A Direct Entropic Approach to Uniform and Spatially Continuous Dynamical Models of Thermoelectric Devices

Abstract

If we accept temperature and entropy as primitive quantities, we can construct a direct approach to a dynamical thermal theory of spatially continuous and uniform processes. The theory of uniform models serves as a simple entry point for learners of modern thermodynamics. Such models can be applied fruitfully to an understanding of (the dynamics of) thermoelectric processes and devices. Entropy, temperature, charge, and voltage allow us to describe the role of energy concisely, and constitutive quantities can be given their natural entropic interpretation. In this paper, aggregate dynamical models of a Peltier device will be created and simulations will be compared to non-steady-state experimental data. Such overall models give us a simple image of the transport of charge and transport, production, and storage of entropy and can be easily extended to the spatially continuous case. Process diagrams for a uniform model can be used to visualize these processes and the role of energy. Device efficiency can be easily read from the model. Apart from external parameters such as load resistances or temperature differences, it depends upon three parameters of the device: internal electric resistance, entropy conductance, and Seebeck coefficient. The Second Law efficiency of a generator suggests how to define the figure of merit (zT) of the thermoelectric material. Distinction between ideal and dissipative processes and the rates at which energy is made available or used allows us to construct a simple argument for the equality of the Seebeck and Peltier coefficients.