Clausius Implies That Nearly Anything Can Be A Thermometer

Wayne M. Saslow

Published 2023-01-25Version 1

There are three types of thermometries. Two are proxies, such as the purely phenomenological resistivity, and those based on statistical mechanics, such as the ideal gas law. The third type is a class of previously described thermodynamic temperature scales based on Clausius and heat flow $dQ$. Such temperature scales are determined by heat inputs $dQ$ satisfying the Clausius condition $\oint dQ/T = 0$ for every closed path in a given region $\Omega$ of $p,V$ space. Thus any stable material can be used as a thermometer. Although a discretized grid $i$ (from which such paths can be composed) leaves $T(p,V)$ underdetermined, even after a temperature $T_0(p_0,V_0)$ is specified, the temperature $T(p,V)$ everywhere within $\Omega$ can be determined by a root-mean-square minimization of $\sum_{i} (\oint_i dQ/T_n)^2$ for some trial temperature function $T_n$. If the Clausius-based method gives a temperature scale of lower accuracy than the best proxy temperature scale, then that proxy temperature scale can be employed with the rms Clausius condition method to improve the accuracy of (i.e., raise the standards for) the dQ measurements to the accuracy of the proxy-based temperature scale.