Ch# 2 Properties of Ch# 2 Properties of Pure SubstancesPure Substances

ObjectivesObjectives

Introduce the concept of a pure substance.Introduce the concept of a pure substance. Discuss the physics of phase-change processes.Discuss the physics of phase-change processes. Illustrate the Illustrate the PP--vv, , TT--vv, and , and PP--T T property diagrams and property diagrams and PP--vv--T T surfaces of surfaces of

pure substances.pure substances. Demonstrate the procedures for determining thermodynamic properties of Demonstrate the procedures for determining thermodynamic properties of

pure substances from tables of property data. pure substances from tables of property data. Describe the hypothetical substance “ideal gas” and the ideal-gas equation Describe the hypothetical substance “ideal gas” and the ideal-gas equation

of state.of state. Apply the ideal-gas equation of state in the solution of typical problems.Apply the ideal-gas equation of state in the solution of typical problems. Introduce the compressibility factor, which accounts for the deviation of Introduce the compressibility factor, which accounts for the deviation of

real gases from ideal-gas behavior.real gases from ideal-gas behavior. Present some of the best-known equations of state. Present some of the best-known equations of state.

Pure SubstancePure Substance

In Chemistry you defined a pure substance as an In Chemistry you defined a pure substance as an element or a compoundelement or a compound

Something that can not be separatedSomething that can not be separated In Thermodynamics we’ll define it as something In Thermodynamics we’ll define it as something

that has a that has a fixed chemical compositionfixed chemical composition throughoutthroughout

Examples of Pure SubstanceExamples of Pure Substance Water, nitrogen, helium, and carbon dioxide, for Water, nitrogen, helium, and carbon dioxide, for

example, are all pure substances.example, are all pure substances. A mixture of water liquid and water vapor, for A mixture of water liquid and water vapor, for

example, is a pure substance because both example, is a pure substance because both phases have the same chemical composition.phases have the same chemical composition.

N2

Air

Water vapor

Water liquid

Pure substance

Example of Non-Pure SubstanceExample of Non-Pure Substance A mixture of liquid air and gaseous air, however, is A mixture of liquid air and gaseous air, however, is

not a pure substance.not a pure substance.

This is because different air components condense at This is because different air components condense at different temperatures at a specified pressures and different temperatures at a specified pressures and thus the composition of liquid air and gas air will be thus the composition of liquid air and gas air will be different.. different..

Phases of Pure SubstancePhases of Pure Substance A phase is identified as having a distinct molecular A phase is identified as having a distinct molecular

arrangement.arrangement. This molecular arrangement is homogeneous This molecular arrangement is homogeneous

throughout the system.throughout the system. The phase separated from the other phases by easily The phase separated from the other phases by easily

identifiable boundary surfaces.identifiable boundary surfaces.

liquid

Solid

vapor

Air Gas

Air liquid

Not a Pure substance

Solid Phase of Pure SubstanceSolid Phase of Pure Substance The molecules in a solid are arranged in a lattice The molecules in a solid are arranged in a lattice

that is repeated throughout.that is repeated throughout. Three dimensional patternThree dimensional pattern Large attractive forces between atoms or Large attractive forces between atoms or

moleculesmolecules The atoms or molecules are in constant motion – The atoms or molecules are in constant motion –

they oscillate in placethey oscillate in place The higher the temperature – the more vibrationThe higher the temperature – the more vibration

Liquid Phase of Pure SubstanceLiquid Phase of Pure Substance

When a solid reaches a sufficiently high When a solid reaches a sufficiently high temperature the velocity (and thus the temperature the velocity (and thus the momentum) of the molecules reach a momentum) of the molecules reach a point where the intermolecular forces are point where the intermolecular forces are partially defeated and groups of the partially defeated and groups of the molecules break away (melting point)molecules break away (melting point)

In liquid the molecular spacing is not In liquid the molecular spacing is not much different from that of solids, much different from that of solids, except that they can rotate and translate except that they can rotate and translate freely (they are not at fixed positions freely (they are not at fixed positions relative to each other)relative to each other)

Distance between molecules increase Distance between molecules increase slightly as a solid turns to liquidslightly as a solid turns to liquid

Gas Phase of Pure SubstanceGas Phase of Pure Substance

In the gas phase, the molecules are far In the gas phase, the molecules are far apart from each other, and a molecular apart from each other, and a molecular order is nonexistent.order is nonexistent.

