Liquid-vapour coexistence of molecular fluids

We derive, for a liquid-vapour system with pairwise interactions, an infinite set of sum rules relating the pressure and temperature to integrals over the density profile and pair correlation function. For approximate forms for the variation of the pair correlation function through the liquid-vapour interface, these sum rules reduce to equations describing the coexistence curve of the fluid. Good agreement with experiment is obtained for all fluids considered.