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Evaluating Volumetric and Other Thermodynamic Properties by Means of Cubic Equations of State

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Abstract

The use of equations of state to evaluate volumetric properties is straightforward for students, at least when the ideal gas equation of state is used. The application of a more complicated equation of state, for example a cubic equation, is a little more difficult, especially for the determination of volume. In addition, the use of such equations to determine some other thermodynamic properties is extremely complex for students both from the numerical and theoretical point of view.

The use of Maple to solve involved equations, to manage obtained functions, and to display functional dependencies allows students to obtain required numerical values as well as to understand the meaning of the calculations.

This work is related to the evaluation of non idealities from several points of view. The Maple sheet allows students to determine volumetric properties and compare values obtained from the ideal gas, the Van der Waals (VW), and the Soave (SRK) equations of state. Several aspects of the calculation such as the effect of pressure, the lowest available volume, the number of roots, and the relation between volume and compressibility factor are analyzed.

Additional thermodynamic properties are considered. Fugacity coefficient and residual enthalpy are determined from well known thermodynamic relationships and the SRK equation of state. Deviations from ideality are analyzed in terms of all the functions determined.

Figure 1. Pressure as a function of volume plot of the ideal (solid black line), Van der Waals (dashed blue line), and Soave, Redlich, and Kwong (dotted red line) isotherms at 115 K in the volume range 0.03 to 2 L.

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Maple 10	CubicEquationsOfState.mw

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Maple 10	CubicEquationsOfState.pdf

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Keywords

Audience: Upper-Division Undergraduate;

Domain: Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Gases; Mathematics / Symbolic Mathematics; Thermodynamics;

JCE Citation