Contribution to a General Theory of Thermocouples

Abstract

Application of thermodynamics of irreversible processes to a thermocouple of which (a) the bars have an arbitrary shape, (b) the properties of the materials are arbitrary functions of temperature, and (c) the composition is, under certain restrictions, inhomogeneous and anisotropic, leads through introduction of a single place coordinate to two nonlinear differential equations describing the stationary distribution of temperature and electrical potential. Output powers and efficiencies are expressed in terms of the temperature gradients in the bars. The maximal values of the efficiencies obtained by variation of the shape of the bars are independent of the shape. Upper bounds of the efficiencies attainable by stationary thermoelectric conversion are derived. If the shape of the bars is restricted to general cylinders and truncated wedges or cones the transient behavior is described by two partial differential equations which contain two independent variables only. A periodic ripple in the electrical current has the same effect as a decrease of the electrical conductivities of the materials.