Equations of State: Summary

The answers to the ConcepTests are given below and will open in a separate window. 
Key points from this module:
  • The ideal gas law (PVtotal = nRT) is an equation of state (EOS). It assumes no interactions between molecules and that molecules occupy no space.
  • Equations of state with additional parameters account for attractive and repulsive forces between molecules. Only cubic EOS are used in this module.
  • The parameters in the cubic EOS are calculated from critical pressures and temperatures and acentric factors.
  • A cubic equation of state can model liquid, vapor, and supercritical fluids and can also determine saturation conditions.
  • The isotherms and isobars for a three-parameter equation of state can have one or three solutions, but when three solutions exist, either one or two are physically meaningful.
  • Corresponding State Principle: all fluids have similar properties at the same values of reduced variables (e.g., at the same reduced pressure (P/Pc) and reduced temperature (T/Tc)).
  • The further the compressibility factor (Z = RT/PV) is from one, the more the fluid deviates from an ideal gas.
  • The critical point is the point where liquid and vapor phases become indistinguishable.
From studying this module, you should now be able to:
  • Calculate properties (U, S, H, A, G, V, f) of real fluids using the Peng-Robinson (PR) equation of state (EOS) spreadsheet, which also uses heat capacity data.
  • Explain why the PR cubic EOS has three roots and what the physical meaning of each root is.
  • Interpret the EOS spreadsheet results to determine which state (root) is most stable.
  • Describe what corresponding states means.
  • Sketch and interpret processes on P-V-T diagrams and their projections.
  • Calculate reduced temperature, reduced pressure, and compressibility factor.
  • Explain which terms are repulsive and which are attractive in a cubic EOS.
Additional Resource:

Screencast: Reading Compressibility Factor Charts

Prepared by John L. Falconer, Department of Chemical and Biological Engineering, University of Colorado Boulder