Cubic Equation of State for the Compressibility Factor

In the Soave–Redlich–Kwong (SRK) equation of state (EOS), the compressibility factor occurs as a solution of the following cubic equation:
,
where and with , , , and . Here is the acentric factor, and are the critical temperature and pressure, and = is the reduced pressure.
When and are greater than one, the supercritical behavior is observed with varying continuously between low (close to zero, liquid-like behavior) and high values (near one, vapor-like behavior).
For specific values of and (when , the saturation pressure, and ), one gets three roots with the smallest and largest corresponding to the liquid and vapor phases. The intermediate value of has no physical significance.
The Demonstration plots for ethane (, , and ) and displays the location and values of its real roots.

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