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Linear Sound Wave in a Rarefied Polyatomic Gas

In: Classical and Relativistic Rational Extended Thermodynamics of Gases

Author

Listed:
  • Tommaso Ruggeri

    (University of Bologna, Department of Mathematics and Research Center on Applied Mathematics)

  • Masaru Sugiyama

    (Nagoya Institute of Technology)

Abstract

In this chapter, we study a linear sound wave in a rarefied polyatomic gas in equilibrium. Thereby we can clarify the validity and the features of the ET14 and ET15 theories established in Chaps. 6 – 8 . In the first half of this chapter, we derive the dispersion relations on the basis of the ET14 theory and of the classical Navier-Stokes and Fourier (NSF) theory. Comparison of these relations with experimental data reveals clearly the superiority of the ET14 theory to the NSF theory. We confine our analysis within sound waves in some rarefied diatomic gases (hydrogen, deuterium, and hydrogen deuteride gases) because suitable experimental data are scarce. We also evaluate the relaxation times, and the shear and bulk viscosities, and the heat conductivity of the gases. In the second half, firstly we emphasize the necessity of the ET15 theory. Then using this theory we study the dispersion relation of a rarefied polyatomic gas with molecular rotational- and vibrational-relaxation processes. We study, in particular, its temperature dependence in the cases where the rotational and vibrational modes may or may not be excited. It is shown that the curve of the attenuation per wavelength with respect to the frequency has up to three peaks depending on the temperature and on the relaxation times. The peak in a low frequency region is studied especially in detail because its experimental measurement is relatively easy.

Suggested Citation

  • Tommaso Ruggeri & Masaru Sugiyama, 2021. "Linear Sound Wave in a Rarefied Polyatomic Gas," Springer Books, in: Classical and Relativistic Rational Extended Thermodynamics of Gases, chapter 0, pages 361-387, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-59144-1_16
    DOI: 10.1007/978-3-030-59144-1_16
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