Thermodynamic temperature without a heat engine

Typically thermodynamics courses do not discuss how to measure absolute thermodynamic temperature T, other than heat engines based on the Carnot cycle. We show that measuring small changes in pressure ΔP, volume ΔV, and heat ΔQ for a system initially in contact with a thermal reservoir at a standard defined temperature T* at a standard point (P*,V*)—such as the triple point of a pure substance—gives T+ΔT at (P*+ΔP,V*+ΔV). This local procedure can be repeated until T(P,V) is determined for all relevant parts of (P,V) space. Understanding this procedure may help make concrete, for both students and faculty, the rather abstract quantity of temperature. It is not expected to displace current thermometric methods for measuring T, which are largely based on statistical mechanics. However, if there is a more accurate method to determine T, the current procedure may give improved values for ΔQ.