The theory of nonequilibrium thermodynamics for inherently irreversible coupled processes is presented and the concept of heat is incorporated appropriately. The theory was applied to the problem of a solid carrying electric and heat currents in the presence of an external magnetic field. The principle of increase of entropy was employed to determine the reversibility or irreversibility of the macroscopic effects involved and to determine the limits on the material’s properties. The dynamic equations show that, in the one-dimensional thermoelectric case, the heat current is not coupled to the electrical phenomenon. In two and three-dimensional cases, the heat current is coupled to the electrical phenomenon only through the influence of the external magnetic field. Areas of disagreement with the literature are pointed out and discussed.

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