Heat and Gravitation. III. Mixtures

TL;DR

This paper develops a thermodynamic action principle approach to mixtures of ideal gases, incorporating gravity and chemical reactions, providing more comprehensive results than traditional methods and aligning well with observations.

Contribution

It introduces an action principle formulation for relativistic thermodynamics of gas mixtures, extending traditional models to include gravity and chemical reactions.

Findings

Derived a modified Gibbs-Dalton hypothesis under gravity.

Obtained results consistent with the Saha equation for ionization.

Demonstrated the framework's applicability to real gases like van der Waals gases.

Abstract

The standard treatment of relativistic thermodynamics does not allow for a systematic treatment of mixtures. It is proposed that a formulation of thermodynamics as an action principle may be a suitable approach to adopt for a new investigation. This third paper of the series applies the action principle to a study of mixtures of ideal gases. The action for a mixture of ideal gases is the sum of the actions for the components, with an entropy that, in the absence of gravity, is determined by the Gibbs-Dalton hypothesis. Chemical reactions such as hydrogen dissociation are studied, with results that include the Saha equation and that are more complete than traditional treatments, especially so when gravitational effects are included. A mixture of two ideal gases is a system with two degrees of freedom and consequently it exhibits two kinds of sound. In the presence of gravity the Gibbs-Dalton hypothesis is modified to get results that agree with observation. The possibility of a parallel treatment of real gases is illustrated by an application to van der Waals gases. The overall conclusion is that experimental results serve to pin down the lagrangian in a very efficient manner. This leads to a convenient theoretical framework in which many dynamical problems can be studied.