chem. eng. thermodynamics (tkk-2137)
DESCRIPTION
14/15 Semester 3. Chem. Eng. Thermodynamics (TKK-2137). Instructor: Rama Oktavian Email: [email protected] 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. - PowerPoint PPT PresentationTRANSCRIPT
Chem. Eng. Thermodynamics(TKK-2137)
14/15 Semester 3
Instructor: Rama OktavianEmail: [email protected] 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
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
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 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
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 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
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.