Geometrothermodynamics of van der Waals systems

TL;DR

This paper applies geometrothermodynamics to analyze the phase transition structure of van der Waals systems, revealing curvature singularities corresponding to phase transitions in a potential-independent manner.

Contribution

It introduces a Legendre invariant formalism to study the equilibrium space of van der Waals systems, providing a comprehensive analysis of phase transitions.

Findings

Identifies all curvature singularities linked to phase transitions.

Demonstrates the invariance of results under different thermodynamic potentials.

Shows the formalism's effectiveness in systems with two thermodynamic degrees of freedom.

Abstract

We explore the properties of the equilibrium space of van der Waals thermodynamic systems. We use an invariant representation of the fundamental equation by using the law of corresponding states, which allows us to perform a general analysis for all possible van der Waals systems. The investigation of the equilibrium space is performed by using the Legendre invariant formalism of geometrothermodynamics, which guarantees the independence of the results from the choice of thermodynamic potential. We find all the curvature singularities of the equilibrium space that correspond to first and second order phase transitions. We compare our results with those obtained by using Hessian metrics for the equilibrium space. We conclude that the formalism of geometrothermodynamics allows us to determine the complete phase transition structure of systems with two thermodynamic degrees of freedom.