Geometrothermodynamic description of real gases using the law of corresponding states

Abstract

We propose a geometric model for the description of the equilibrium space of real gases based on the Legendre invariant formalism of geometrothermodynamics. We investigate the curvature of three different Legendre invariant metrics and show that the corresponding singularities are related to the critical points of the response functions, the isotherms in a pressure-volume diagram, and the stability conditions. This implies that it is necessary to consider all Legendre invariant metrics to completely describe the critical behavior of real gases in terms of curvature singularities.