Temperature entropy analysis of a solid state thermoelectric cooling device

This article presents a general thermodynamic framework for the operation of a thermoelectric cooler using the Gibbs law and simple energy balance derived from the Gauss theorem. The methodology demonstrated herein bridges the different approaches normally employ by physicists and engineers where the irreversible thermodynamic formulation is cast using the appropriate engineering variables, namely the Joule, Peltier and Thomson heat as well as the material properties. An expression for the entropy flux is expressed in terms of the key parameters employed for the thermoelectric operation. Following the classical temperature-entropy (T-s) formulation, which has all the virtues of energy flow identification, the processes along the p-n legs of the thermoelectric module, contributing to both useful and dissipative losses, are clearly mapped and discussed.