Relationship of thermoelectricity to electronic entropy

Abstract

It is shown that $S_X$, the partial molal entropy of electrons in material $X$, is given by $S_X=-F{\alpha }_X$, where $F$ is Faraday's constant and ${\alpha }_X$ the absolute thermoelectric power of $X$. This result depends on three propositions. (1) The Kelvin relations are valid for all thermoelectric materials. (2) Under isothermal conditions, the Peltier effect is truly reversible. (3) For a degenerate free-electron Fermi gas, the thermoelectric power is proportional to the entropy.