Van der Waals gas

A mean-field fluid model with excluded-volume and attractive-interaction parameters, described by the Van der Waals equation. Its pressure law alone does not fix every thermal property: the caloric closure of the van der Waals equation supplies the additional internal-energy assumption.

For the one-mole Van der Waals equation with constant parameters, integrate $dF=-pdV$ 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.