A Numberable Set of Exact Solutions for the Macroscopic Approach to Extended Thermodynamics of Polyatomic Gases with Many Moments

Abstract

A new model for Polyatomic Gases with an arbitrary but fixed number of moments has been recently proposed and investigated in the framework of Extended Thermodynamics; the arbitrariness of the number of moments is linked to a numberNand the resulting model is called anN-Model. This model has been elaborated in order to take into account the entropy principle, the Galilean relativity principle, and some symmetry conditions. It has been proved that the solution for all these conditions exists, but it has not been written explicitly because hard notation is necessary; it has only been shown how the theory is self-generating in the sense that if we know the closure of theN-Model, then we will be able to find that of(N+1)-Model. Up to now only a single particular solution has been found in this regard. Instead of this, we find here a numberable set of exact solutions which hold for every fixed numberN.

The General Exact Solution for the Many Moments Macroscopic Approach to Extended Thermodynamics of Polyatomic Gases

“…We firstly note that in (4) and (5) in the expression for h ′k which is present in eq. (26) of [17].…”

“…In fact, we can take for h ′ the sum of the present expression (4), of the expression (4) of [2] and of (5) in [4]. Similarly, we can take for h ′k the sum of the present expression (5), of the expression (5) of [2] and of (6) in [4]. The result is also a solution of the conditions (3) and, in the particular case N = 1, it is equal to (4) and (5) of [2].…”