14/15 Semester 3
Chem. Eng. Thermodynamics
(TKK-2137)
Instructor: Rama Oktavian
Email: rama.oktavian86@gmail.com
Office Hr.: M.13-15, Tu. 13-15, W. 13-15, Th. 13-15, F. 09-11
Outlines
1. PVT behavior
2. Equation of State (EoS)
3. Property relation
PVT behavior
P-T Diagram of pure substances
F=2
F=1
F=0
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??
f ( P, V , T )  0
For example, if V is considered a function of T and P
•Volume expansivity
•Isothermal compressibility
1  V 
  
V  T  P
Thus:
dV
 dT  dP
V
See example 3.1
1  V 

V  P T
  
Equation of State
PVT Relationship??
f ( P, V , T )  0
•If  and  is constant (for liquid)
 V2 
ln     T2  T1    P2  P1 
 V1 
Simple EoS
The value of  and  has been determined for some of liquids
PVT relationship
Equation of State
•Equation of State (EoS)
f ( P, V , T )  0
•Gas ideal (simplest EoS)
-volume individual = 0
PV  RT
- no interaction
valid for low pressure
•Real gas
Compressibility factor (Z)
PV  ZRT
for ideal gas, Z = 1
Equation of State
Virial EoS
B C
D
 2  3  .........
V V
V
Z  1  BP  C P 2  DP 3  .........
Z  1
B C
, : 2-body interaction dan 3-body interaction
V V3
Truncated Virial EoS
B
Z  1
V
Z  1  BP
Z  1  BP
Aplikasi:
• Valid for gas
• There is significant
molecular interaction
• Truncated Virial EoS for low
pressure
1
Z
P
Equation of State
Virial EoS
Equation of State
Virial EoS
Density-series virial coefficients B and C for Nitrogen
Equation of State
Virial EoS - application
Equation of State
Cubic EoS
- Involve more theoretical background
- Can be applied for gas and liquid
property(application for VLE)
1. Van der Waals EoS (1873)
P
 2P 
 P 

  0;  2   0

V

Tc
 V Tc
C
P
Cair+Uap
VL
a
volume
Tc
T<Tc
VV
2
2
c
RT
a
 2
V b V
27 R T
RT
;b  c
64 Pc
8Pc
V
T>Tc
Intermolecular attraction
If b=0 and a/V2=o
become ideal gas EoS
Equation of State
Cubic EoS
The van der waals EOS
Generic Cubic EOS
Isotherm as given by a cubic EOS
Equation of State
Cubic EoS
general form
(REID,
PRAUZNITZ, POLING,
PROPERTIES OF GASES AND
LIQUIDS, 4th ED., 1986)
EQUATION
u
w
VAN DER
WALLS
0
0
REDLICHKWONG
1
0
SOAVEREDLICHKWONG
1
0
PENGROBINSON
2
RT
a
P
 2
V  b V  ubV  wb 2
b
a
27 R 2Tc2
RTc
64 Pc
8 Pc
0.08664 RTc 0.42748R 2T 2.5
Pc
PcT 0.5


2
f  0.48  1.574  0.176 2
c
-1

2 2
0
.
42748
R
Tc
0.08664 RTc
1  f 1  Tr0.5
Pc
P


0.0778 RTc 0.45724 R 2Tc2
2
1  f 1  Tr0.5 
Pc
Pc
f  0.37464  1.54226  0.26992 2
Equation of State
Critical 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
  1  log P

sat
r
Tr 0.7
Equation of State
General form of EoS
 Equations 3.49 through 3.56 summarize a generic form for the
cubic EoS
 values for parameters are
Equation of State
General form of EoS
 Rework Example 3.8
Equation of State
Generalized correlation EoS
2-parameter corresponding state principle (CSP)
Z  Z Tr , Pr  Valid for simple fluid (Ar, Kr and Xe)
where
T
P
Tr  ; Pr 
Tc
Pc
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 State
Generalized correlation EoS
3-parameter corresponding state principle (CSP)
Z  Z Tr , Pr , 
Pitzer and Curl correlation (1955, 1957)
Z  Z 0  Z 1
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 State
Generalized correlation EoS
The Lee/Kesler correlation provides suitable results for gases
which are nonpolar and slightly polar
Tne nature of The Lee/Kesler correlation for Z0 = F0 (Tr,Pr)
Equation of State
Generalized correlation EoS
Pitzer Correlation for the Second Virial Coefficient :
Where:
B 0  0.083 
0.422
Tr0.422
B1  0.139 
0.172
Tr4.2
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 State
Generalized correlation EoS
Lee/Kesler corr (points)
(straight lines)
<2% differ
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%
Equation of State
Generalized correlation for liquids
Rackett equation (Racket, J. Chem. Eng. Data, 15 (1970) 514-517:
estimation of molar volume of saturated liquids
With accuracy of 1-2%
Lyderson, Greenkorn and Hougen:
estimation of liquid molar volume
Equation of State
Generalized correlation for liquids
Generalized density correlation for liquids
Equation of State
Generalized correlation for liquids
For amonia at 310 K, estimate the density of
a)The saturated liquid density
b)The liquid at 100 bar
Saturated Liquid
Solution:
a.Using Rackett eq.
Tc= 405.7 K, Vc= 72.47Zc= 0.242 from
App. B
V
sat
 Vc Z
(1Tr ) 0.287
c
 28.33 cm3mol 1
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 r  2.38
Equation of State
Generalized correlation for liquids
 r  2.38
V  VCr 
72.47
 30.45 cm3mol 1
2.38
Compared to exp. data the result is
higher 6.5%
Other method:
2.38
V2  V1
 r1
r 2
 2.34 
V2  29.14

 2.38 
V2  28.65 cm3mol 1
The result is agreed with
the exp. data.