On the impossibility of isothermal heat transfer and its implications for thermal physics

TL;DR

This paper explores the fundamental impossibility of isothermal heat transfer, proposing a revised entropy expression for ideal gases that challenges traditional statistical interpretations and enhances understanding of thermodynamic entropy.

Contribution

It derives a volume-independent entropy expression for ideal gases and establishes a new general relation between entropy and internal energy, questioning classical assumptions.

Findings

Revised entropy expression for ideal gases independent of volume

Demonstrates incompatibility of classical entropy with internal energy

Provides a new thermodynamic relation linking entropy and internal energy

Abstract

The physical impossibility of heat transfer under isothermal conditions implies that the classical expression for the entropy of the ideal gas may not be compatible with the internal energy of the gas itself. A corrected expression of the ideal gas entropy is derived here. It is independent on volume. This result is shown to be at a variance with the statistical interpretations of entropy as a quantity that is related to the number of microstates compatible with the macroscopic state of the system. It also offers a better understanding of the thermodynamic notion of entropy. The present analysis also establishes a general equation that links the entropy of a system to its internal energy.