824 ln(p)][2397684

ln(p)][102118802 ln(p)][101786280

ln(p)][101285144 ln(p)][1005-5518190E t

(45)

Error is in the range 007

b Saturated steam and boiling water pressure versus temperature

5098158] -t 107261845 t102974345 - t101096061

t103381446 - t107363934 t10316exp[-7789p

2-24-36-

4-95-126-15

(46)

Error is in the range of 005

c Enthalpy of boiling water versus temperature

1-

2-53-74-9

10359463 t 417927

t10723854 - t10706612 t10833022h (47)

d Enthalpy of saturated steam versus temperature

250044 t 187334

t10103177 - t10151237 t10332313 - h 2-33-64-8

(48)

e Entropy of boiling water versus pressure

130250 ln(p)10315672

(ln(p))10167802 (ln(p))10145398 (ln(p))10973390s

2-

2-33-44-5

(49)

f Entropy of saturated steam versus pressure

736130 ln(p)10336497 - (ln(p)10760363 (ln(p)10-538843s -12-43-4 (41

0)

Water properties (temperatures from 0 to 300 oC)

(From 0 to 100 oC at 1013 bar and for higher temperatures for boiling pressure)

g Density [kgm3]

22-23-

3-54-75-106-13

10999945 t 10410381 t10726539 -

t10428877 t10208168 - t10556465 t10-644703

(411

)

3 ln - natural logarithm

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 11

h Specific heat at constant pressure cp [J(kg K)]

30-21-

3-34-65-86-11p

10421629 t 10370637 - t10109452

t10142353 -t10976851 t10317259 - t10400424c

(412

)

i Thermal conductivity [W(m K)]

11-23-

3-64-95-116-112

10549688 t 10285413 t10210253 -

t10672554 t10740918 - t10187737 - t1036594410

(413

)

j Thermal diffusivity a [m2s]

pca (414)

k Dynamic viscosity [Pa s]

748230 t 10322128 - t10218237

t10103401 - t10272328 t1077Exp(-291810

2-22-

3-64-95-126

(415)

l Kinematic viscosity [m2s]

(416)

m Coefficient of volume expansion [1K]

1-1-23-35-

4-85-106-134

10684475 -t 10163711 t10182013 -t10158931

t10746034 - t10170218 t10-12877310

(417

)

Some important properties for heat transfer calculations are presented in Table 48 It is obvious

that they depend on temperature much more than on pressure Because of that for almost all industrial

calculations the influence of pressure can be ignored

Table 411 Water Density Specific Heat Thermal Conductivity and Dynamic Viscosity versus

Temperature and Pressure

]mkg[ 3 )]Kkg(J[cp )]Km(W[ ]sPa[106

]bar[p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o

0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 1295

20 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 1001

30 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 803

40 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 657

50 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 554

60 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 475

70 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 12

80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 360

90 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287

150 9221 9273 4275 4237 0693 0699 188 190

200 8707 8776 4455 4396 0672 0679 138 140

250 8059 8161 4781 4681 0624 0636 112 115

300 7154 7346 5661 5275 0542 0558 91 94

350 6006 8206 0452 75

360 547 12560 0412 69

Saturated steam properties (0 lt t lt 210 oC or 0006 bar lt p lt 1908 bar)

n Density of saturated steam

00203297 + p0554983 +p000557908 - p8000014411= 23 (418)

o Specific heat at constant pressure of saturated steam

186459 +t 0784614 + t000461955 + t93000009956 =c 23p (419)

p Thermal conductivity of saturated steam

0404835 -t 00474611 +t8000026173 - t3939000000064=10 232 (420)

q Dynamic viscosity of saturated steam

81587 +t 00375325 + t281000000762=10 26 (421)

Superheated steam properties (250 lt t lt 550 oC or 1961 bar lt p lt 5884 bar)

Table 412 Superheated Steam

]mkg[ 3 )]Kkg(J[cp )]Km(W[102

]sPa[10 6

p[bar] 1961 3923 5884 1961 3923 5884 1961 3923 5884 1961 3923 5884

t [oC]

220 9588 2935 373 168

230 9285 2784 383 174

240 9025 2633 393 177

250 8787 1962 2554 3647 403 453 181 183

280 2937 4438 532 198

290 2808 4028 505 202

300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205

350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225

400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246

450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268

500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289

550 1606 2353 784 312

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 13

18 Physical Properties of Selected Solid Materials

Table 413 Properties of Selected Solids at 25 oC

Substance

kgm3 pc

[kJ(kg K)]

Asphalt 2120 167

Brick (common) 1800 084

Carbon (diamond) 3250 051

Carbon (graphite) 2000ndash2500 061

Coal 1200ndash1500 126

Concrete 2200 088

Glass (plate) 2500 080

Glass (wool) 200 066

Granite 2750 089

Ice (0 oC) 917 204

Paper 700 120

Plexiglas 1180 144

Polystyrene 920 230

Polyvinyl chloride 1380 096

Rubber (soft) 1100 167

Salt (rock) 2100ndash2500 092

Sand (dry) 1500 080

Silicon 2330 070

Snow (firm) 560 210

Wood (hard oak) 720 126

Wood (soft pine) 510 138

Wool 100 172

Table 414 Properties of Selected Metals at 25 oC

Metals

kgm3

pc

[kJ(kg

K)] Aluminum 2700 090

Copper (commercial) 8300 042

Brass (60-40) 8400 038

Gold 19300 013

Iron (cast) 7272 042

Iron (Steel 304 St) 7820 046

Lead 11340 013

Magnesium (2 Mn) 1778 100

Nickel (10 Cr) 8666 044

Silver (999 Ag) 10524 024

Sodium 971 121

Tin 7304 022

Tungsten 19300 013

Zinc 7144 039

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 14

Table 415 Thermal Expansion Coefficients and

Thermal Conductivity of Solids

Material

Thermal

Expansion

Coefficient

(times10-6ordmC)

Thermal

Conductivity

(WmmiddotK)