Molecules move about at random, Molecules move about at random, continually colliding with each other and continually colliding with each other and the walls of the container they are inthe walls of the container they are in

High kinetic energyHigh kinetic energy In order to liquefy, lots of that kinetic In order to liquefy, lots of that kinetic

energy must be releasedenergy must be released

Liquid phase to Gas PhaseLiquid phase to Gas Phase

Let us study what would happen when we heat a liquid phase of pure Let us study what would happen when we heat a liquid phase of pure substance at a constant pressuresubstance at a constant pressure

Piston cylinder device – maintains constant pressure

Liquid Water

T

v

1

2

5

3 4

Phase Change Processes on a T-v diagram

Phase Change Processes on a T-v diagramPhase Change Processes on a T-v diagram

Consider a piston-cylinder device with water Consider a piston-cylinder device with water inside at 20inside at 20ooC and 1 atm pressure .C and 1 atm pressure .

At this P and T, water is called compressed At this P and T, water is called compressed (or subcooled) liquid state.(or subcooled) liquid state.

Compressed liquid means that it is not about Compressed liquid means that it is not about to vaporize.to vaporize.

The system is heated and the piston is allowed The system is heated and the piston is allowed to float and thus the pressure will be constant. to float and thus the pressure will be constant.

T and v will increase until the system reaches T and v will increase until the system reaches 100 C at which any addition of heat will 100 C at which any addition of heat will cause some of the liquid to vaporizecause some of the liquid to vaporize

The temperature at which a pure substance The temperature at which a pure substance changes phase is called the saturation changes phase is called the saturation temperature, Ttemperature, Tsatsat. .

At TAt Tsatsat, Liquid and vapor phases are in , Liquid and vapor phases are in equilibrium. equilibrium.

A liquid that is about to vaporize is called Saturated Liquid.

Adding more heat will cause Adding more heat will cause boiling to start. Liquid gradually boiling to start. Liquid gradually evaporates (state 3) but evaporates (state 3) but temperature will remain constant, temperature will remain constant, Why?Why?

The only change is the increase in The only change is the increase in the specific volume (v) until it the specific volume (v) until it reaches state 4 (saturated vapor). reaches state 4 (saturated vapor).

Heating the system further, will Heating the system further, will increase both the temperature and increase both the temperature and specific volume (state 5). This specific volume (state 5). This single-phase state is called single-phase state is called “Superheated vapor”“Superheated vapor”

Repeat this experiment for higher Repeat this experiment for higher pressures.pressures.

Similar curves will be obtained but Similar curves will be obtained but at higher sat. temperature.at higher sat. temperature.

Note that the sat. liquid specific Note that the sat. liquid specific volume (vvolume (vsat,lsat,l ) will increase while ) will increase while the sat. vapor specific volume the sat. vapor specific volume (v(vsat,gsat,g ) will decrease ) will decrease

A substance between saturated liquid (state 2) and saturated vapor (state 4) is called saturated liquid-vapor mixture.

A vapor that is about to condense is called Saturated vapor.

Saturation Temperature and Pressure Saturation Temperature and Pressure

Water at a pressure of 101.325 kPa, TWater at a pressure of 101.325 kPa, Tsatsat is 100 is 100ooC. Conversely, at a C. Conversely, at a

temperature of 100temperature of 100ooC, PC, Psatsat is 101.325 kPa. is 101.325 kPa.

Latent heat: fusion and vaporization.Latent heat: fusion and vaporization. The magnitude of the latent heats depend on the temperature or The magnitude of the latent heats depend on the temperature or

pressure at which the phase change occur.pressure at which the phase change occur.

