Empirical Test of the Kelvin Relation in Thermoelectricity

The Kelvin relation (KR) π = αT, where π the Peltier coefficient, α the thermopower, and T the absolute temperature, was derived in 1851, and is a cornerstone in thermoelectricity. In 1931 Onsager showed the Kelvin relation is a specific case of a reciprocal relation governing coupled linear force-flow processes in nonequilibrium thermodynamics. While generally accepted in theory, the KR has proven difficult to verify experimentally due to problems with measuring π independently. Here, we present an accurate way to empirically test the Kelvin relation using a new method to determine π that is free of Joule heating, self-corrects for Fourier conduction, and does not require knowing any material properties of the thermoelectric materials under test. Our test measures (π /α) at several different values of temperature difference ΔT= (T_H - T_C) but with the same value of T_Av = ½(T_H + T_C). If ΔT is small enough, then the validity of the KR means the measured (π /α) should be a constant equal to T_Av of the thermopile under test, independent of ΔT and insensitive to thermal contact resistances. We will present the results of such measurements taken on a Bi₂Te₃ thermopile, where we found the KR is valid to within the measurement uncertainty of ≤ 0.5% for ΔT up to 50 K with T_Av = 330.20K. Finally, the limits of the linear response assumption will be discussed.

Supported by NSF award no. DMR-2206888.