Aluminum 230 237

Aluminum Alloy 230 ndash

Brass 191 ndash 212 ndash

Brass Noval 211 ndash

Brass Red (80 Cu

20 Zn) 191 ndash

Brick 500 ndash 700 ndash

Bronze Regular 180 ndash 210 ndash

Bronze Manganese 200 ndash

Concrete 700 ndash 140 ndash

Copper 166 ndash 176 410

Copper Alloy 170 ndash

Glass 500 ndash 110 ndash

Gold ndash 317

Iron ndash 802

Iron (Cast) 990 ndash 120 ndash

Iron (Wrought) 120 -

Lead ndash 353

Magnesium 252 156

Magnesium Alloy 261 ndash 288 ndash

Monel (67 Ni 30

Cu) 140 ndash

Nickel 130 907

Nylon Polyamide 750 ndash 100 ndash

Platinum ndash 716

Rubber 130 ndash 200 ndash

Silicon ndash 148

Silver ndash 429

Solder Tin-Lead ndash 300 ndash 498

Steel 100 ndash 180 ndash

Tin ndash 666

Titanium ndash 219

Titanium Alloy 800 ndash 100 ndash

Tungsten 430 174

Zinc 302 116

Table 416 Density Melting and Boiling Points of

Solids

Material

Density

[times1000

kgm3]

Melting

Point

[oC]

Boiling

Point

[oC]

Aluminum 271 6603 2519

Aluminum Alloy 264 ndash

28

5650 ndash

6600 ndash

Brass 84 ndash

875 9300 ndash

Brass Noval 84 ndash ndash

Brass Red (80 Cu 20

Zn) 875 1000 ndash

Brick (Compression) 18 ndash

24 ndash- ndash

Bronze Regular 78 ndash

88 1050 ndash

Bronze Manganese 83 ndash ndash

Carbon 225 4492 3642

Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash

24 ndash ndash

Copper 894 1085 2562

Copper Alloy 823 9250 ndash

Cork 015 ndash

02 ndash ndash

Glass 24 ndash

28 ndash ndash

Gold 1932 1064 2856

Iron (Cast) 787 1538 2861

Iron (Wrought) 7 ndash 74 ndash ndash-

Magnesium [Mg] 74 ndash

78 ndash ndash

Magnesium Alloy 113 3275 1749

Monel (67 Ni 30 Cu) 174 6500 1090

Nickel [Ni] 177 1246 2061

Nylon Polyamide 884 1330 ndash

Platinum 889 1455 2913

Rubber 11 - -

Silver 214 1768 3825

Solder Tin-Lead 096 ndash

13 ndash ndash

Steel 233 1382 ndash

Stone Granite

(Compression) 1049 9618 2162

Stone

Limestone (Compression)

817 ndash

1134 2150 ndash

Stone Marble

(Compression) 785 1425 ndash

Tin 26 ndash ndash

Titanium 2 ndash29 ndash ndash

Titanium Alloy 26 ndash

29 ndash ndash

Wood Ash (Bending) 26 ndash ndash

Wood Douglas Fir

(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287

Wood Southern Pine

(Bending) 451 ndash ndash

Zinc 193 3422 5555

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 10

a Saturated steam and boiling water temperature versus pressure3

112

31-42-

5-36-5

109963430 ln(p)][102794824 ln(p)][2397684

ln(p)][102118802 ln(p)][101786280

ln(p)][101285144 ln(p)][1005-5518190E t

(45)

Error is in the range 007

b Saturated steam and boiling water pressure versus temperature

5098158] -t 107261845 t102974345 - t101096061

t103381446 - t107363934 t10316exp[-7789p

2-24-36-

4-95-126-15

(46)

Error is in the range of 005

c Enthalpy of boiling water versus temperature

1-

2-53-74-9

10359463 t 417927

t10723854 - t10706612 t10833022h (47)

d Enthalpy of saturated steam versus temperature

250044 t 187334

t10103177 - t10151237 t10332313 - h 2-33-64-8

(48)

e Entropy of boiling water versus pressure

130250 ln(p)10315672

(ln(p))10167802 (ln(p))10145398 (ln(p))10973390s

2-

2-33-44-5

(49)

f Entropy of saturated steam versus pressure

736130 ln(p)10336497 - (ln(p)10760363 (ln(p)10-538843s -12-43-4 (41

0)

Water properties (temperatures from 0 to 300 oC)

(From 0 to 100 oC at 1013 bar and for higher temperatures for boiling pressure)

g Density [kgm3]

22-23-

3-54-75-106-13

10999945 t 10410381 t10726539 -

t10428877 t10208168 - t10556465 t10-644703

(411

)

3 ln - natural logarithm

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 11

h Specific heat at constant pressure cp [J(kg K)]

30-21-

3-34-65-86-11p

10421629 t 10370637 - t10109452

t10142353 -t10976851 t10317259 - t10400424c

(412

)

i Thermal conductivity [W(m K)]

11-23-

3-64-95-116-112

10549688 t 10285413 t10210253 -

t10672554 t10740918 - t10187737 - t1036594410

(413

)

j Thermal diffusivity a [m2s]

pca (414)

k Dynamic viscosity [Pa s]

748230 t 10322128 - t10218237

t10103401 - t10272328 t1077Exp(-291810

2-22-

3-64-95-126

(415)

l Kinematic viscosity [m2s]

(416)

m Coefficient of volume expansion [1K]

1-1-23-35-

4-85-106-134

10684475 -t 10163711 t10182013 -t10158931

t10746034 - t10170218 t10-12877310

(417

)

Some important properties for heat transfer calculations are presented in Table 48 It is obvious

that they depend on temperature much more than on pressure Because of that for almost all industrial

calculations the influence of pressure can be ignored

Table 411 Water Density Specific Heat Thermal Conductivity and Dynamic Viscosity versus

