thermodynamics state polytechnic of malang 2017virial equation 2. 1 v c v b rt pv c z π= π π...
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![Page 1: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/1.jpg)
Volumetric Properties of Pure Fluid
Application of
The Virial Equation
Prepared By : Agung Ari Wibowo ST., M.Sc
Thermodynamics
State Polytechnic of Malang 2017
![Page 2: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/2.jpg)
Ideal Gas and Real Gas
Ideal Gas Real Gas
V1V2
What are the differences?
Ideal Gas
β’ No molecular interactionβ’ Exist at Low Pressureβ’ PV = RT
Real Gas
β’ Molecular interactionβ’ Compressibility Factorβ’ PV = ZRT
![Page 3: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/3.jpg)
Compressibility Factor
RT
BP
RT
PVZ 1
21
V
C
V
B
RT
PVZ
ππ
πππ
= π΅β² + 2πΆβ²π + 3π·β²π2 +β―
π ~1
π
Z of Gas Methane at Various Temperature
Virial Equation :
![Page 4: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/4.jpg)
Virial Equation
21.
V
C
V
B
RT
PVZc
Calculate V and Z for Isopropanol gas at 200 C and 10 Bar. By the following equation : a. Ideal Gas
RT
BP
RT
PVZb 1. B = -388 cm3/mol
C = -26.000 cm6/mol2
![Page 5: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/5.jpg)
Virial Equation
a. Ideal GasPV = RT Z = 1V = RT/P
=83,14 cm3bar/mol Kβ 473,15 K
10 πππ
= 3934 cm3/mol
V = 3934 -388= 3546 cm3/mol
RT
BP
RT
PVZb 1.
π =π π
π+ π΅ Lihat perbedaannya !!
V1 > V2 , disebabkan oleh ZZ2 = 1- 0,099 = 0,901
V1
V2
![Page 6: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/6.jpg)
Virial Equation
21.
V
C
V
B
RT
PVZc
π =π π
π1 +
π΅
π+
πΆ
π2
π = 3934 1 +π΅
π+
πΆ
π2
Perlu dilakukan iterasiTebak nilai V awal = V gas idealV0 = 3934 cm3/mol
Masukan ke persamaan = 3934 1 +π΅
π+
πΆ
π2
V1 trial 1 = 3934 1 +β388
3934+
β26000
39342= 3539 cm3/mol
Check apakah sama dengan V0 , ternyata tidak sama
V2 trial 2 = 3934 1 +β388
3539+
β26000
35392= 3495 cm3/mol
Diulang terus sampe Vn = Vn-1
V = 3488 cm3/mol
![Page 7: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/7.jpg)
Cubic Equation of State
![Page 8: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/8.jpg)
Van Der Waals EOS
Proposed by J.D van der Waals 1873
π =π π
π β πβ
π
π2
βa and b are positive constantβ
Given values of a and b for a particular fluid, one can calculate P as a function of V for various values of T c
c
c
c
P
RTb;
P
TRa
864
27 22
![Page 9: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/9.jpg)
A Generic Cubic EOS
π =π π
π β πβ
π(π)
(π + ππ)(π + ππ)
β’ π πππ π have same value vor all substance
β’ π π are temperature dependent, and different
for each EOSβ’ b also dependent parameter and different for
each EOSEOS :1. Van der Waals2. Redlich/Kwong (RK)3. Soave/Redlich/Kwong (SRK)4. Peng/Robinson (PR)
![Page 10: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/10.jpg)
A Generic Cubic EOS
π =π π
π β πβ
π(π)
(π + ππ)(π + ππ)
π π = ππ(ππ)π
2ππ2
ππΆ
π = Ξ©π ππΆππΆ
EOS Calculation :
Value of Tc , Pc, and π are listed in App. B
ππ =π
ππΆ; ππ =
π
ππΆ
![Page 11: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/11.jpg)
A Generic Cubic EOS
EOS Calculation Liquid:
PV = ZRT
![Page 12: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/12.jpg)
Generalized Equation for Gases
![Page 13: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/13.jpg)
Pitzer Correlation
The most well known correlation related with EOS, is correlation developed by Pitzer and coworkers :
a. Compressiblity Factor (Z)b. Second Virial Eq (B)
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 Gener
alized-correlation Tables (Lee and Kesler, AIChE J., 21, 5
10-527 (1975) provided in App. E, p. 667
Compressibility Factor :
![Page 14: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/14.jpg)
Pitzer Correlation
Second Virial Eq Correlation
π = 1 +π΅π
π π
Original Form :
π = 1 + αΈππππ
By Correlation:
αΈ=π΅ππΆ
π ππΆ
αΈ =π΅0 + ππ΅1
π΅0 = 0.083 +0.422
ππ1.6
π΅1 = 0139 +0.172
ππ4.2
Pitzer Correlation:
![Page 15: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/15.jpg)
Generalized Correlation
Third Virial Eq Correlation
π = 1 + π΅π + πΆπ2
Original Form :
π = 1 + αΈπππππ
+ Δπππππ
Δ =πΆ0 + ππΆβ²
πΆ0 = 0.01407 +0.024322
ππβ
0.00313
ππ10.5
By Correlation:
π =1
π
Δ =πΆππΆ
2
π 2ππΆ2
πΆβ² = β0.02676 +0.05539
ππ2.7 β
0.00242
ππ10.5
![Page 16: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/16.jpg)
Generalized Equation for Liquids
![Page 17: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/17.jpg)
Generalized Correlation for Liquids
Generalized 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%ππππ‘ = ππΆππΆ(1βππ)
0.2857
ππ =π
ππ=ππΆπ
π2 = π1ππ1ππ2
If we know T1 we can evaluate ππ1
![Page 18: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/18.jpg)
EOS Application
In Calculation of process design, estimation of fluid properties is a must.
To choose the most suitable methods, here is the guide
![Page 19: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/19.jpg)
EOS Application
![Page 20: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/20.jpg)
EOS Application
![Page 21: Thermodynamics State Polytechnic of Malang 2017Virial Equation 2. 1 V C V B RT PV c Z π= π
π π 1+ π + π 6 π=3934 1+ π + π 6 Perlu dilakukan iterasi Tebak](https://reader036.vdocuments.mx/reader036/viewer/2022081409/608bf10ae7380c01b23dbf85/html5/thumbnails/21.jpg)