Ultrarelativistic limit of a Rarefied Gas with Internal Structure

TL;DR

This paper investigates the ultra-relativistic limit of a relativistic gas with internal structure, revealing how the energy behavior depends on the degrees of freedom and providing explicit characteristic velocities.

Contribution

It demonstrates the existence of a critical degree of freedom value that determines the ultra-relativistic energy limit of structured gases, extending previous models.

Findings

For small degrees of freedom, the energy limit matches the Synge energy for monatomic gases.

For larger degrees of freedom, the energy increases with the degree of freedom.

Explicit expressions for characteristic velocities of the hyperbolic system are provided.

Abstract

The aim of this letter is to check the ultra-relativistic limit of a recent model proposed by Pennisi and Ruggeri [Ann. Phys. 377, 414 (2017)] for a relativistic gas with internal structure. Considering an Eulerian fluid we prove that there exists a critical value of the degree of freedom such that for smaller values of this quantity the ultra relativistic limit of the energy of a gas with structure is the same as the Synge energy for monatomic gases, while for larger degrees of freedom the energy increases with the degree of freedom itself. The limiting equations are accompanied with the explicit expression of the characteristic velocities of the hyperbolic system.