Variational Method in Thermodynamics of Two-Component Charged Gas

Michael Grinfeld^1, and Pavel Grinfeld²

¹The U.S. Army Research Laboratory, Aberdeen Proving Ground, USA

²Mathematics Department, Drexel University, Philadelphia, USA

Cite this paper:
Michael Grinfeld and Pavel Grinfeld. Variational Method in Thermodynamics of Two-Component Charged Gas. Applied Mathematics and Physics. 2021; 9(1):10-15. doi: 10.12691/amp-9-1-3

Abstract

Based on appropriately generalized Gibbs’ variational methodology, we analyzed two-component systems with electrostatic interaction. We begin by formulating isoperimetric-type variational problems, and then proceed with calculation of the first and second variations of the corresponding functionals. The first variation is used for establishing the conditions of equilibrium of the systems under study, whereas the second – is for establishing conditions of stability of equilibrium configurations. The established conditions of equilibrium permit calculating distributions of the mass densities of the components as well as distributions of entropy (or temperature) and the electric potential. To that end, we have to solve a system of four integral equations and one algebraic.

Keywords:
plasma thermodynamics Gibbs variational principles plasma stability equations of state

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