Isotherms of Peng-Robinson Equation of State

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Equations of state, determined empirically or theoretically, can determine the thermodynamic properties of fluids. Equations of state correlate the temperature, pressure, and volume of fluids.


Because of its simplicity, the Peng–Robinson equation of state (a cubic equation) is extensively used to predict the behavior of several fluids with reasonable accuracy. Its input parameters are the critical temperature, critical pressure, and accentric factor.

A common way to represent equations of state is to plot isotherms in the - plane. This Demonstration plots isotherms of a generic fluid, showing the influence of the parameters on the shape of the curves.

The critical isotherm is shown as a reference. Cubic equations have distinct characteristics for temperatures above and below the critical point.

Cubic equations can produce metastable regions and non-physical regions (negative pressures, for example).


Contributed by: Fábio Fortkamp (August 2013)
Open content licensed under CC BY-NC-SA



Snapshot 1: temperatures below critical value

Snapshot 2: temperatures above critical value

Snapshot 3: combination of parameters that produce non-physical negative pressures


[1] J. R. Elliot and C. T. Lira, Introductory Chemical Engineering Thermodynamics, Upper Saddle River, NJ: Prentice Hall, 1999.

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