On the fundamental aspect of the first Kelvin's relation in thermoelectricity

TL;DR

This paper reexamines Kelvin's first relation in thermoelectricity, revealing it reflects fundamental mechanisms of energy conversion and heat flow reorganization, beyond its traditional mathematical interpretation.

Contribution

It demonstrates that Kelvin's first relation embodies deeper physical insights into thermoelectric phenomena, beyond its conventional mathematical role.

Findings

Kelvin's first relation indicates coexistence of energy conversion and heat flow reorganization.

It challenges the view of the relation as merely a mathematical link.

The relation reveals fundamental mechanisms in thermoelectric systems.

Abstract

Kelvin's relations may be considered as cornerstones in the theory of thermoelectricity. Indeed, they gather together the three thermoelectric effects, associated respectively with Seebeck, Peltier and Thomson, to get a unique and consistent description of thermoelectric phenomena. However, their physical status in literature are quite different. On the one hand, the second Kelvin's relation is associated with the microscopic reversibility, considered as a fundamental thermodynamical property. On the other hand, the first Kelvin's relation is traditionally introduced only as a convenient mathematical relation between Seebeck and Thomson coefficients. In the present article, we stress that, contrary to common believes, this relation may demonstrates deeper insights than a bold mathematical expression between thermoelectric coefficients. It actually reflects the coexistence of two different mechanisms taking place inside thermoelectric systems: Energy conversion and reorganization of heat flow when Seebeck coefficient varies.