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Abstract

The objective of the present chapter is to explain in detail the new ET theory of rarefied polyatomic gases and dense gases with 14 independent fields (ET14), that is, the mass density, the velocity, the temperature, the shear stress, the dynamic pressure, and the heat flux. We adopt the system of field equations with a binary hierarchy structure. We show that the constitutive equations can be determined explicitly by the caloric and thermal equations of state as in the monatomic ET13 theory. We also analyze physically important systems, that is, a rarefied polyatomic gas, a gas with the virial equations of state, a hard-sphere system, and a van der Waals gas. Lastly we show that the ET13 theory of rarefied monatomic gases is derived from the ET14 theory as a singular limit.

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References

  1. I. MĆ¼ller, T. Ruggeri, Rational Extended Thermodynamics, 2nd edn. (Springer, New York, 1998)

    BookĀ  MATHĀ  Google ScholarĀ 

  2. E. Ikenberry, C. Truesdell, On the pressure and the flux of energy in a gas according to Maxwellā€™s kinetic theory. J. Ration. Mech. Anal. 5, 1 (1956)

    MathSciNetĀ  MATHĀ  Google ScholarĀ 

  3. H. Engholm Jr., G.M. Kremer, Thermodynamics of a diatomic gas with rotational and vibrational degrees of freedom. Int. J. Eng. Sci. 32(8), 1241 (1994)

    Google ScholarĀ 

  4. G. M. Kremer, Extended thermodynamics and statistical mechanics of a polyatomic ideal gas. J. Non-Equilib. Thermodyn. 14, 363 (1989)

    MATHĀ  Google ScholarĀ 

  5. G.M. Kremer, Extended thermodynamics of molecular ideal gases. Continuum Mech. Thermodyn. 1, 21 (1989)

    ArticleĀ  MathSciNetĀ  Google ScholarĀ 

  6. I.-S. Liu, Extended thermodynamics of fluids and virial equations of state. Arch. Ration. Mech. Anal. 88, 1 (1985)

    MATHĀ  Google ScholarĀ 

  7. G.M. Kremer, Extended thermodynamics of non-ideal gases. Physica A 144, 156 (1987)

    ArticleĀ  Google ScholarĀ 

  8. I.-S. Liu, G.M. Kremer, Hyperbolic system of field equations for viscous fluids. Mat. Aplic. Comp. 9(2), 123 (1990)

    Google ScholarĀ 

  9. I.-S. Liu, J.A. Salvador, Hyperbolic system for viscous fluids and simulation of shock tube flows. Continuum Mech. Thermodyn. 2, 179 (1990)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  10. G.M. Kremer, On extended thermodynamics of ideal and real gases, in Extended Thermodynamics Systems, ed. by S. Sieniutycz, P. Salamon (Taylor and Francis, New York, 1992)

    Google ScholarĀ 

  11. M.C. Carrisi, M.A. Mele, S. Pennisi, On some remarkable properties of an extended thermodynamics model for dense gases and macromolecular fluids. Proc. R. Soc. A 466, 1645 (2010)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  12. T. Ruggeri, Symmetric hyperbolic system of conservative equations for a viscous conducting fluid. Acta Mech. 47, 167 (1983)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

  13. T. Arima, S. Taniguchi, T. Ruggeri, M. Sugiyama, Extended thermodynamics of dense gases. Continuum Mech. Thermodyn. 24, 271 (2011)

    ArticleĀ  Google ScholarĀ 

  14. F. Mallinger, Generalization of the Grad theory to polyatomic gases. INRIA Research Report (1998), p. 3581

    Google ScholarĀ 

  15. A. MĆ¼nster, Statistical Thermodynamics, vol. 2 (Springer, Berlin/Heidelberg/New York, 1974)

    Google ScholarĀ 

  16. N.F. Carnahan, K.E. Starling, Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51, 635 (1969)

    ArticleĀ  Google ScholarĀ 

  17. T. Arima, S. Taniguchi, T. Ruggeri, M. Sugiyama, Monatomic rarefied gas as a singular limit of polyatomic gas in extended thermodynamics. Phys. Lett. A 377, 2136 (2013)

    ArticleĀ  MathSciNetĀ  MATHĀ  Google ScholarĀ 

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Ruggeri, T., Sugiyama, M. (2015). RET 14-Field Theory of Polyatomic Gas and Dense Gas. In: Rational Extended Thermodynamics beyond the Monatomic Gas. Springer, Cham. https://doi.org/10.1007/978-3-319-13341-6_5

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