Chem. Eng. Thermodynamics (TKK-2137) 14/15 Semester 3 Instructor: Rama Oktavian Office Hr.: M.13-15, Tu , W , Th , F

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

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

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 Isothermal compressibility Thus: See example 3.1

Equation of State PVT Relationship?? If  and  is constant (for liquid) Simple EoS The value of  and  has been determined for some of liquids PVT relationship

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

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

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) C Cair+Uap V P TcTc T>T c T<T c VLVL V 1. Van der Waals EoS (1873) volume Intermolecular attraction If b=0 and a/V 2 =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, 4 th ED., 1986) EQUATIONuwba VAN DER WALLS 00 REDLICH- KWONG 10 SOAVE- REDLICH- KWONG 10 PENG- ROBINSON 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: T r = T/T c and P r = P/P c  accentric factor is based on vapor pressure at T r = 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) 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 “  ” by K. S. Pitzer and coworkers

Equation of State Generalized correlation EoS 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, AIChE J., 21, (1975) provided in App. E, p. 667

Equation of State Generalized correlation EoS Tne nature of The Lee/Kesler correlation for Z 0 = F 0 (T r,P r ) The Lee/Kesler correlation provides suitable results for gases which are nonpolar and slightly polar

Equation of State Generalized correlation EoS 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, (see p , Poling et al.2001 “The properties of gases and liquids 5 th ed. MCGRAW-HILL Int. Ed.)

Equation of State Generalized correlation EoS 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% <2% differ (straight lines) Lee/Kesler corr (points)

Equation of State Generalized correlation for liquids  Rackett equation (Racket, J. Chem. Eng. Data, 15 (1970) : estimation of molar volume of saturated liquids  Lyderson, Greenkorn and Hougen: estimation of liquid molar volume With accuracy of 1-2%

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= K, Vc= 72.47Zc= from App. B This compared to the exp. Value cm3/mol. b. Compreesed liquid density: Reduced Condition  Tr= K, Pr= From Fig. 3.17

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