Entropy uniqueness determines temperature

Abstract

A thermometer is a temperature proxy, usually with a fixed number of parameters. When a nearly ideal gas or a similarly simple system is not available, the determination of a temperature scale is difficult, and has been subject to debate. Entropy uniqueness, due to Clausius, provides a fundamental theoretical criterion to answer this question. By measuring the heat flow dQ around a grid in p–V space, with M elemental areas, one can test a proposed temperature scale Tn by computing , the rms deviation, from the desired value of zero. This approach also can be used to determine which of a group of n thermometers has the most accurate temperature scale Tn. As background we discuss Clausius’s development of the mathematics and the concept of entropy. An shows how energy conservation permits one to eliminate the zigs and zags that appear in the Clausius construction for a general Carnot cycle.

Addendum on ‘Entropy uniqueness determines temperature’

“…With a specific dispute between two distinguished low temperature physicists in mind, the author recently considered [1], for a given region of p-v (pressure-volume) space, how to tell which of two temperature scales is preferable. It was shown that minimizing an rms entropy deviation, based on measuring heat flow into the system dQ m and a trial temperature scale T (with an agreed-upon number of parameters), can determine the parameters and thus determine the temperature scale.…”

“…If dQ m can be measured more accurately than P m , then temperature can be determined more accurately using dQ m . (One can imagine a space or deep sea probe whose temperature sensor has malfunctioned, and one is forced to measure temperature in an expected manner, such as proposed in [1].) However, any temperature-dependent property P m can be refined using an rms deviation method to find a dimensionless correction factor G, so that the corrected P m satisfies P = P m G. (G can depend on p and v.) In this way one can improve the accuracy of measurements of P m to make their accuracy comparable to those of dQ m , and thus dQ m -derived temperature measurements.…”