Saturation Temperature and Pressure Saturation Temperature and Pressure

At a given pressure, the temperature at which a At a given pressure, the temperature at which a pure substance changes phase is called the pure substance changes phase is called the saturation temperature. Likewise the pressure.saturation temperature. Likewise the pressure.

Critical PointCritical Point The critical point is defined as the The critical point is defined as the

point at which the saturated liquid point at which the saturated liquid and saturated vapor states are and saturated vapor states are identical.identical.

At the critical pressure, there will be At the critical pressure, there will be no distinct phase change process. no distinct phase change process. Instead, the specific volume of the Instead, the specific volume of the substance will continually increase substance will continually increase and at all times there will be only and at all times there will be only one phase present. one phase present.

The saturated liquid states can be The saturated liquid states can be connected by a line called the connected by a line called the saturated liquid line. saturated liquid line.

The saturated vapor states can be The saturated vapor states can be connected by another line, called connected by another line, called the saturated vapor line, to form a the saturated vapor line, to form a phase dome. phase dome.

Three main regions can be Three main regions can be identified.identified.

vsat,l and vsat,g will be the same and we speak of Pcrit, Tcrt, and vcrit.

Phase Change Processes on a P-v diagram Phase Change Processes on a P-v diagram

Decrease P gradually but Decrease P gradually but keep T constant.keep T constant.

Water boils at PWater boils at Psatsat

The pressure at which a The pressure at which a pure substance changes pure substance changes phase is called the phase is called the saturation pressure Psaturation pressure Psatsat..

At PAt Psatsat, Liquid and vapor , Liquid and vapor

phases are in equilibrium. phases are in equilibrium. From State 2 to 4, no From State 2 to 4, no

weights are removed weights are removed (P=constant) and T is kept (P=constant) and T is kept constant but heating constant but heating causes liquid to vaporize. causes liquid to vaporize.

State 1T = 150 C

State 2T = 150 C

State 3T = 150 C

State 4T = 150 C

State 5T = 150 C

1

2 3 4

5

P-v diagrams with Solid Phase P-v diagrams with Solid Phase

P – v diagram of substance that P – v diagram of substance that contracts on freezingcontracts on freezing

P – v diagram of substance that P – v diagram of substance that expands on freezing (such as expands on freezing (such as water)water)

Triple point Triple point

Under some conditions all three Under some conditions all three phases of substance coexist in phases of substance coexist in equilibrium at states along the equilibrium at states along the triple line.triple line.

The states on the triple line of The states on the triple line of substance have the same pressure substance have the same pressure and temperature but different v.and temperature but different v.

The triple line appears as a point The triple line appears as a point on the P-T diagram.on the P-T diagram.

The triple point of water occurs The triple point of water occurs at T= 0.01 C and P=0.6113 Kpaat T= 0.01 C and P=0.6113 Kpa

liquid

Solid

vapor

Property DiagramsProperty Diagrams

P-T diagram P-T diagram

(or Phase diagram)(or Phase diagram) The P-T diagram is often called The P-T diagram is often called

phase diagram since all three phase diagram since all three phases are separated by three lines, phases are separated by three lines, namely the sublimation line namely the sublimation line (between solid and vapor regions), (between solid and vapor regions), the vaporization line (between the vaporization line (between liquid and vapor regions), and the liquid and vapor regions), and the melting line (between solid and melting line (between solid and liquid).liquid).

P-v-T surfaces

P

T

T

v

P

v

viewTop

e

Temperatur

viewv

P view

TP

You can plot P, T, V on a You can plot P, T, V on a three dimensional graphthree dimensional graph

Thermodynamics Tables Thermodynamics Tables The relationship among thermodynamic properties are too complex to be The relationship among thermodynamic properties are too complex to be

expressed in simple equations and thus, properties are measured and/or expressed in simple equations and thus, properties are measured and/or calculated and then presented in a tabulated form.calculated and then presented in a tabulated form.