Temperature and Pressure

]mkg[ 3 )]Kkg(J[cp )]Km(W[ ]sPa[106

]bar[p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o

0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 1295

20 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 1001

30 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 803

40 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 657

50 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 554

60 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 475

70 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 12

80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 360

90 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287

150 9221 9273 4275 4237 0693 0699 188 190

200 8707 8776 4455 4396 0672 0679 138 140

250 8059 8161 4781 4681 0624 0636 112 115

300 7154 7346 5661 5275 0542 0558 91 94

350 6006 8206 0452 75

360 547 12560 0412 69

Saturated steam properties (0 lt t lt 210 oC or 0006 bar lt p lt 1908 bar)

n Density of saturated steam

00203297 + p0554983 +p000557908 - p8000014411= 23 (418)

o Specific heat at constant pressure of saturated steam

186459 +t 0784614 + t000461955 + t93000009956 =c 23p (419)

p Thermal conductivity of saturated steam

0404835 -t 00474611 +t8000026173 - t3939000000064=10 232 (420)

q Dynamic viscosity of saturated steam

81587 +t 00375325 + t281000000762=10 26 (421)

Superheated steam properties (250 lt t lt 550 oC or 1961 bar lt p lt 5884 bar)

Table 412 Superheated Steam

]mkg[ 3 )]Kkg(J[cp )]Km(W[102

]sPa[10 6

p[bar] 1961 3923 5884 1961 3923 5884 1961 3923 5884 1961 3923 5884

t [oC]

220 9588 2935 373 168

230 9285 2784 383 174

240 9025 2633 393 177

250 8787 1962 2554 3647 403 453 181 183

280 2937 4438 532 198

290 2808 4028 505 202

300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205

350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225

400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246

450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268

500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289

550 1606 2353 784 312

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 13

18 Physical Properties of Selected Solid Materials

Table 413 Properties of Selected Solids at 25 oC

Substance

kgm3 pc

[kJ(kg K)]

Asphalt 2120 167

Brick (common) 1800 084

Carbon (diamond) 3250 051

Carbon (graphite) 2000ndash2500 061

Coal 1200ndash1500 126

Concrete 2200 088

Glass (plate) 2500 080

Glass (wool) 200 066

Granite 2750 089

Ice (0 oC) 917 204

Paper 700 120

Plexiglas 1180 144

Polystyrene 920 230

Polyvinyl chloride 1380 096

Rubber (soft) 1100 167

Salt (rock) 2100ndash2500 092

Sand (dry) 1500 080

Silicon 2330 070

Snow (firm) 560 210

Wood (hard oak) 720 126

Wood (soft pine) 510 138

Wool 100 172

Table 414 Properties of Selected Metals at 25 oC

Metals

kgm3

pc

[kJ(kg

K)] Aluminum 2700 090

Copper (commercial) 8300 042

Brass (60-40) 8400 038

Gold 19300 013

Iron (cast) 7272 042

Iron (Steel 304 St) 7820 046

Lead 11340 013

Magnesium (2 Mn) 1778 100

Nickel (10 Cr) 8666 044

Silver (999 Ag) 10524 024

Sodium 971 121

Tin 7304 022

Tungsten 19300 013

Zinc 7144 039

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 14

Table 415 Thermal Expansion Coefficients and

Thermal Conductivity of Solids

Material

Thermal

Expansion

Coefficient

(times10-6ordmC)

Thermal

Conductivity

(WmmiddotK)

Aluminum 230 237

Aluminum Alloy 230 ndash

Brass 191 ndash 212 ndash

Brass Noval 211 ndash

Brass Red (80 Cu

20 Zn) 191 ndash

Brick 500 ndash 700 ndash

Bronze Regular 180 ndash 210 ndash

Bronze Manganese 200 ndash

Concrete 700 ndash 140 ndash

Copper 166 ndash 176 410

Copper Alloy 170 ndash

Glass 500 ndash 110 ndash

Gold ndash 317

Iron ndash 802

Iron (Cast) 990 ndash 120 ndash

Iron (Wrought) 120 -

Lead ndash 353

Magnesium 252 156

Magnesium Alloy 261 ndash 288 ndash

Monel (67 Ni 30

Cu) 140 ndash

Nickel 130 907

Nylon Polyamide 750 ndash 100 ndash

Platinum ndash 716

Rubber 130 ndash 200 ndash

Silicon ndash 148

Silver ndash 429

Solder Tin-Lead ndash 300 ndash 498

Steel 100 ndash 180 ndash

Tin ndash 666

Titanium ndash 219

Titanium Alloy 800 ndash 100 ndash

Tungsten 430 174

Zinc 302 116

Table 416 Density Melting and Boiling Points of

Solids

Material

Density

[times1000

kgm3]

Melting

Point

[oC]

Boiling

Point

[oC]

Aluminum 271 6603 2519

Aluminum Alloy 264 ndash

28

5650 ndash

6600 ndash

Brass 84 ndash

875 9300 ndash

Brass Noval 84 ndash ndash

Brass Red (80 Cu 20

Zn) 875 1000 ndash

Brick (Compression) 18 ndash

24 ndash- ndash

Bronze Regular 78 ndash

88 1050 ndash

Bronze Manganese 83 ndash ndash

Carbon 225 4492 3642

Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash

24 ndash ndash

Copper 894 1085 2562

Copper Alloy 823 9250 ndash

Cork 015 ndash

02 ndash ndash

Glass 24 ndash

28 ndash ndash

Gold 1932 1064 2856

Iron (Cast) 787 1538 2861

Iron (Wrought) 7 ndash 74 ndash ndash-

Magnesium [Mg] 74 ndash

78 ndash ndash

Magnesium Alloy 113 3275 1749

Monel (67 Ni 30 Cu) 174 6500 1090

Nickel [Ni] 177 1246 2061

Nylon Polyamide 884 1330 ndash

Platinum 889 1455 2913

Rubber 11 - -

Silver 214 1768 3825

Solder Tin-Lead 096 ndash

13 ndash ndash

Steel 233 1382 ndash

Stone Granite

(Compression) 1049 9618 2162

Stone

Limestone (Compression)

817 ndash

1134 2150 ndash

Stone Marble

(Compression) 785 1425 ndash

Tin 26 ndash ndash

Titanium 2 ndash29 ndash ndash

Titanium Alloy 26 ndash

29 ndash ndash

Wood Ash (Bending) 26 ndash ndash

Wood Douglas Fir

(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287

Wood Southern Pine

(Bending) 451 ndash ndash

Zinc 193 3422 5555

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 11

h Specific heat at constant pressure cp [J(kg K)]

