Empirical test of the Kelvin relation in a Bi2Te3 thermopile

Abstract

The Kelvin relation (KR) connecting the Peltier coefficient Π, the thermopower α, and the absolute temperature T via Π = αT is a cornerstone of thermoelectric (TE) physics. It is also a widely recognized example of an Onsager reciprocal relation, a foundational principle in nonequilibrium irreversible thermodynamics. While the KR is routinely invoked to understand TE systems, it has surprisingly little rigorous empirical verification. Accurate experimental tests of the KR are complicated by several factors, including non-Peltier heat flows such as Joule heating or Fourier thermal conduction, uncharacterized thermal contact impedances, and the need for Peltier and thermopower effects to be measured on the same thermopile at the same temperatures. Most empirical assessments of the KR have either made questionable simplifications or been limited in accuracy to several percent. Here, we present a test of the KR that is free of the difficulties of prior experiments and relies only on conventional voltage, current, and temperature measurements, so that it could be performed on any thermopile. Conducting the test on a Bi2Te3 thermopile, the empirical ratio Π/α is found to equal T within a relative deviation < 0.5% for T in the range of 320–340 K. This result is quantitatively consistent with the KR and justifies the use of the KR in TE applications to reasonably high accuracy.