On the Thermoelectricity of W. Thomson: Towards a Theory of Thermoelastic Conductors

Abstract

Thomson’s classical analysis (1851, 1854a, 1854b) of thermoelectricity is cast into a modern form by means of contemporary thermodynamic methods based on the introduction of a free energy depending on strain, electrical charge and temperature. The present analysis identifies the phenomenological coefficients in Thomson’s theory in terms of standard thermodynamic functions derivable from the free energy, lending support to the interpretation of his relations as authentic thermostatic relations. As an extension of Thomson’s theory, the present work provides an analysis of the effect of tensile stress or pressure on thermoelectricity. As a counterpoint to the analysis of Boltzmann (1877) and the representation of Onsager (1931), it is argued that the Onsager relations must be modified to include thermodynamically orthogonal forces and fluxes of the type identified by Ziegler (1970) and Edelen (1974). This allows for reversible coupling between the flow of heat and electricity postulated by Thomson and suggests the possibility of non-dissipative heat flux associated with microscopic thermoelectric effects. The present analysis does not include a description of superficial charge concentration in conductors, which poses an interesting challenge for further analysis.