Thermoelectric Thomson's relations revisited for a linear energy converter

TL;DR

This paper revisits the thermocouple model as a linear irreversible thermodynamic energy converter, generalizing Thomson's relations and analyzing energy behavior in different operation modes.

Contribution

It introduces a generalized framework for Thomson's relations in linear converters, linking phenomenological coefficients to operation modes and extending classical thermoelectric theory.

Findings

Generalized Thomson's relations for linear converters

Relationships between phenomenological coefficients and operation modes

Analysis of energy flow in heat engine and refrigerator modes

Abstract

In this paper we revisit the thermocouple model, as a linear irreversible thermodynamic energy converter. As is well known, the linear model of the thermocuple is one of the classics in this branch. In this model we note two types of phenomenological coefficients: the first comes from some microscopic models, such as the coefficient associated with the electric conductivity, and the second comes from experimental facts such as the coefficient associated with the thermoelectric power. We show that in the last case, these coefficients can be related to the operation modes of the converter. These relationships allow us to propose a generalization of the first and second Thomson's relations. For this purpose we develop the ideas of non-isothermal linear converters, operated directly (heat engine) and indirect (refrigerator). In addition to this development we analyze the energy described by these converters.