Chem. Eng. Thermodynamics(TKK-2137)

14/15 Semester 3

Instructor: Rama OktavianEmail: rama.oktavian86@gmail.comOffice Hr.: M.13-15, Tu. 13-15, W. 13-15, Th. 13-15, F. 09-11

Outlines

1. PVT behavior 1. PVT behavior

2. Equation of State (EoS) 2. Equation of State (EoS)

3. Property relation 3. Property relation

PVT behavior

F = 2F = 1

F = 0

P-T Diagram of pure substances

PVT behavior

P-T Diagram of pure substances

- no indication of volume

- limits to phases are noted by the triple point and the critical point

- the slopes of the phase change lines indicate the impact of temperature or pressure on phase changes

- pressure has a significant impact on the saturation boiling point

- pressure has a limited impact on the melt temperature (liquid and solid)

- fluid region is where vapor & liquid cannot be differentiated

PVT behavior

P-V Diagram of pure substances

PVT behavior

PVT Relationship??

0),,( TVPfFor example, if V is considered a function of T and P

• Volume expansivity

PT

V

V

1

• Isothermal compressibility

TP

V

V

1

dPdTV

dV Thus:

See example 3.1

Equation of State

PVT Relationship??0),,( TVPf

• If b and k is constant (for liquid)

12121

2ln PPTTV

V

Simple EoS

The value of b and k has been determined for some of liquids

PVT relationship

Equation of State

• Equation of State (EoS)

0),,( TVPf

• Gas ideal (simplest EoS)

RTPV -volume individual = 0- no interaction

• Real gas

valid for low pressure

Compressibility factor (Z)

ZRTPV

for ideal gas, Z = 1

Equation of StateVirial　 EoS

.........V

D

V

C

V

BZ

321

.........PDPCPBZ 321

:3V

C,

V

B 2-body interaction dan 3-body interaction

Truncated Virial　 EoS

V

BZ 1 PBZ 1

Z

P

1

PBZ 1

Aplikasi:• Valid for gas• There is significant

molecular interaction• Truncated Virial EoS for low

pressure

Equation of StateVirial　 EoS

Equation of StateVirial　 EoS

Density-series virial coefficients B and C for Nitrogen

Equation of StateVirial　 EoS - application

Equation of StateCubic EoS

- Involve more theoretical background- Can be applied for gas and liquid

property(application for VLE)

C

Cair+Uap

V

P

Tc T>TcT<Tc

VL VV

1. Van der Waals EoS (1873)

2V

a

bV

RTP

volume

Intermolecular attraction

If b=0 and a/V2=obecome ideal gas EoS

002

2

cc TT V

P;

V

P

c

c

c

c

P

RTb;

P

TRa

864

27 22

Equation of StateCubic EoS

The van der waals EOS

Generic Cubic EOS

Isotherm as given by a cubic EOS

Equation of StateCubic EoS

general form (REID, PRAUZNITZ, POLING, PROPERTIES OF GASES AND LIQUIDS, 4th ED., 1986)

22 wbubVV

a

bV

RTP

EQUATION u w b a

VAN DER WALLS

0 0

REDLICH-KWONG

1 0

SOAVE-REDLICH-KWONG

1 0

PENG-ROBINSON

2 -1

c

c

P

RT

8 c

c

P

TR

64

27 22

c

c

P

RT08664.0

c

c

P

RT08664.0

c

c

P

RT0778.0

5.0

5.2242748.0

TP

TR

c

25.022

1142748.0

rc

c TfP

TR

2176.0574.148.0 f

25.022

1145724.0

rc

c TfP

TR

226992.054226.137464.0 f

Equation of StateCritical properties and accentric factor

most cubic equations calculate parameters at critical points

references are in the form of reduced temperatures: Tr = T/Tc and Pr = P/Pc

accentric factor is based on vapor pressure at Tr = 0.7

7.0log1 rT

satrP

Equation of StateGeneral form of EoS

Equations 3.49 through 3.56 summarize a generic form for the cubic EoS

values for parameters are

Equation of StateGeneral form of EoS

Rework Example 3.8

Equation of StateGeneralized correlation EoS

2-parameter corresponding state principle (CSP)

rr P,TZZ Valid for simple fluid (Ar, Kr and Xe)

cr

cr P

PP;

T

TT

where

Two-parameter theorem of corresponding states:

All fluids, when compared at the same reduce temperature and reduce pressure, have approximately the same compressibility factor, and all deviate from ideal-gas behavior to about the same degree

• For simple fluids (Ar, Kr and Xe), it is very nearly exact.• Systimatic deviations are abserved for complex fluids

Introduction of “ ” by K. S. Pitzer and coworkers

Equation of StateGeneralized correlation EoS

3-parameter corresponding state principle (CSP)

,P,TZZ rr

Pitzer and Curl correlation (1955, 1957)

10 ZZZ

Dimana Z0 dan Z1 fungsi (Tr=T/Tc) dan (Pr=P/Pc)The values can be determined from The Lee/Kesler Generalized-correlation Tables (Lee and Kesler, AIChE J., 21, 510-527 (1975) provided in App. E, p. 667

Equation of StateGeneralized correlation EoS

Tne nature of The Lee/Kesler correlation for Z0 = F0 (Tr,Pr)

The Lee/Kesler correlation provides suitable results for gases which are nonpolar and slightly polar

Equation of StateGeneralized correlation EoS

2.41

422.00

172.0139.0

422.0083.0

r

r

TB

TB

Where:

Pitzer Correlation for the Second Virial Coefficient :

The most popular and reliable correlation for the second Virial correlation is provided by Tsonopoulos, et al., 1975, 1978, 1979, 1989, 1990, 1997.(see p. 4.13-4.17, Poling et al.2001 “The properties of gases and liquids 5th ed. MCGRAW-HILL Int. Ed.)

Equation of StateGeneralized correlation EoS

Comparison of correlation for Z0. The virial-coefficient is represented by the straight lines; the Lee/Kesler correlation, by the points. In the region above the dashed line the two correlation differ by less than 2%

<2% differ

(straight lines)Lee/Kesler corr (points)

Equation of StateGeneralized correlation for liquids

Rackett equation (Racket, J. Chem. Eng. Data, 15 (1970) 514-517: estimation of molar volume of saturated liquids

Lyderson, Greenkorn and Hougen: estimation of liquid molar volume

With accuracy of 1-2%

Equation of StateGeneralized correlation for liquids

Generalized density correlation for liquids

Equation of StateGeneralized correlation for liquids

For amonia at 310 K, estimate the density ofa)The saturated liquid densityb)The liquid at 100 bar

Saturated Liquid

Solution:a. Using Rackett eq.

Tc= 405.7 K, Vc= 72.47Zc= 0.242 from App. B

13)1( molcm 33.28287.0 rT

ccsat ZVV

This compared to the exp. Value 29.14 cm3/mol.

b. Compreesed liquid density: Reduced Condition Tr= 0.764 K, Pr= 0.887

From Fig. 3.17 38.2r

Equation of StateGeneralized correlation for liquids

2.38

13molcm 45.3038.2

47.72

38.2

r

CV

r

V

Compared to exp. data the result is higher 6.5%

Other method:

13

2

2

2

112

molcm 65.28

38.2

34.214.29

V

V

VVr

r

The result is agreed with the exp. data.