The calculation of the thermodynamic properties of the van der Waals fluid is not trivial and most of its properties are rarely discussed because of mathematical difficulties. I describe a numerical approach that produces the full thermodynamic behavior of the van der Waals fluid with little effort. The numerical approach is particularly useful for showing the behavior of the specific heat, the isothermal compressibility, and the coefficient of thermal expansion at and near the critical point. The results of these computations show some surprising properties and give new insights into the mean-field description of the liquid-gas transition.
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Figures similar to those in this paper were made with vpython during my thermal physics courses and can be produced from the vpython programs that are included in the supplemental materials. The figures in this paper were produced with matplotlib (<matplotlib.org>), which is a Python 2D plotting library that produces figures of higher quality for publication. Both vpython and matplotlib are excellent for teaching.