30-21-

3-34-65-86-11p

10421629 t 10370637 - t10109452

t10142353 -t10976851 t10317259 - t10400424c

(412

)

i Thermal conductivity [W(m K)]

11-23-

3-64-95-116-112

10549688 t 10285413 t10210253 -

t10672554 t10740918 - t10187737 - t1036594410

(413

)

j Thermal diffusivity a [m2s]

pca (414)

k Dynamic viscosity [Pa s]

748230 t 10322128 - t10218237

t10103401 - t10272328 t1077Exp(-291810

2-22-

3-64-95-126

(415)

l Kinematic viscosity [m2s]

(416)

m Coefficient of volume expansion [1K]

1-1-23-35-

4-85-106-134

10684475 -t 10163711 t10182013 -t10158931

t10746034 - t10170218 t10-12877310

(417

)

Some important properties for heat transfer calculations are presented in Table 48 It is obvious

that they depend on temperature much more than on pressure Because of that for almost all industrial

calculations the influence of pressure can be ignored

Table 411 Water Density Specific Heat Thermal Conductivity and Dynamic Viscosity versus

Temperature and Pressure

]mkg[ 3 )]Kkg(J[cp )]Km(W[ ]sPa[106

]bar[p 0981 9807 1961 0981 9807 1961 0981 9807 1961 0981 9807 1961

]C[t o

0 9998 10048 10096 4216 4195 4178 0551 0555 0558 1785 1776 1756

10 9997 10042 10087 4191 4178 4158 0576 0579 0584 1305 1295 1295

20 9982 10025 10067 4183 4162 4141 0599 0604 0608 1001 1001 1001

30 9956 9999 1004 4174 4158 4132 0618 0622 0628 802 803 803

40 9922 9964 10005 4174 4153 4128 0634 0638 0644 653 655 657

50 9880 9924 9964 4174 4153 4128 0648 0652 0657 549 551 554

60 9833 9876 9918 4178 4153 4128 0659 0664 0669 470 472 475

70 9778 9822 9865 4178 4158 4132 0668 0672 0678 406 408 411

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 12

80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 360

90 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287

150 9221 9273 4275 4237 0693 0699 188 190

200 8707 8776 4455 4396 0672 0679 138 140

250 8059 8161 4781 4681 0624 0636 112 115

300 7154 7346 5661 5275 0542 0558 91 94

350 6006 8206 0452 75

360 547 12560 0412 69

Saturated steam properties (0 lt t lt 210 oC or 0006 bar lt p lt 1908 bar)

n Density of saturated steam

00203297 + p0554983 +p000557908 - p8000014411= 23 (418)

o Specific heat at constant pressure of saturated steam

186459 +t 0784614 + t000461955 + t93000009956 =c 23p (419)

p Thermal conductivity of saturated steam

0404835 -t 00474611 +t8000026173 - t3939000000064=10 232 (420)

q Dynamic viscosity of saturated steam

81587 +t 00375325 + t281000000762=10 26 (421)

Superheated steam properties (250 lt t lt 550 oC or 1961 bar lt p lt 5884 bar)

Table 412 Superheated Steam

]mkg[ 3 )]Kkg(J[cp )]Km(W[102

]sPa[10 6

p[bar] 1961 3923 5884 1961 3923 5884 1961 3923 5884 1961 3923 5884

t [oC]

220 9588 2935 373 168

230 9285 2784 383 174

240 9025 2633 393 177

250 8787 1962 2554 3647 403 453 181 183

280 2937 4438 532 198

290 2808 4028 505 202

300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205

350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225

400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246

450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268

500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289

550 1606 2353 784 312

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 13

18 Physical Properties of Selected Solid Materials

Table 413 Properties of Selected Solids at 25 oC

Substance

kgm3 pc

[kJ(kg K)]

Asphalt 2120 167

Brick (common) 1800 084

Carbon (diamond) 3250 051

Carbon (graphite) 2000ndash2500 061

Coal 1200ndash1500 126

Concrete 2200 088

Glass (plate) 2500 080

Glass (wool) 200 066

Granite 2750 089

Ice (0 oC) 917 204

Paper 700 120

Plexiglas 1180 144

Polystyrene 920 230

Polyvinyl chloride 1380 096

Rubber (soft) 1100 167

Salt (rock) 2100ndash2500 092

Sand (dry) 1500 080

Silicon 2330 070

Snow (firm) 560 210

Wood (hard oak) 720 126

Wood (soft pine) 510 138

Wool 100 172

Table 414 Properties of Selected Metals at 25 oC

Metals

kgm3

pc

[kJ(kg

K)] Aluminum 2700 090

Copper (commercial) 8300 042

Brass (60-40) 8400 038

Gold 19300 013

Iron (cast) 7272 042

Iron (Steel 304 St) 7820 046

Lead 11340 013

Magnesium (2 Mn) 1778 100

Nickel (10 Cr) 8666 044

Silver (999 Ag) 10524 024

Sodium 971 121

Tin 7304 022

Tungsten 19300 013

Zinc 7144 039

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 14

Table 415 Thermal Expansion Coefficients and

Thermal Conductivity of Solids

Material

Thermal

Expansion

Coefficient

(times10-6ordmC)

Thermal

Conductivity

(WmmiddotK)

