Temperature upper bound of an ideal gas

Area of Science:

• Thermodynamics
• Ideal Gas Systems
• Statistical Mechanics

Background:

• The first law of thermodynamics is typically formulated without considering heat's direct impact on energy density.
• The stability criterion of thermal equilibrium needs extension for non-equilibrium systems.

Purpose of the Study:

• To investigate the thermodynamics of a heat-conducting ideal gas.
• To analyze the influence of heat on energy density and thermal equilibrium stability.

Main Methods:

• Utilizing action formulation for the first law of thermodynamics.
• Applying the existence condition of a local Lorentz boost between Eckart and Landau-Lifshitz observers.

Main Results:

• Heat contributes to energy density through the term $$ (q: heat, n: number density, Θ: temperature).
• A unique minimum for energy density is identified at $$ .
• Temperature upper bounds suppress heat's influence on energy density quadratically.

Conclusions:

• The derived conditions explain the subtle heat dependence of energy density in typical thermodynamic scenarios.
• This study provides a theoretical framework for understanding heat transport effects in ideal gases.