The uniqueness of the integration factor associated with the exchanged heat in thermodynamics

TL;DR

This paper proves that only 1/T can serve as the integration factor for exchanged heat in thermodynamics, challenging the definition of entransy as a state function and highlighting errors in previous derivations.

Contribution

It establishes the uniqueness of 1/T as the integration factor for exchanged heat, invalidating other proposed state functions like entransy.

Findings

Only 1/T can serve as the integration factor for exchanged heat.

The definition of entransy as a state function is incorrect.

Errors exist in derivations assuming constant heat capacity C_V.

Abstract

State functions play important roles in thermodynamics. Different from the process function, such as the exchanged heat $\delta Q$ and the applied work $\delta W$, the change of the state function can be expressed as an exact differential. We prove here that, for a generic thermodynamic system, only the inverse of the temperature, namely $1/T$, can serve as the integration factor for the exchanged heat $\delta Q$. The uniqueness of the integration factor invalidates any attempt to define other state functions associated with the exchanged heat, and in turn, reveals the incorrectness of defining the entransy $E_{vh}=C_VT^2 /2$ as a state function by treating $T$ as an integration factor. We further show the errors in the derivation of entransy by treating the heat capacity $C_V$ as a temperature-independent constant.