Aluminum 230 237

Aluminum Alloy 230 ndash

Brass 191 ndash 212 ndash

Brass Noval 211 ndash

Brass Red (80 Cu

20 Zn) 191 ndash

Brick 500 ndash 700 ndash

Bronze Regular 180 ndash 210 ndash

Bronze Manganese 200 ndash

Concrete 700 ndash 140 ndash

Copper 166 ndash 176 410

Copper Alloy 170 ndash

Glass 500 ndash 110 ndash

Gold ndash 317

Iron ndash 802

Iron (Cast) 990 ndash 120 ndash

Iron (Wrought) 120 -

Lead ndash 353

Magnesium 252 156

Magnesium Alloy 261 ndash 288 ndash

Monel (67 Ni 30

Cu) 140 ndash

Nickel 130 907

Nylon Polyamide 750 ndash 100 ndash

Platinum ndash 716

Rubber 130 ndash 200 ndash

Silicon ndash 148

Silver ndash 429

Solder Tin-Lead ndash 300 ndash 498

Steel 100 ndash 180 ndash

Tin ndash 666

Titanium ndash 219

Titanium Alloy 800 ndash 100 ndash

Tungsten 430 174

Zinc 302 116

Table 416 Density Melting and Boiling Points of

Solids

Material

Density

[times1000

kgm3]

Melting

Point

[oC]

Boiling

Point

[oC]

Aluminum 271 6603 2519

Aluminum Alloy 264 ndash

28

5650 ndash

6600 ndash

Brass 84 ndash

875 9300 ndash

Brass Noval 84 ndash ndash

Brass Red (80 Cu 20

Zn) 875 1000 ndash

Brick (Compression) 18 ndash

24 ndash- ndash

Bronze Regular 78 ndash

88 1050 ndash

Bronze Manganese 83 ndash ndash

Carbon 225 4492 3642

Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash

24 ndash ndash

Copper 894 1085 2562

Copper Alloy 823 9250 ndash

Cork 015 ndash

02 ndash ndash

Glass 24 ndash

28 ndash ndash

Gold 1932 1064 2856

Iron (Cast) 787 1538 2861

Iron (Wrought) 7 ndash 74 ndash ndash-

Magnesium [Mg] 74 ndash

78 ndash ndash

Magnesium Alloy 113 3275 1749

Monel (67 Ni 30 Cu) 174 6500 1090

Nickel [Ni] 177 1246 2061

Nylon Polyamide 884 1330 ndash

Platinum 889 1455 2913

Rubber 11 - -

Silver 214 1768 3825

Solder Tin-Lead 096 ndash

13 ndash ndash

Steel 233 1382 ndash

Stone Granite

(Compression) 1049 9618 2162

Stone

Limestone (Compression)

817 ndash

1134 2150 ndash

Stone Marble

(Compression) 785 1425 ndash

Tin 26 ndash ndash

Titanium 2 ndash29 ndash ndash

Titanium Alloy 26 ndash

29 ndash ndash

Wood Ash (Bending) 26 ndash ndash

Wood Douglas Fir

(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287

Wood Southern Pine

(Bending) 451 ndash ndash

Zinc 193 3422 5555

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 12

80 9718 9763 9806 4195 4166 4141 0674 0679 0685 355 357 360

90 9653 9698 9742 4208 4174 4149 068 0685 0691 315 317 320

100 963 9674 4187 4158 069 0695 285 287

150 9221 9273 4275 4237 0693 0699 188 190

200 8707 8776 4455 4396 0672 0679 138 140

250 8059 8161 4781 4681 0624 0636 112 115

300 7154 7346 5661 5275 0542 0558 91 94

350 6006 8206 0452 75

360 547 12560 0412 69

Saturated steam properties (0 lt t lt 210 oC or 0006 bar lt p lt 1908 bar)

n Density of saturated steam

00203297 + p0554983 +p000557908 - p8000014411= 23 (418)

o Specific heat at constant pressure of saturated steam

186459 +t 0784614 + t000461955 + t93000009956 =c 23p (419)

p Thermal conductivity of saturated steam

0404835 -t 00474611 +t8000026173 - t3939000000064=10 232 (420)

q Dynamic viscosity of saturated steam

81587 +t 00375325 + t281000000762=10 26 (421)

Superheated steam properties (250 lt t lt 550 oC or 1961 bar lt p lt 5884 bar)

Table 412 Superheated Steam

]mkg[ 3 )]Kkg(J[cp )]Km(W[102

]sPa[10 6

p[bar] 1961 3923 5884 1961 3923 5884 1961 3923 5884 1961 3923 5884

t [oC]

220 9588 2935 373 168

230 9285 2784 383 174

240 9025 2633 393 177

250 8787 1962 2554 3647 403 453 181 183

280 2937 4438 532 198

290 2808 4028 505 202

300 7806 1661 2695 2311 2788 3621 456 479 510 201 203 205

350 7082 1471 2313 2219 2478 2834 512 531 557 222 223 225

400 6485 1335 2064 2198 2365 2554 570 587 608 243 244 246

450 5999 1225 1877 2202 2319 2445 629 644 663 265 267 268

500 5587 1134 1729 2206 2294 2386 693 706 722 287 288 289

550 1606 2353 784 312

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 13

18 Physical Properties of Selected Solid Materials

Table 413 Properties of Selected Solids at 25 oC

Substance

kgm3 pc

[kJ(kg K)]

Asphalt 2120 167

Brick (common) 1800 084

Carbon (diamond) 3250 051

Carbon (graphite) 2000ndash2500 061

Coal 1200ndash1500 126

Concrete 2200 088

Glass (plate) 2500 080

Glass (wool) 200 066

Granite 2750 089

Ice (0 oC) 917 204

Paper 700 120

Plexiglas 1180 144

Polystyrene 920 230

Polyvinyl chloride 1380 096

Rubber (soft) 1100 167

Salt (rock) 2100ndash2500 092

Sand (dry) 1500 080

Silicon 2330 070

Snow (firm) 560 210

Wood (hard oak) 720 126

Wood (soft pine) 510 138

Wool 100 172

Table 414 Properties of Selected Metals at 25 oC

Metals

kgm3

pc

[kJ(kg

K)] Aluminum 2700 090

Copper (commercial) 8300 042

Brass (60-40) 8400 038

Gold 19300 013

Iron (cast) 7272 042

Iron (Steel 304 St) 7820 046

Lead 11340 013

Magnesium (2 Mn) 1778 100

Nickel (10 Cr) 8666 044

Silver (999 Ag) 10524 024

Sodium 971 121

Tin 7304 022

Tungsten 19300 013

Zinc 7144 039

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 14

Table 415 Thermal Expansion Coefficients and

Thermal Conductivity of Solids

Material

Thermal

Expansion

Coefficient

(times10-6ordmC)

