Thermoelectrical potential and derivation of Kelvin relation for thermoelectric materials

Current research on thermoelectricity is primarily focused on the exploration of materials with enhanced performance, resulting in a lack of fundamental understanding of the thermoelectric effect. Such circumstance is not conducive to the further improvement of the efficiency of thermoelectric conversion. Moreover, available physical images of the derivation of the Kelvin relations are ambiguous. Derivation processes are complex and need a deeper understanding of thermoelectric conversion phenomena. In this paper, a new physical quantity 'thermoelectrical potential' from the physical nature of the thermoelectric conversion is proposed. The quantity is expressed as the product of the Seebeck coefficient and the absolute temperature, i.e., ST. Based on the thermoelectrical potential, we clarify the conversion of the various forms of energy in the thermoelectric effect by presenting a clear physical picture. Results from the analysis of the physical mechanism of the Seebeck effect indicate that the thermoelectrical potential, rather than the temperature gradient field, exerts a force on the charge carriers in the thermoelectric material. Based on thermoelectric potential, the Peltier effects at different material interfaces can be macroscopically described. The Kelvin relation is rederived using the proposed quantity, which simplified the derivation process and elucidated the physical picture of the thermoelectrical conversion.