The equilibrium manifold of the van der Waals gas

Abstract

We investigate the geometric properties of the equilibrium manifold of a thermodynamic system, determined by the Van der Waals equation of state. We use the formalism of geometrothermodynamics to obtain results that are invariant under the Legendre transforms, that is, independent of the choice of the thermodynamic potential. The most important concepts of geometrothermodynamics are presented and explained in a simple way, without the use of technical mathematical details. The metric of the equilibrium manifold is calculated in explicit form through the corresponding coordinates, which can be interpreted as the internal energy and volume of the gas. It is proved that the equilibrium manifold is curved due to the existence of thermodynamic interaction. This means that there is an interaction between the gas particles, which disappears in the ideal gas limit. In addition, it is proved that the curvature singularities are located at those points where first-order phase transitions occur.