Thermal

Conductivity

(WmmiddotK)

Aluminum 230 237

Aluminum Alloy 230 ndash

Brass 191 ndash 212 ndash

Brass Noval 211 ndash

Brass Red (80 Cu

20 Zn) 191 ndash

Brick 500 ndash 700 ndash

Bronze Regular 180 ndash 210 ndash

Bronze Manganese 200 ndash

Concrete 700 ndash 140 ndash

Copper 166 ndash 176 410

Copper Alloy 170 ndash

Glass 500 ndash 110 ndash

Gold ndash 317

Iron ndash 802

Iron (Cast) 990 ndash 120 ndash

Iron (Wrought) 120 -

Lead ndash 353

Magnesium 252 156

Magnesium Alloy 261 ndash 288 ndash

Monel (67 Ni 30

Cu) 140 ndash

Nickel 130 907

Nylon Polyamide 750 ndash 100 ndash

Platinum ndash 716

Rubber 130 ndash 200 ndash

Silicon ndash 148

Silver ndash 429

Solder Tin-Lead ndash 300 ndash 498

Steel 100 ndash 180 ndash

Tin ndash 666

Titanium ndash 219

Titanium Alloy 800 ndash 100 ndash

Tungsten 430 174

Zinc 302 116

Table 416 Density Melting and Boiling Points of

Solids

Material

Density

[times1000

kgm3]

Melting

Point

[oC]

Boiling

Point

[oC]

Aluminum 271 6603 2519

Aluminum Alloy 264 ndash

28

5650 ndash

6600 ndash

Brass 84 ndash

875 9300 ndash

Brass Noval 84 ndash ndash

Brass Red (80 Cu 20

Zn) 875 1000 ndash

Brick (Compression) 18 ndash

24 ndash- ndash

Bronze Regular 78 ndash

88 1050 ndash

Bronze Manganese 83 ndash ndash

Carbon 225 4492 3642

Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash

24 ndash ndash

Copper 894 1085 2562

Copper Alloy 823 9250 ndash

Cork 015 ndash

02 ndash ndash

Glass 24 ndash

28 ndash ndash

Gold 1932 1064 2856

Iron (Cast) 787 1538 2861

Iron (Wrought) 7 ndash 74 ndash ndash-

Magnesium [Mg] 74 ndash

78 ndash ndash

Magnesium Alloy 113 3275 1749

Monel (67 Ni 30 Cu) 174 6500 1090

Nickel [Ni] 177 1246 2061

Nylon Polyamide 884 1330 ndash

Platinum 889 1455 2913

Rubber 11 - -

Silver 214 1768 3825

Solder Tin-Lead 096 ndash

13 ndash ndash

Steel 233 1382 ndash

Stone Granite

(Compression) 1049 9618 2162

Stone

Limestone (Compression)

817 ndash

1134 2150 ndash

Stone Marble

(Compression) 785 1425 ndash

Tin 26 ndash ndash

Titanium 2 ndash29 ndash ndash

Titanium Alloy 26 ndash

29 ndash ndash

Wood Ash (Bending) 26 ndash ndash

Wood Douglas Fir

(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287

Wood Southern Pine

(Bending) 451 ndash ndash

Zinc 193 3422 5555

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 13

18 Physical Properties of Selected Solid Materials

Table 413 Properties of Selected Solids at 25 oC

Substance

kgm3 pc

[kJ(kg K)]

Asphalt 2120 167

Brick (common) 1800 084

Carbon (diamond) 3250 051

Carbon (graphite) 2000ndash2500 061

Coal 1200ndash1500 126

Concrete 2200 088

Glass (plate) 2500 080

Glass (wool) 200 066

Granite 2750 089

Ice (0 oC) 917 204

Paper 700 120

Plexiglas 1180 144

Polystyrene 920 230

Polyvinyl chloride 1380 096

Rubber (soft) 1100 167

Salt (rock) 2100ndash2500 092

Sand (dry) 1500 080

Silicon 2330 070

Snow (firm) 560 210

Wood (hard oak) 720 126

Wood (soft pine) 510 138

Wool 100 172

Table 414 Properties of Selected Metals at 25 oC

Metals

kgm3

pc

[kJ(kg

K)] Aluminum 2700 090

Copper (commercial) 8300 042

Brass (60-40) 8400 038

Gold 19300 013

Iron (cast) 7272 042

Iron (Steel 304 St) 7820 046

Lead 11340 013

Magnesium (2 Mn) 1778 100

Nickel (10 Cr) 8666 044

Silver (999 Ag) 10524 024

Sodium 971 121

Tin 7304 022

Tungsten 19300 013

Zinc 7144 039

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 14

Table 415 Thermal Expansion Coefficients and

Thermal Conductivity of Solids

Material

Thermal

Expansion

Coefficient

(times10-6ordmC)

Thermal

Conductivity

(WmmiddotK)

Aluminum 230 237

Aluminum Alloy 230 ndash

Brass 191 ndash 212 ndash

Brass Noval 211 ndash

Brass Red (80 Cu

20 Zn) 191 ndash

Brick 500 ndash 700 ndash

Bronze Regular 180 ndash 210 ndash

Bronze Manganese 200 ndash

Concrete 700 ndash 140 ndash

Copper 166 ndash 176 410

Copper Alloy 170 ndash

Glass 500 ndash 110 ndash

Gold ndash 317

Iron ndash 802

Iron (Cast) 990 ndash 120 ndash

Iron (Wrought) 120 -

Lead ndash 353

Magnesium 252 156

Magnesium Alloy 261 ndash 288 ndash

Monel (67 Ni 30

Cu) 140 ndash

Nickel 130 907

Nylon Polyamide 750 ndash 100 ndash

Platinum ndash 716

Rubber 130 ndash 200 ndash

Silicon ndash 148

Silver ndash 429

Solder Tin-Lead ndash 300 ndash 498

Steel 100 ndash 180 ndash

Tin ndash 666

Titanium ndash 219

Titanium Alloy 800 ndash 100 ndash

Tungsten 430 174

Zinc 302 116

Table 416 Density Melting and Boiling Points of

Solids

Material

Density

[times1000

kgm3]

