The central role of the Peltier coefficient in thermoelectric cooling

Abstract

This paper discusses the special role that the Peltier effect plays in thermoelectric cooling. From a particular energy balance for a thermocouple, we can conclude that the Peltier component pumps out the energy of all other terms: Joule, Fourier, Seebeck, and thermoelectric cooling. We emphasize also that in this energy balance, there is a need to include a new contribution, named after Seebeck that usually is not considered in the literature. We discuss a new method to evaluate the Peltier coefficient using measurements of the two temperature gradients at the junction of a thermocouple. An arrangement has been built to explore this method. A precise value for the Peltier coefficient of a thermocouple has been obtained but which deviates from the Kelvin relation. A better design of the experimental device is needed.

On the different formalisms for the transport equations of thermoelectricity: A review

“…On the contrary, the Thomson coe cient can be measured in a single conductor, using an integrated form of (22) [38,40,49]. Absolute values of the Seebeck coe cient have, nevertheless, been calculated from the temperature dependence of the Thomson coe cient or assigning a zero value to the Seebeck coe cient of a superconductor.…”

“…Remarkably, equation (18) shows that the measured electric potential di erence 2 − 1 is related to the Seebeck coe cient in the electrochemical formalism. Because voltages are measured more easily than heat generation, the Peltier coe cient is often evaluated from Thomson's relation [9,39,40], but its relative value between two conductors can be measured. The rst term in the right-hand side of (18) vanishes, regardless of the temperature distribution, if the circuit between points 1 and 2 is made of only one conductor; a statement closely related to the law of homogeneous materials [24].…”

“…Recently, a new formulation of the thermoelectricity transport equations based on experimentally observable quantities has been proposed [36][37][38][39][40]. The observable electric potential when the potential di erence in (18) is measured with probes of material R is de ned as [36][37][38] …”

“…The e ect is obviously independent of our choice of uxes and forces, but it can be illustrated with the greatest simplicity in terms of the ux of energy (internal plus electrostatic). The total energy ux density E is widely employed as the "thermal" ux density [2,23,30,[38][39][40]44], and (7) allows us to identify the corresponding "electrical" driving force as e = ∇(̃ / )/ . Contrarily to e in other formalisms, named after their associated electric potential, the driving force ∇(̃ / )/ cannot be interpreted as the negative gradient of an electric potential.…”

“…Novel recent approaches to the subject [36][37][38][39][40] are also discussed. The prevalence of the electrochemical formalism is explained.…”