Temperature upper bound of an ideal gas

Abstract

We study thermodynamics of a heat-conducting ideal gas system. The study is based on i) the first law of thermodynamics from action formulation which expects heat-dependence of energy density and ii) the existence condition of a (local) Lorentz boost between an Eckart observer and a Landau-Lifshitz observer--a condition that extends the stability criterion of thermal equilibrium. The implications of these conditions include: i) Heat contributes to the energy density through the combination $q/n{\Theta }^2$ where $q$, $n$, and $\Theta$ represent heat, the number density, and the temperature, respectively. ii) The energy density has a unique minimum at $q=0$. iii) The temperature upper bound suppresses the heat dependence of the energy density inverse quadratically. This result explains why the expected heat dependence is difficult to observe in ordinary situation thermodynamics.

arXiv comment9 pages, 2 figure, some changes, to appear in Heliyon

References in corpus (19)

• Thermodynamics of Spacetime: The Einstein Equation of State
• Thermodynamical Aspects of Gravity: New insights
• Relativistic Fluid Dynamics: Physics for Many Different Scales
• Black Hole Thermodynamics
• Relativistic fluid dynamics: physics for many different scales
• Thermal Dynamics in General Relativity
• Thermodynamical instabilities of perfect fluid spheres in General Relativity
• Tolman temperature gradients in a gravitational field
• A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics
• Tolman-like temperature gradients in stationary spacetimes
• Thermodynamic Equilibrium in General Relativity
• Gravity from Quantum Information
• Classical relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated reference frame
• Is dark energy from cosmic Hawking radiation?
• Equation of State in the Presence of Gravity
• Emergent dual holographic description as a non-perturbative generalization of the Wilsonian renormalization group
• Heat conduction in general relativity
• Entropy of Self-Gravitating Anisotropic Matter
• Matter Equation of State in General Relativity

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