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Grinfeld, M., Grinfeld, P., The Gibbs method in thermodynamics of heterogeneous substances carrying electric charges, Results in Physics, 6 (2016) 194-195.

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Article

Variational Method in Thermodynamics of Two-Component Charged Gas

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

2Mathematics Department, Drexel University, Philadelphia, USA


Applied Mathematics and Physics. 2021, Vol. 9 No. 1, 10-15
DOI: 10.12691/amp-9-1-3
Copyright © 2021 Science and Education Publishing

Cite this paper:
Michael Grinfeld, 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.

Correspondence to: Michael  Grinfeld, The U.S. Army Research Laboratory, Aberdeen Proving Ground, USA. Email: michael.grinfeld4.civ@mail.mil

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.

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