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Mechanics and thermodynamics: A link between the two theories

Henri Gouin

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.

Mechanics and thermodynamics: A link between the two theories

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.
Paper Structure (21 sections, 50 equations, 1 figure)

This paper contains 21 sections, 50 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminary remarks on differential calculus
  3. Change of independent variables
  4. Poisson bracket relations
  5. Application to thermodynamic calculations
  6. Specific state, entropy, internal energy
  7. Pressure, temperature
  8. Choice of variables
  9. Thermodynamic potentials
  10. Equation of state
  11. Calorimetric coefficients
  12. Relations between calorimetric coefficients
  13. Application of thermodynamics to the study of fluid equilibrium
  14. Case of isolated fluid
  15. Case of fluid enclosed in a container where pressure and temperature are imposed
  16. ...and 6 more sections

Figures (1)

  • Figure 1: Surface $(\Im)$ projected onto the plane $Ov\eta$