A new succinct proof on the equivalence of the Nernst equation and the vanishing heat capacity at absolute zero temperature

TL;DR

This paper demonstrates the theoretical equivalence between the Nernst equation and the vanishing heat capacity at absolute zero, providing a new proof based on thermodynamic principles.

Contribution

It introduces a succinct proof establishing the mutual deducibility and equivalence of two fundamental thermodynamic concepts.

Findings

Nernst equation and heat capacity at absolute zero are equivalent

The proof is based on Euler chain rule of thermodynamic quantities

Discussion on existing literature's conclusions

Abstract

By starting from the Euler chain rule of three thermodynamic quantities, it is proved that both the Nernst equation and the vanishing heat capacity at absolute zero temperature are mutually deducible and equivalent. Simultaneously, it is pointed out that the conclusions of the relevant literature are worthy of discussion.