Saturated liquid-vapor region

Table A4 T entryTable A5 P entry

Tab

le A

7C

om

pre

sse

Liq

uid

Table A8Saturated ice-vapor

Table

A6

Superhea

ted

water

(or v

apor)

In single-phase regions, any In single-phase regions, any two properties will fix the two properties will fix the state.state.

In two phase regions, any In two phase regions, any two properties (except P and two properties (except P and T) will fix the state. P and T T) will fix the state. P and T are dependent on each other.are dependent on each other.

Enthalpy − A Combination PropertyEnthalpy − A Combination Property

In the analysis of certain types of processes, particularly in power In the analysis of certain types of processes, particularly in power generation and refrigeration, we frequently encounter the combination of generation and refrigeration, we frequently encounter the combination of internal energy U, and pressure-volume product PV. That is internal energy U, and pressure-volume product PV. That is

Before 1930, h was referred to as heat content or total heat.Before 1930, h was referred to as heat content or total heat. After 1930, it is referred to as enthalpy (from the Greek word enthalpien After 1930, it is referred to as enthalpy (from the Greek word enthalpien

which means to heat)which means to heat)

PVUH pυuh

Saturated Liquid and Saturated Vapor States Saturated Liquid and Saturated Vapor States Table A-4Table A-4 Saturated liquid-vapor Saturated liquid-vapor

mixture falls under the P-v mixture falls under the P-v (or T-v) dome. (or T-v) dome.

Its properties can be obtained Its properties can be obtained from Water Tables A-4 and from Water Tables A-4 and A-5A-5

T

P =

cons

t.

vgvf

Saturated Liquid and Saturated Vapor States Saturated Liquid and Saturated Vapor States Table A-5Table A-5 In Table A-5 (page 832), In Table A-5 (page 832),

Pressure is listed in the left Pressure is listed in the left column as the independent column as the independent variable.variable.

Use whichever table is Use whichever table is convenient.convenient.

Enthalpy of vaporization or Enthalpy of vaporization or latent heat latent heat

the amount of energy needed the amount of energy needed to vaporize a unite mass of to vaporize a unite mass of saturated liquid at a given saturated liquid at a given temperature or pressuretemperature or pressure

fgfg vvv

fgfg hhh

Example 2-1:Example 2-1:Saturated Liquid and Saturated VaporSaturated Liquid and Saturated Vapor A rigid tank contains 50 kg of saturated liquid water at 90A rigid tank contains 50 kg of saturated liquid water at 90ooC. Determine C. Determine

the pressure in the tank and the volume of the tank. (Table A-4)the pressure in the tank and the volume of the tank. (Table A-4)

(Answers: 70.14 kPa, 0.0518 m) (Answers: 70.14 kPa, 0.0518 m)

Example 2-2:Example 2-2:Saturated Liquid and Saturated VaporSaturated Liquid and Saturated Vapor A piston-cylinder device contains 2 ftA piston-cylinder device contains 2 ft33 of saturated water vapor at 50-psia pressure. Determine the of saturated water vapor at 50-psia pressure. Determine the

temperature of the vapor and the mass of the vapor inside the cylinder. (Table A-5E)temperature of the vapor and the mass of the vapor inside the cylinder. (Table A-5E)

(Answers: 281.03(Answers: 281.03ooF, 0.235 lbm) F, 0.235 lbm)

Example 2-3:Example 2-3:Saturated Liquid and Saturated VaporSaturated Liquid and Saturated Vapor A mass of 200 g of saturated liquid water is completely vaporized at a

constant pressure of 100 kPa. Determine (a) the volume change and (b) the amount of energy added to the water.

