Thermodynamic Equilibrium of Multi-Temperature Gas Mixtures

Abstract

This theoretical paper deals with the thermodynamic equilibrium of multi-temperature gas mixtures. After a brief review of basic notions and methods relative to the chemical equilibrium of gas mixtures in complete thermal equilibrium, the fundamental relations energy and entropy describing the thermodynamics of gas mixtures in disequilibrium with respect to energy and mass exchanges are formally introduced. Possible constraints arising from the subset of state parameters associated with the molecular degrees of freedom are recognized and the importance of the role they play in determining the thermodynamic equilibrium of the system is discussed. In particular, the influence that a partially constrained thermal equilibrium exercises on the equations governing the associated chemical equilibrium is made evident by performing the equilibrium analysis for the cases of entropic and energetic freezing of the molecular degrees of freedom; the analysis shows that the minimization/maximization of energy/entropy may not necessarily lead to the vanishing of the chemical reaction affinities and that, therefore, the uniqueness of the chemical equilibrium equations is lost when the thermal equilibrium is partially constrained. The equivalence of the fundamental relations energy and entropy to determine the equilibrium conditions is shown to be maintained also in multi-temperature circumstances; the problem of the lack of such equivalence for the Helmholtz and Gibbs potentials is briefly mentioned. As an application, the chemical equilibrium of a two-temperature partially ionized gas is considered with the purpose to show how the uncertainty associated with the two-temperature Saha equation can be resolved in the framework of the theory proposed in this work.