= Isothermal free-energy change of a Van der Waals gas
{title2=$\Delta F=-RT\ln[(V_2-b)/(V_1-b)]+a(1/V_1-1/V_2)$}
For the one-mole <Van der Waals equation> with constant parameters, integrate $dF=-p\,dV$ along an isotherm to obtain the displayed difference. The attractive contribution has a positive change on expansion, whereas the translational term lowers free <energy>. Thermodynamic consistency independently gives $\Delta U=a(1/V_1-1/V_2)$ and $\Delta S=R\ln[(V_2-b)/(V_1-b)]$. These homogeneous-branch expressions are not a substitute for equilibrium convexification through a subcritical coexistence region.
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