1415 Semester 3 Chem Eng Thermodynamics TKK2137 Instructor

14/15 Semester 3 Chem. Eng. Thermodynamics (TKK-2137) Instructor: Rama Oktavian Email: rama. oktavian 86@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 (Eo. S) 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? ? For example, if V is considered a function of T and P • Volume expansivity Thus: See example 3. 1 • Isothermal compressibility

Equation of State PVT Relationship? ? • If b and k is constant (for liquid) Simple Eo. S The value of b and k has been determined for some of liquids PVT relationship

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

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

Equation of State Virial Eo. S

Equation of State Virial Eo. S Density-series virial coefficients B and C for Nitrogen

Equation of State Virial Eo. S - application

Equation of State Cubic Eo. S - Involve more theoretical background - Can be applied for gas and liquid property(application for VLE) P 1. Van der Waals Eo. S (1873) C Cair+Uap VL VV volume Tc T<Tc V T>Tc Intermolecular attraction If b=0 and a/V 2=o become ideal gas Eo. S

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

Equation of State Cubic Eo. S general form (REID, PRAUZNITZ, POLING, PROPERTIES OF GASES AND LIQUIDS, 4 th ED. , 1986) EQUATION u w VAN DER WALLS 0 0 REDLICHKWONG 1 0 SOAVEREDLICHKWONG 1 0 PENGROBINSON 2 -1 b a

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

Equation of State General form of Eo. S § Equations 3. 49 through 3. 56 summarize a generic form for the § cubic Eo. S values for parameters are

Equation of State General form of Eo. S § Rework Example 3. 8

Equation of State Generalized correlation Eo. S 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

Equation of State Generalized correlation Eo. S 3 -parameter corresponding state principle (CSP) Pitzer and Curl correlation (1955, 1957) Dimana Z 0 dan Z 1 fungsi (Tr=T/Tc) dan (Pr=P/Pc) The values can be determined from The Lee/Kesler Generalized-correlation Tables (Lee and Kesler, AICh. E J. , 21, 510 -527 (1975) provided in App. E, p. 667

Equation of State Generalized correlation Eo. S The Lee/Kesler correlation provides suitable results for gases which are nonpolar and slightly polar Tne nature of The Lee/Kesler correlation for Z 0 = F 0 (Tr, Pr)

Equation of State Generalized correlation Eo. S Pitzer Correlation for the Second Virial Coefficient : Where: 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 5 th ed. MCGRAW-HILL Int. Ed. )

Equation of State Generalized correlation Eo. S Lee/Kesler corr (points) (straight lines) <2% differ Comparison of correlation for Z 0. 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 q. Rackett equation (Racket, J. Chem. Eng. Data, 15 (1970) 514 -517: estimation of molar volume of saturated liquids With accuracy of 1 -2% q. 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. 47 Zc= 0. 242 from App. B This compared to the exp. Value 29. 14 cm 3/mol. b. Compreesed liquid density: Reduced Condition Tr= 0. 764 K, Pr= 0. 887 From Fig. 3. 17

Equation of State Generalized correlation for liquids Compared to exp. data the result is higher 6. 5% Other method: 2. 38 The result is agreed with the exp. data.