Use of crystal polymorphs for resolving an equilibrium liquid’s state on supercooling to 0 K

There are two ways by which an equilibrium liquid’s heat capacity, Cp,liq, is seen to decrease to zero on cooling to 0 K: (i) decrease abruptly first to the Cp of its ordered crystal at T>0 K, and thereafter the crystal’s Cp decrease to zero at 0 K, and (ii) decrease continuously to zero at 0 K. The prohibitively long time needed for Cp measurements at sufficiently low temperatures has prevented one from determining the relative merits of these two inferences. Here, we propose a method for doing so by a comparative analysis of the Cp data of an equilibrium liquid and of its two crystalline forms, one of which is orientationally disordered. The method is then used to test these merits with the available Cp and entropy data of ethanol. The results support the inference of a continuous decrease in Cp to zero at 0 K, but not that of an abrupt decrease.