Dynamical pressure in a polyatomic gas: Interplay between kinetic theory and extended thermodynamics

The aim of this paper is to compare different kinetic approaches to a polyatomic rarefied gas: the kinetic approach via a continuous energy parameter I and the mixture-like one, based on discrete internal energy. We prove that if we consider only 6 moments for a non-polytropic gas the two approaches give the same symmetric hyperbolic differential system previously obtained by the phenomenological Extended Thermodynamics. Both meaning and role of dynamical pressure become more clear in the present analysis.