Thermodynamics of phase transitions and chemical reactions in the presence of quasistatic electromagnetic fields

Abstract

Phase transitions and chemical reactions in the presence of electromagnetic fields are considered. The field-dependent differential of the internal energy is described using four basic independent terms. These terms stand for the differentials of heat T-hatdS, mechanical work -P-hatdV, work associated with mass transfer \ensuremath{\zeta}-hatdN, and work delivered by the current source VH\ensuremath{\cdot}dB. In this context, the field-dependent temperature T-hat, pressure P-hat, and chemical potential \ensuremath{\zeta}-hat are the intensive conjugates of the field-independent entropy S, volume V, and mass N, respectively. In this context isothermal and isobaric processes in the presence of the field must satisfy the condition of fixed T-hat and fixed P-hat, respectively. In an isothermal process, the heat delivered to a system where an entropy change \ensuremath{\Delta}S occurs is T-hat\ensuremath{\Delta}S. Consequently, the latent heat of phase transition l-hat, which is T-hat\ensuremath{\Delta}s, is T-hat/T times its value in the absence of the field. An extended Clausius-Clapeyron equation is derived, where the effect of the field is expressed in terms of an equivalent entropy change due to the phase transition. Different forms of mass action laws are formulated, so as to account for the effect of the field on pressures or activities of reactants and products of chemical reactions. These pressures, or activities, are modified by field-dependent factors, so that the reaction constant remains a sole function of temperature, irrespective of the presence or absence of the field. For permeable materials, these correction factors are positive, but less than unity, and their effect is to increase the corresponding pressures, or activities, above their 'field free' equilibrium values. The van't Hoff equation for a single reaction is extended in terms of the change in the heat of reaction due to the presence of the field. Simultaneous reactions that in the absence of the field are independent, become interdependent when the field is present through their collective effect on the mixture permeability. The effect of replacing the constraint of a fixed B field, by a fixed H field, is shown to result in reversal of the effect of the field on phase transitions and chemical reactions. Finally, it is shown that on a molecular scale of paramagnetic substances such as paramagnetic ideal gases, the magnetic effect is expected to be significant at low cryogenic temperatures. At sufficiently low temperatures, this effect can become dominant. At ordinary temperatures, the field can have a dominant effect on colloidal particles having diameters of a few nanometers and larger.