On the equivalence of the Nernst theorem and its consequence

TL;DR

This paper demonstrates that the Nernst theorem and its derived consequence are equivalent, providing insights into heat capacities at ultra-low temperatures and introducing a new research method in thermodynamics.

Contribution

It rigorously proves the equivalence between the Nernst theorem and its consequence, and derives the temperature dependence of heat capacities at ultra-low temperatures.

Findings

Heat capacities approach zero as temperature approaches absolute zero.

Derived the general form of heat capacities at ultra-low temperatures.

Provided a new research method based on the consequence of the Nernst theorem.

Abstract

One general consequence of the Nernst theorem is derived, i.e., the various heat capacities of a thermodynamic system under different constraints approach zero as the temperature approaches absolute zero. The temperature dependence of the heat capacity of any thermodynamic system at ultra-low temperatures is revealed through this consequence. Moreover, the general form and the simplest expression of the heat capacities of thermodynamic systems at ultra-low temperatures are deduced. Some significant discussion and results are given. One new research method is provided by using this consequence. Finally, the equivalence between the Nernst theorem and its consequence is rigorously proved, so that this consequence may be referred to another description of the third law of thermodynamics.