Abstract
Molecular extended thermodynamics of rarefied polyatomic gases is characterized by the system composed of two hierarchies of balance equations for the moments of a distribution function. The internal degrees of freedom of a molecule are properly taken into account in the distribution function. By the reasoning of physical relevance, the truncation orders of the two hierarchies are proved to be not independent of each other. And the two closure procedures based on the maximum entropy principle (MEP) and on the entropy principle are also proved to be equivalent to each other. Characteristic velocities of a hyperbolic system of the balance equations for a polyatomic gas are compared to those obtained for a monatomic gas. The lower bound estimate for the maximum equilibrium characteristic velocity established for a monatomic gas is proved to be valid also for a rarefied polyatomic gas, that is, the estimate is independent of the degrees of freedom of a molecule. As a consequence, also for polyatomic gases, when the number of moments increases the maximum characteristic velocity becomes unbounded.
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Notes
- 1.
Upon inspection it can be seen that in the one-dimensional case, for any N and M, \(\{F_{i_{1}i_{2}\ldots i_{A}}\), \(0\leqslant A\leqslant N\}\) is mapped into {F p, q , \(0\leqslant p + 2q\leqslant N\}\), and \(\{G_{lli_{1}i_{2}\ldots i_{A'}}\), \(0\leqslant A'\leqslant M\}\) is mapped into {G p′, q′, \(0\leqslant p' + 2q'\leqslant M\}\).
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Ruggeri, T., Sugiyama, M. (2015). Molecular ET Theory of Rarefied Polyatomic Gas. In: Rational Extended Thermodynamics beyond the Monatomic Gas. Springer, Cham. https://doi.org/10.1007/978-3-319-13341-6_10
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DOI: https://doi.org/10.1007/978-3-319-13341-6_10
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