Dispersion relation for sound in rarefied polyatomic gases based on extended thermodynamics

Non-linear extended thermodynamics of real gases with 6 fields

“…By using the representation theorem for isotropic functions and from (10), the compatibility with the entropy balance law is easily satisfied. As the dependence on the velocity is prescribed by the Galilean invariance (4), the natural question is that whether the relations (4) are compatible with the constraints (10) arisen from the entropy principle.…”

“…This situation is observed in many gases such as rarefied hydrogen gases and carbon dioxide gases at some temperature ranges [9,10,5]. But at the same time, it has an advantage to offer us a more affordable hyperbolic partial differential system.…”

Entropy Principle and Recent Results in Non-Equilibrium Theories

“…The theory includes as a singular limit the 13-moment theory for rarefied monatomic gases [101] and this new approach has also been applied to the derivation of a 6-moment theory [102] which extends the Meixner's model [103,104]. The validity of the theory has been confirmed by comparing its predictions to experimental evidence, for rarefied polyatomic gases, in the case of ultrasonic waves [105] and shock waves [106,107].…”

Extended Thermodynamics for Dense Gases up to Whatever Order and with Only Some Symmetries

“…We firstly note that the second term in Equation (39) is zero thanks to Equation (33). We can take the derivative with respect to λ of what remains and substitute Equation (31). We obtain a relation and note that:…”

“…A new approach has been proposed in [24] and other articles, such as [25][26][27][28][29][30][31][32][33][34][35][36][37][38], which overcomes this problem by considering two blocks of balance equations. In this framework, we have recently studied two different cases: one deals with rarefied polyatomic gases [37], even if the reduced set of applicability is not indicated in the title of that paper.…”