This Demonstration plots the enthalpies and entropies for a real gas and an ideal gas as a function of temperature, relative to a reference state at a selected pressure and temperature, using the Peng–Robinson equation of state and ideal-gas heat capacities. Select argon, benzene, or carbon dioxide with buttons. For each gas, the temperature scale is adjusted so the plots are only shown above the critical temperature. Select enthalpy or entropy departure function, which is the difference between the thermodynamic property (enthalpy, entropy) for a real gas and an ideal gas at the same temperature and pressure. You can vary the pressure with the slider. Select "compare departure functions" to view departure functions for all three gases as a function of temperature at 15 MPa. Click "show labels" to label each departure function curve with the corresponding gas.
Enthalpy H and entropy S are calculated using the Peng–Robinson equation of state (EOS) for a real gas and the ideal gas law for an ideal gas:
where H is in kJ/mol and S is in J/[mol K]; the superscript ig represents an ideal gas, the subscript R refers to the reference state, and (H − Hig) and (S − Sig) are the enthalpy and entropy departure functions for a real gas calculated from the Peng–Robinson EOS, while HRig and SRig are the ideal gas enthalpy and entropy at the reference state.
where CpA, CpB, CpC, and CpD are heat capacity constants (Cp = CpA + CpB T + CpC T2 + CpD T3), T is temperature (K), and P is pressure (MPa).
where Z is the compressibility factor, Tr is the reduced temperature (dimensionless, not to be confused with TR), Tc is the critical temperature (K), ω is the acentric factor, and κ and α are constants.
where A and B are constants, Pr is the reduced pressure (dimensionless, not to be confused with PR), and Pc is the critical pressure (MPa).
These equations are used to calculate the compressibility factor Z:
where q, r, m, a2, a1, and a0 are constants used for simplification.
This simulation was created in the Department of Chemical and Biological Engineering at University of Colorado Boulder for LearnChemE.com by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a Mathematica simulation by Rachael L. Baumann and Neil Hendren. It was prepared with financial support from the National Science Foundation (DUE 2336987 and 2336988) in collaboration with Washington State University. Address any questions or comments to LearnChemE@gmail.com.