Melting

Point

[oC]

Boiling

Point

[oC]

Aluminum 271 6603 2519

Aluminum Alloy 264 ndash

28

5650 ndash

6600 ndash

Brass 84 ndash

875 9300 ndash

Brass Noval 84 ndash ndash

Brass Red (80 Cu 20

Zn) 875 1000 ndash

Brick (Compression) 18 ndash

24 ndash- ndash

Bronze Regular 78 ndash

88 1050 ndash

Bronze Manganese 83 ndash ndash

Carbon 225 4492 3642

Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash

24 ndash ndash

Copper 894 1085 2562

Copper Alloy 823 9250 ndash

Cork 015 ndash

02 ndash ndash

Glass 24 ndash

28 ndash ndash

Gold 1932 1064 2856

Iron (Cast) 787 1538 2861

Iron (Wrought) 7 ndash 74 ndash ndash-

Magnesium [Mg] 74 ndash

78 ndash ndash

Magnesium Alloy 113 3275 1749

Monel (67 Ni 30 Cu) 174 6500 1090

Nickel [Ni] 177 1246 2061

Nylon Polyamide 884 1330 ndash

Platinum 889 1455 2913

Rubber 11 - -

Silver 214 1768 3825

Solder Tin-Lead 096 ndash

13 ndash ndash

Steel 233 1382 ndash

Stone Granite

(Compression) 1049 9618 2162

Stone

Limestone (Compression)

817 ndash

1134 2150 ndash

Stone Marble

(Compression) 785 1425 ndash

Tin 26 ndash ndash

Titanium 2 ndash29 ndash ndash

Titanium Alloy 26 ndash

29 ndash ndash

Wood Ash (Bending) 26 ndash ndash

Wood Douglas Fir

(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287

Wood Southern Pine

(Bending) 451 ndash ndash

Zinc 193 3422 5555

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 14

Table 415 Thermal Expansion Coefficients and

Thermal Conductivity of Solids

Material

Thermal

Expansion

Coefficient

(times10-6ordmC)

Thermal

Conductivity

(WmmiddotK)

Aluminum 230 237

Aluminum Alloy 230 ndash

Brass 191 ndash 212 ndash

Brass Noval 211 ndash

Brass Red (80 Cu

20 Zn) 191 ndash

Brick 500 ndash 700 ndash

Bronze Regular 180 ndash 210 ndash

Bronze Manganese 200 ndash

Concrete 700 ndash 140 ndash

Copper 166 ndash 176 410

Copper Alloy 170 ndash

Glass 500 ndash 110 ndash

Gold ndash 317

Iron ndash 802

Iron (Cast) 990 ndash 120 ndash

Iron (Wrought) 120 -

Lead ndash 353

Magnesium 252 156

Magnesium Alloy 261 ndash 288 ndash

Monel (67 Ni 30

Cu) 140 ndash

Nickel 130 907

Nylon Polyamide 750 ndash 100 ndash

Platinum ndash 716

Rubber 130 ndash 200 ndash

Silicon ndash 148

Silver ndash 429

Solder Tin-Lead ndash 300 ndash 498

Steel 100 ndash 180 ndash

Tin ndash 666

Titanium ndash 219

Titanium Alloy 800 ndash 100 ndash

Tungsten 430 174

Zinc 302 116

Table 416 Density Melting and Boiling Points of

Solids

Material

Density

[times1000

kgm3]

Melting

Point

[oC]

Boiling

Point

[oC]

Aluminum 271 6603 2519

Aluminum Alloy 264 ndash

28

5650 ndash

6600 ndash

Brass 84 ndash

875 9300 ndash

Brass Noval 84 ndash ndash

Brass Red (80 Cu 20

Zn) 875 1000 ndash

Brick (Compression) 18 ndash

24 ndash- ndash

Bronze Regular 78 ndash

88 1050 ndash

Bronze Manganese 83 ndash ndash

Carbon 225 4492 3642

Ceramic 2 ndash 3 3870 ndash

Concrete 23 ndash

24 ndash ndash

Copper 894 1085 2562

Copper Alloy 823 9250 ndash

Cork 015 ndash

02 ndash ndash

Glass 24 ndash

28 ndash ndash

Gold 1932 1064 2856

Iron (Cast) 787 1538 2861

Iron (Wrought) 7 ndash 74 ndash ndash-

Magnesium [Mg] 74 ndash

78 ndash ndash

Magnesium Alloy 113 3275 1749

Monel (67 Ni 30 Cu) 174 6500 1090

Nickel [Ni] 177 1246 2061

Nylon Polyamide 884 1330 ndash

Platinum 889 1455 2913

Rubber 11 - -

Silver 214 1768 3825

Solder Tin-Lead 096 ndash

13 ndash ndash

Steel 233 1382 ndash

Stone Granite

(Compression) 1049 9618 2162

Stone

Limestone (Compression)

817 ndash

1134 2150 ndash

Stone Marble

(Compression) 785 1425 ndash

Tin 26 ndash ndash

Titanium 2 ndash29 ndash ndash

Titanium Alloy 26 ndash

29 ndash ndash

Wood Ash (Bending) 26 ndash ndash

Wood Douglas Fir

(Bending) 73 2319 2602

Wood Oak (Bending) 454 1668 3287

Wood Southern Pine

(Bending) 451 ndash ndash

Zinc 193 3422 5555

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 15

19 Software IV ndash 4 Thermodynamic Properties of Water and Steam

Water and steam are probably the most frequently used fluids in industry This is the reason why they

are accorded such special attention in this Toolbox This paragraph provides all of the relevant

constants and equations used for the creation of software which enables the computation of the

thermodynamic properties of water and steam

Software can be used for solving the following ten problems that appear in practice

