Extended thermodynamics of real gases with dynamic pressure: An extension of Meixnerʼs theory

Abstract Basing on the recent theory of extended thermodynamics of dense gases, we study a thermodynamic theory of gases with the energy transfer from molecular translational mode to internal modes as an extension of Meixnerʼs theory. We focus our attention on the simplest case with only one dissipative process due to the dynamic pressure. The dispersion relation for sound derived from the present theory is compared with that from Meixnerʼs theory. Kinetic theoretical basis of the present approach is also discussed.

[1]  Tommaso Ruggeri,et al.  Moment equations in the kinetic theory of gases and wave velocities , 1997 .

[2]  I. Liu,et al.  Hyperbolic system for viscous fluids and simulation of shock tube flows , 1990 .

[3]  G. M. Kremer.  Extended thermodynamics of non-ideal gases , 1987 .

[4]  Francesco Salvarani,et al.  A kinetic model allowing to obtain the energy law of polytropic gases in the presence of chemical reactions , 2005 .

[5]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[6]  J. Meixner,et al.  Absorption und Dispersion des Schalles in Gasen mit chemisch reagierenden und anregbaren Komponenten. I. Teil , 1943 .

[7]  P. Mazur,et al.  Non-equilibrium thermodynamics, , 1963 .

[8]  M. C. Carrisi,et al.  On some remarkable properties of an extended thermodynamic model for dense gases and macromolecular fluids , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[9]  Maximum entropy principle for rarefied polyatomic gases , 2013 .

[10]  Allan D. Pierce,et al.  Physical acoustics : principles and methods , 1965 .

[11]  W. Dreyer,et al.  Maximisation of the entropy in non-equilibrium , 1987 .

[12]  I. Müller,et al.  Rational Extended Thermodynamics , 1993 .

[13]  Liu I-Shih.  Extended thermodynamics of fluids and virial equations of state , 1985 .

[14]  Tommaso Ruggeri,et al.  Hyperbolic Principal Subsystems: Entropy Convexity and Subcharacteristic Conditions , 1997 .

[15]  T. Ruggeri,et al.  Galilean invariance and entropy principle for systems of balance laws , 1989 .

[16]  Takashi Arima,et al.  Dispersion relation for sound in rarefied polyatomic gases based on extended thermodynamics , 2013 .

[17]  Tommaso Ruggeri,et al.  Entropy principle for the moment systems of degree $\alpha$ associated to the Boltzmann equation. Critical derivatives and non controllable boundary data , 2002 .

[18]  Tommaso Ruggeri,et al.  Dispersion relation in the high frequency limit and non linear wave stability for hyperbolic dissipative systems , 1992 .

[19]  T. Teichmann,et al.  Introduction to physical gas dynamics , 1965 .

[20]  G. M. Kremer.  Extended thermodynamics of molecular ideal gases , 1989 .