On the Laws of Thermodynamics in Classical Non-Inertial Frames

TL;DR

This paper provides a rigorous mathematical analysis demonstrating that the fundamental thermodynamic laws and key quantities remain invariant under transformations between non-inertial reference frames in classical mechanics.

Contribution

It introduces a strictly mathematical methodology to analyze thermodynamic laws in non-inertial frames, proving their invariance under spatial transformations.

Findings

Thermodynamic laws are invariant in non-inertial frames.

Main thermodynamic quantities do not change under non-inertial transformations.

Transformation laws for temperature, pressure, and other quantities are established.

Abstract

This work consists in the theorical development on the analysis of the Thermodynamic Laws and thermodynamic systems in relative motion, according to the laws of Classical Mechanics. The difference of this work for many of the literature is the methodology used. We follow a strictly mathematical line, instead of a phenomenological line. We proved that the First and Second Laws of Thermodynamics in non-inertial frames remain invariant under any spatial translation between reference frames in motion. From the results obtained, we show the transformation of the main thermodynamic quantities as temperature, pressure, chemical potential, internal energy, heat, state equation for an ideal gas and efficiency of Carnot's machine are also invariant under any transformation between non-inertial reference frames.