1 Given T [oC] and v [m3kg]

2 Given T [oC] and P [bar]

3 Given T [oC] and h [kJkg]

4 Given T [oC] and s [kJ(kg K)]

5 Given v [m3kg] and P [bar]

6 Given v [m3kg] and h [kJkg]

7 Given v [m3kg] and s [kJ(kg K)]

8 Given P [bar] and h [kJkg]

9 Given P [bar] and s [kJ(kg K)]

10 Given s [kJ(kg K)] and h [kJkg]

The software calculates the saturated parameters of water for the first of given values if this value is

lower than the critical one

Constants Tc = 647286 K R = 461518 [J(kg K)] E = 00048

Pc = 22089 MPa Tp = 33815 a = 001

ρc = 3170 kgm3 uo = 23750207 [Jkg] Ta = 1000

To = 27316 [K] so = 66965776 [J(kg K)] c = 1544912141

a = 001

(a) Pressure ndash Specific Volume ndash Temperature Equation - P = P(vT)

T

2 QQ1TRP (422)

Where

7

1j

8

1i

10

9i

9iji

E1ijaji

2jjac AeAQ (423)

7

1j

8

2i

j10j9E2i

jaji2j

jac

T

A)E1(AEe)1i(AQ (424)

and

T

Ta 732jfor52 jac1a

6341a 732jfor1000ja

A(1 1) = 0029492937 A(2 1) = -000013213917 A(3 1) = 000000027464632

A(4 1) = -36093828E-10 A(5 1) = 34218431E-13 A(6 1) = -24450042E-16

A(7 1) = 15518535E-19 A(8 1) = 59728487E-24 A(9 1) = -041030848

A(10 1) = -00004160586

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 16

A(1 2) = -0005198586 A(2 2) = 00000077779182 A(3 2) = -0000000033301902

A(4 2) = -16254622E-11 A(5 2) = -17731074E-13 A(6 2) = 12748742E-16

A(7 2) = 13746153E-19 A(8 2) = 15597836E-22 A(9 2) = 03373118

A(10 2) = -000020988866

A(1 3) = 00068335354 A(2 3) = -0000026149751 A(3 3) = 0000000065326396

A(4 3) = -26181978E-11 A(5 3) = 0 A(6 3) = 0

A(7 3) = 0 A(8 3) = 0 A(9 3) = -013746618

A(10 3) = -000073396848

A(1 4) = -00001564104 A(2 4) = -000000072546108 A(3 4) = -92734289E-09

A(4 4) = 4312584E-12 A(5 4) = 0 A(6 4) = 0

A(7 4) = 0 A(8 4) = 0 A(9 4) = 00067874983

A(10 4) = 0000010401717

A(1 5) = -00063972405 A(2 5) = 0000026409282 A(3 5) = -0000000047740374

A(4 5) = 5632313E-11 A(5 5) = 0 A(6 5) = 0

A(7 5) = 0 A(8 5) = 0 A(9 5) = 013687317

A(10 5) = 00006458188

A(1 6) = -00039661401 A(2 6) = 0000015453061 A(3 6) = -000000002914247

A(4 6) = 29568796E-11 A(5 6) = 0 A(6 6) = 0

A(7 6) = 0 A(8 6) = 0 A(9 6) = 007984797

A(10 6) = 00003991757

A(1 7) = -000069048554 A(2 7) = 00000027407416 A(3 7) = -0000000005102807

A(4 7) = 39636085E-12 A(5 7) = 0 A(6 7) = 0

A(7 7) = 0 A(8 7) = 0 A(9 7) = 0013041253

A(10 7) = 0000071531353

(b) Ideal as isochoric specific heat equation ndash )T(cc 0v

0v

6

1i

2i0v T)i(Gc (425)

where G(1) = 46000

G(2) = 1011249

G(3) = 083893

G(4) = -0000219989

G(5) = 0000000246619

G(6) = -0000000000097047

(c) Saturation Pressure Equation ndash )T(pp satsatsat

8

1i

)1i(

psat

sat

c

c

tsaTTa)i(F1

T

T

P

pln (426)

where

F(1) = -7419242

F(2) = 029721

F(3) = -01155286

F(4) = 0008685635

F(5) = 0001094098

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 17

F(6) = -000439993

F(7) = 0002520658

F(8) = -00005218684

(d) Saturated Liquid Density Equation ndash f = f(Tsat)

8

1i

3i

c

cfT

T1)i(D1 (427)

where D(1) = 36711257

D(2) = -28512396

D(3) = 2226524

D(4) = -88243852

D(5) = 20002765

D(6) = -26122557

D(7) = 18297674

D(8) = -5335052

(e) The specific internal energy of a simple compressible substance is generally expressible as

dT

PTP

1dT)T(cuu

0

2

T

T

0v0

0

(428)

The first integration is at zero density and the second is at constant temperature T0 = 200 [K] is

chosen reference temperature The constant u0 is simply a term used to set the datum for u as desired

The enthalpy of such a substance is

vPuh (429)

Datum for water is set to be

uo = 23750207 [Jkg]

The entropy is determined as

dT

PR

1)ln(RdT

T

)T(css

0

2

T

T

0v

0

0

(430)

Here s0 is a constant that can be chosen to set the datum for s as desired For water it is set as

so = 66965776 [J(kg K)]

The enthalpy of vaporization is calculated from the Clapeyron equation

sat

satgffg

dT

dPvvTh (431)

The specific enthalpy of boiling liquid is

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom

Part III ndash Toolbox 4

ENERGY UNITS CONVERSIONS THERMO-PHYSICAL PROPERTIES AND OTHER ENGINEERING DATA 18

fgvf hhh (432)

The entropy of vaporization is given by

T

hs

fg

fg (433)

and the specific entropy of boiling liquid is

fgvf sss (434)

References

Gas Data wwwairliquidecom

Properties of Common Solid Materials wwwefundacom

Reynolds WC (1979) Thermodynamic Properties in SI Stanford University Stanford

Sonntag RE Borgnakke C Van Wylen GJ (1998) Fundamentals of Thermodynamics John

Wiley amp Sons Inc

wwwchemputecomftphtm

wwwchemicalogiccom

The Engineering Toll Box wwwengineeringtollboxcom