Generalized van der Waals equation of state

The quantitative thermodynamic effect of adding a weak, long-range attraction to inverse-power repulsive potentials is studied. The resulting phase diagrams exhibit two fluid phases and a solid phase, a critical point, a triple point, and, for sufficiently soft repulsions, an additional solid phase with an additional triple point. The effects of attractions other than van der Waals’ are studied too by using a simple analytic model for the canonical partition function. Although such models exhibit a wide variety of thermodynamic behavior, they are still not general enough to reproduce the results of high-temperature measurements on liquid metals.