In this work, we develop the general theory for analyzing the thermodynamic consistency of the Richardson–Duhmann model for vacuum thermionic energy converters. In addition to the electron fluxes from emitter to collector and vice versa, we calculate the energy and entropy fluxes associated to them. The calculation of the entropy fluxes is what allows us to conclude that the model is consistent by verifying that both at the emitter and at the collector the entropy generation rate is positive. In the process, we review the Richardson–Duhmann model in order to assure that the assumptions we make for calculating the energy and entropy fluxes are consistent. We also generalize the Richardson–Duhmann model in order to consider Fermi–Dirac statistics.
Theory and performance of auxiliary discharge thermionic energy converters