2018/03/02 by Shawn W. Walker, Walker, Shawn W. · 1 citation
Physics and Astronomy · Chemistry · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Dynamics #Advanced Physical and Chemical Molecular Interactions
paper · pdf · doi:10.48550/arxiv.1803.08136
Various types of equilibrium processes involve electric fields. In some\ncases, the electrical energy appears to be negative (e.g. if the voltage is\nfixed by an external source). This paper explains how to derive the correct\nthermo-dynamic potential for electro-static phenomena, whether the voltage is\nfixed, or the charge is fixed, or some combination is fixed. In particular, we\nexplain, in complete detail, why fixing the voltage introduces "a minus sign"\nin the electrical energy.\n Two explanations are given. The first explanation is based on a\nlumped-parameter argument (i.e. a lumped-capacitor model). The second\nexplanation uses a distributed parameter model (i.e. a partial differential\nequation (PDE) model) of a dielectric medium, in this case, we allow for\nnon-linearity and external polarization effects. Connections with Legendre\n(duality) transforms are also discussed.\n