Polytropic gas modelling at kinetic and macroscopic levels

In this paper, we consider the kinetic model of continuous type describing a polyatomic gas in two different settings corresponding to choice functional space used define macroscopic quantities. Such introduces single variable supposed capture all phenomena related more complex structure molecule. In particular, provide direct comparison these settings, and show their equivalence after distribution function is rescaled cross section reformulated. We then focus on for which rigorous existence uniqueness result homogeneous case recently proven. Using proposed that analysis together with maximum entropy principle, establish models six fourteen fields. moments, calculate exact, nonlinear, production term prove its total agreement extended thermodynamics. Moreover, moments model, new expressions relaxation times transport coefficients linearized setting, yield both matching experimental data dependence shear viscosity upon temperature satisfactory theoretical value Prandtl number.