Mechanics and thermodynamics: A link between the two theories

TL;DR

This paper explores the fundamental connection between mechanics and thermodynamics, emphasizing the importance of a proper internal energy formulation to unify fluid mechanics and thermodynamic principles.

Contribution

It clarifies how the principle of virtual work with an appropriate internal energy links mechanics and thermodynamics in fluid mechanics.

Findings

The principle of virtual work with specific internal energy is effective for fluid mechanics.

A well-chosen internal energy function is crucial for linking the two theories.

The approach is accessible to mathematicians interested in the theoretical foundations.

Abstract

In this note, we analyze the relationships that should govern the use of thermodynamics in fluid mechanics in a way that we believe is understandable to mathematicians. We also aim to better define the reasons why mechanics and thermodynamics must be correctly linked by showing that the principle of virtual work expressed using a specific internal energy is perfectly suited to fluid mechanics problems, provided that a well-chosen internal energy is proposed.