(Answers: 0.3368 m3, 451.6 kJ)

In the saturated liquid-vapor mixture, the mass fraction of vapor is called In the saturated liquid-vapor mixture, the mass fraction of vapor is called the QUALITY (x) and is expresses asthe QUALITY (x) and is expresses as

Derivation:Derivation:

Saturated Liquid-Vapor MixtureSaturated Liquid-Vapor Mixture

total

g

gf

g

m

m

mm

mx

P or T

f ggf

Gas mg vg

Liquidmf vf

fgfg

fgf

fgf

gf

ggfg

ggff

gf

vvvwherexvvv

vvxvvxvvxv

vmvmmvmvmmv

VVV

)()1(

)(

Average PropertiesAverage Properties

In the saturated mixture region, the average value of any intensive property In the saturated mixture region, the average value of any intensive property y is given as:y is given as:

where f stands for saturated liquid and g for saturated vapor. For example:where f stands for saturated liquid and g for saturated vapor. For example:

y y x y y

y x yf g f

f fg

( )

In the saturated mixture region, the average value of any intensive property y is In the saturated mixture region, the average value of any intensive property y is given as:given as:

where f stands for saturated liquid and g for saturated vapor. For example:where f stands for saturated liquid and g for saturated vapor. For example:

The average properties of the mixtures are always between the values of the The average properties of the mixtures are always between the values of the saturated liquid and the saturated vapor properties. That issaturated liquid and the saturated vapor properties. That is

Average PropertiesAverage Properties

y y x y y

y x yf g f

f fg

( )

When x = 0 we have all liquid, and y = yWhen x = 0 we have all liquid, and y = yff

0

When x = 1 we have all gas, and y = yWhen x = 1 we have all gas, and y = yf f + y+ yfgfg = y = ygg

1= yg

gavgf yyy

X = 0 X = 1

Saturated Liquid-Vapor MixtureSaturated Liquid-Vapor Mixture

Quality is an intensive propertyQuality is an intensive property

T

vvvg

P=con

st.

Tsat

T

vf

vvvg

T=const.

P

Psat

P

mixture saturated

ff

ff

gf

sat

sat

Tor Pgiven at h h h

Tor Pgiven at u u u

Tor Pgiven at v vv

Tgiven at P P

Pgiven at T T

Example 2- 4:Example 2- 4:Saturated Liquid-vapor mixture (continued)Saturated Liquid-vapor mixture (continued) A rigid tank contains 10 kg of water at 90A rigid tank contains 10 kg of water at 90ooC. If 8 kg of water is in the C. If 8 kg of water is in the

liquid form and the rest is in the vapor form, determine (a) the pressure in liquid form and the rest is in the vapor form, determine (a) the pressure in the tank and (b) the volume of the tank. the tank and (b) the volume of the tank.

(Answers: 70.14 kPa, 4.73 m(Answers: 70.14 kPa, 4.73 m33) )

Example 2-5:Example 2-5:Saturated Liquid-vapor mixture (continued)Saturated Liquid-vapor mixture (continued) An 80-L vessel contains 4 kg of refrigerant 134a at a pressure of 160 kPa. An 80-L vessel contains 4 kg of refrigerant 134a at a pressure of 160 kPa.

Determine a) the temperature of the refrigerant, b) the quality, c) the Determine a) the temperature of the refrigerant, b) the quality, c) the enthalpy of the refrigerant, and d) the volume occupied by the vapor phase. enthalpy of the refrigerant, and d) the volume occupied by the vapor phase.

(Answers: -15.62(Answers: -15.62ooC, 0.158, 62.7 kJ/kg, 0.0777 mC, 0.158, 62.7 kJ/kg, 0.0777 m33) )

Superheated Vapor Table A-6Superheated Vapor Table A-6

In the region to the right of the saturated vapor line, a substance exists as In the region to the right of the saturated vapor line, a substance exists as superheated vapor (single phase).superheated vapor (single phase).

P

vvvg

T=const.

Superheated VaporSuperheated Vapor

vapordsuperheate

g

g

g

sat

sat

Tor Pgiven at h h

Tor Pgiven at u u

Tor Pgiven at v v

Tgiven at P P

Pgiven at T T

T

vvvg

P=con

st.

Tsat

T

vf

vvvg

T=const.

