#### 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 (PV
^{total}= 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/P
_{c}) and reduced temperature (T/T_{c})). - 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*