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.Keywords Thomson effect · Seebeck effect · Peltier effect · Volta effect · Piezo-thermoelectricity · Onsager relations · Thermodynamic orthogonality

Edelen’s dissipation potentials and the visco-plasticity of particulate media

“…Thus, as suggested by the example of granular dilatancy, non-dissipative forces may reflect non-dissipative and possibly non-holonomic constraints of the type envisaged by the thermodynamical treatment of Green et al [23]. On the other hand, such forces serve also to represent reversible coupling of otherwise dissipative processes, as suggested by a recent analysis of thermoelectricity [22] (which overlooks Green et al [23]). Other examples are afforded by the reversible coupling of reactions and other transport processes in biological systems.…”

“…in which the (co)vector g(x), X → X * , with g r = e •g = 0, is otherwise arbitrary and not necessarily the gradient of a scalar, and in which the fourth equality follows from (22). Substituting the decomposition g = g r e * + (I − e * ⊗ e)g into ( 54), one finds the correct form for the dissipative component η r of η, independently of the form of g.…”

“…Ziegler's orthogonality, confounded in[22] with the orthogonality represented by υ and u in (79), requires that the latter be zero.…”

Thermoelectricity: Thomson vs Onsager, with advice from Maxwell

“…In a previous work 3 , hereinafter referred to as Ref. 1, the present author provides a review of Thomson's thermoelectricity recasting it into a modern equilibriumthermodynamic form that provides a transparent interpretation of various thermoelectric quantities in terms of standard thermodynamic quantities.…”

Dissipation Potentials for Reaction-Diffusion Systems

“…Whenever the quantity D = −μ i r i is non-negative definite, it represents the dissipation in the entropy balance (Clausius–Duhem) inequality. See, e.g., the classical treatment in ref , pp 702–703, and the more recent treatments, ,,, each involving some nonessential differences in the thermodynamics. While many of the papers just cited assume that chemical kinetics are strictly dissipative, they do not avail themselves of Edelen’s potentials.…”