Thermodynamics of electroquasistatic systems: The parallel plate capacitor

Abstract The thermodynamics of electroquasistatic systems is considered using the parallel plate capacitor. This simple system facilitates rigorous analysis of the field and is used to derive directly the dielectric chemical potential of dielectric materials which are subject to different constraints. The constraints are imposed on field and geometrical variables and on physical parameters of the contents of the capacitor. Different constraints yield different forms of the dielectric chemical potential depending on the energy exchange between the field and coupled current and mechanical sources. If the constraints impose an increase in the energy that is stored in the field as mass is added to it, then the dielectric chemical potential turns out to be positive. The reverse is also true. In an ideal lossless system, the stored energy can be retrieved electrically and mechanically. It is shown that the dielectric chemical potential of a dielectric which exists in one region of the capacitor can be a function of the properties of this region, as well as those of the rest of the capacitor. In this sense, isolation of regions in the capacitor, with respect to changes of energy due to addition of mass, may not be physically meaningful. Finally, the effect of the polarization energy stored in a dielectric ionized solution in the context of the electrochemical potential is considered. It is shown that the electrochemical potential consists of terms due to chemical, and primary and secondary field-charge interactions. The well-known electric potential energy density of single charges gives rise to the primary effect, whereas the dielectric energy density stored in a polarized ionic solution is the reason for the secondary effect.