Monatomic-Gas Limit in Molecular ET of Polyatomic Gas

The difference in the theoretical structure between monatomic gas and polyatomic gas in highly nonequilibrium states is discussed from the viewpoint of molecular extended thermodynamics (molecular ET) of rarefied gases, which is free from the local equilibrium assumption. The molecular ET theories of these two types of gas are based on the moment balance equations with different hierarchy structures due to whether the internal degrees of freedom of a molecule are incorporated in their distribution functions or not. In particular, the number of balance equations in the molecular ET theory of polyatomic gases is greater than the number in the corresponding theory of monatomic gases. In this chapter we prove that the solutions for polyatomic gases converge, in the limit where the degrees of freedom of a molecule D tend to 3, to the ones for monatomic gases provided that we impose appropriate initial conditions compatible with monatomic gases. Thus a molecular ET theory of rarefied monatomic gases can be identified as a singular limit of the corresponding molecular ET theory of rarefied polyatomic gases. As illustrative examples, the asymptotic behaviors when D → 3 in the dispersion relation of ultrasonic sound and in the shock wave structure are shown.