Thermodynamics of Electrically Conducting Fluids

Abstract

By consideration of the equations of motion and the electromagnetic theory of a moving medium, the reversible work done on a fluid, per unit mass, in a small change of state is shown to be −pd(1/ρ) + E · d(D/ρ) + H · d(B/ρ), where p is the pressure due to the joint action of the mechanical and electromagnetic changes; ρ is the density; E and B are, respectively, the electric field strength and magnetic induction; D and H are, respectively, the electric and magnetic excitation. Only the nonrelativistic version of Minkowski's theory has been used in this derivation. This formula provides the basis for a complete study of the thermodynamics of fluid medium under the action of both electromagnetic and mechanical changes. As an application, basic formulas which may be used to calculate the electrocaloric effect, the magnetocaloric effect, and electro- and magnetostriction effects are deduced. In particular, the additional pressure and pondermotive force due to these effects are obtained in a simple manner which, from the thermodynamic point of view, is better than Kortweg and Helmholtz' derivation given in the classical electromagnetic theory. As a second application, the energy equation of magnetohydromechanics is derived. The derivation is more general than previous derivations in that it does not presuppose the form of the electromagnetic constitutive equations (e.g., D = εE, B = μH) which the medium satisfies.