 Isothermal free-energy change of a Van der Waals gas

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.