P

Psat

P

Compressed liquid Table A-7Compressed liquid Table A-7 In the region to the left of the saturated liquid line, a substance exists as In the region to the left of the saturated liquid line, a substance exists as

compressed liquid.compressed liquid.

T

v

Compressed LiquidCompressed Liquid

liquid compressed

f

f

f

sat

sat

Tor Pgiven at h h

Tor Pgiven at u u

Tor Pgiven at v v

Tgiven at P P

Pgiven at T T

T

vvvg

P=con

st.

Tsat

T

vf

A general approximationA general approximation

In the absence of compressed liquid data, a general approximation is to treat In the absence of compressed liquid data, a general approximation is to treat compressed liquid as saturated liquid at the given temperature. Such that compressed liquid as saturated liquid at the given temperature. Such that

If the compression is moderate, the properties do not vary significantly with If the compression is moderate, the properties do not vary significantly with pressure. But they do vary with temperaturepressure. But they do vary with temperature

Tfyy

@

264

T

vv vf

P=5

Mpa

.

80

Approximate value

Precise value

Acceptable

5 Mpa

vv vf

T=264

P

T=80

Wrong value

Precise value

Wrong

Linear InterpolationLinear Interpolation

AA BB

100100 55

200200 1010

130 y

5105

100200100130

y

Linear Interpolation (Continued)Linear Interpolation (Continued)

Now

T Psat

X1= 140 y1= 0.3615X = 143 y = ?X2= 145 y2= 0.4154

Psat 0.3615143 140145 140

0.4154 0.3615( )

Psat 0.394 kPa

)( 1212

11 yy

xx

xxyy

1 1

2 1 2 1

y y x x

y y x x

Example 2-7Example 2-7Superheated Vapor Superheated Vapor

Determine the temperature of water at a state of P = 0.5 MPa and h = 2890 Determine the temperature of water at a state of P = 0.5 MPa and h = 2890 kJ/kg. kJ/kg.

(Answers: 216.4 (Answers: 216.4 ooC) C)

Example on Compressed LiquidExample on Compressed Liquid

Example 2-8:Example 2-8: Determine the internal energy of Determine the internal energy of

compressed liquid water at 80compressed liquid water at 80ooC C and 5 MPa using (a) data from the and 5 MPa using (a) data from the compressed liquid table and (b) compressed liquid table and (b) saturated liquid data. What is the saturated liquid data. What is the error involved in the second case? error involved in the second case? (Answers: 333.72 kJ/kg, 334.86 (Answers: 333.72 kJ/kg, 334.86 kJ/kg, 0.34%) kJ/kg, 0.34%)

80

Mpa

5

99263.

80

The Use of Steam Table to Determine The Use of Steam Table to Determine PropertiesProperties

Example 2-9:Example 2-9: Determine the missing properties and the phase descriptions in the Determine the missing properties and the phase descriptions in the

following table for water.following table for water.

Reference State and Reference ValuesReference State and Reference Values

The values of u, h, and s cannot be measured directly, and they are The values of u, h, and s cannot be measured directly, and they are calculated from measurable properties using the relations between calculated from measurable properties using the relations between thermodynamic properties. However, those relations give the changes in thermodynamic properties. However, those relations give the changes in properties, not the values of properties at specified state.properties, not the values of properties at specified state.

For water, the state saturated liquid at 0.01For water, the state saturated liquid at 0.01ooC is taken as the reference C is taken as the reference state, and the internal energy and entropy are assigned zero values at that state, and the internal energy and entropy are assigned zero values at that sate.sate.

For refrigerant 134a, the state saturated liquid at -40For refrigerant 134a, the state saturated liquid at -40ooC is taken as the C is taken as the reference state, and the enthalpy and entropy are assigned zero values at reference state, and the enthalpy and entropy are assigned zero values at that state. that state.

In thermodynamics we are concerned with the changes in properties, and In thermodynamics we are concerned with the changes in properties, and the reference chosen has no consequences in the calculations.the reference chosen has no consequences in the calculations.