Chem. Eng. Thermodynamics (TKK-2137)

1. 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

2. Outlines 1. PVT behavior 2. Equation of State (EoS) 3. Property relation

3. PVT behavior P-T Diagram of pure substances F = 2 F = 1 F = 0

4. 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

5. PVT behavior P-V Diagram of pure substances

6. PVT behavior PVT Relationship?? For example, if V is considered a function of T and P • Volume expansivity • Isothermal compressibility Thus: See example 3.1

7. Equation of State PVT Relationship?? • If band kis constant (for liquid) Simple EoS The value of band khas been determined for some of liquids PVT relationship

8. Equation of State • Equation of State (EoS) • Gas ideal (simplest EoS) -volume individual = 0 - no interaction valid for low pressure • Real gas Compressibility factor (Z) for ideal gas,Z = 1

9. Equation of State Virial　EoS 2-body interaction dan 3-body interaction Truncated Virial　EoS • Aplikasi: • Valid for gas • There is significant molecular interaction • Truncated VirialEoSfor low pressure 1 Z P

10. Equation of State Virial　EoS

11. Equation of State Virial　EoS Density-series virial coefficients B and C for Nitrogen

12. Equation of State VirialEoS - application

13. P C Cair+Uap Tc T>Tc T<Tc VL VV V 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) volume Intermolecular attraction If b=0 and a/V2=o become ideal gas EoS

14. Equation of State Cubic EoS The van der waals EOS Generic Cubic EOS Isotherm as given by a cubic EOS

15. Equation of State Cubic EoS general form (REID, PRAUZNITZ, POLING, PROPERTIES OF GASES AND LIQUIDS, 4th ED., 1986)

16. 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

17. 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

18. Equation of State General form of EoS • Rework Example 3.8

19. Equation of State Generalized correlation EoS 2-parameter corresponding state principle (CSP) Valid for simple fluid (Ar, Kr and Xe) 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 “w” by K. S. Pitzer and coworkers

20. Equation of State Generalized correlation EoS 3-parameter corresponding state principle (CSP) Pitzer and Curl correlation (1955, 1957) 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

21. 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)

22. Equation of State Generalized correlation EoS 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.) Where:

23. Equation of State Lee/Kesler corr (points) Generalized correlation EoS (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%

24. 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

25. Equation of State Generalized correlation for liquids Generalized density correlation for liquids

26. Equation of State Generalized correlation for liquids • For amonia at 310 K, estimate the density of • The saturated liquid density • The liquid at 100 bar • Solution: • Using Rackett eq. • Tc= 405.7 K, Vc= 72.47Zc= 0.242from • App. B Saturated Liquid 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

27. Equation of State Generalized correlation for liquids Compared to exp. data the result is higher 6.5% 2.38 Other method: The result is agreed with the exp. data.

28. Thank You !