Thermodynamics of ideal gases in quasistatic electromagnetic fields.

Abstract

The thermodynamics of ideal gases in the presence of quasistatic electromagnetic fields is considered. It is shown that thermodynamic properties of continua, in the presence of these fields, can be characterized by two conjugate sets of variables consisting of three extensive field-independent, and three intensive field-dependent variables. These sets are entropy, volume, and mass, i.e., {S,V,N}, and field-dependent temperature, pressure, and chemical potential, i.e., {T^,P^,\ensuremath{\zeta}}, respectively. The second set has the same thermodynamic role as {T,P,\ensuremath{\zeta}} that prevails in the absence of fields. In this context, T^, P^, and \ensuremath{\zeta}^ must be uniform at equilibrium and, consequently, T, P, and \ensuremath{\zeta} can have discontinuous jumps across interfaces that separate materials of different electromagnetic properties. Ideal gases that follow the Langevin equation are affected by a fixed B field, so that T^ increases, whereas both P^ and \ensuremath{\zeta}^ decrease as compared to their values in the absence of the field. The equation of state of ideal gases in fields has been formulated in terms of T^ and P^. Using this equation, it is shown that the change in the pressure P, which is induced by the field, is positive at fixed B, whereas it is negative, but smaller, if H is fixed. Magnetic susceptibilities are defined at either fixed density, or at fixed pressure as two distinct and different thermodynamic variables. The susceptibility at fixed density follows the Curie-Wiess law. In contrast, the one defined at fixed pressure, being inversely proportional to the temperature squared, follows a different law. The fundamental equation of ideal gases in the presence of magnetic fields is derived. The field-dependent energy \^U is shown to be a function of S, V, and N and of the field-dependent entropy \ifmmode \hat{S}\else \^{S}\fi{}, and vice versa. Both \^U and \ifmmode \hat{S}\else \^{S}\fi{} are functions of S, V, and N and the magnetic induction B. Field-dependent specific heats of ideal gases, and relations between them, have been formulated under different constraints. At fixed B, the field-induced increase in the specific heat is proportional to the ratio of magnetic to thermal energy squared. Ideal gases that are contained in discrete systems, under the action of magnetic fields, follow an equation of state that can be different than the one which is applicable for cases involving continua. This equation of state is not unique in the sense that it consists of field-dependent variables which are functions of the geometry of the discrete system, and their forms vary according to the constraints imposed on the discrete system and its surroundings. In the presence of fixed intensity magnetic fields, mixtures of permeable ideal gases are shown to satisfy the Gibbs theorem, and, at fixed B, their entropy of mixing is larger than the value prevailing when the field is absent. Finally, the formulas and results obtained for ideal gases in magnetic fields can be applied to ideal gases in electric fields, through appropriate replacement of magnetic variables by their electric counterparts. \textcopyright{} 1996 The American Physical Society.