Abstract
In this chapter, we study a linear sound wave in a rarefied polyatomic gas in equilibrium with the aim of clarifying the validity and the features of the ET14 theory established in Chap. 5 We derive the dispersion relations on the basis of the ET14 theory and of the classical Navier-Stokes 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 and are mainly restricted to rarefied gases. We also evaluate the relaxation times, and the shear and bulk viscosities and the heat conductivity of the gases.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
I. Müller, T. Ruggeri, Rational Extended Thermodynamics, 4th edn. (Springer, New York, 1998)
T.G. Winter, G.L. Hill, High-temperature ultrasonic measurements of rotational relaxation in hydrogen, deuterium, nitrogen, and oxygen. J. Acoust. Soc. Am. 42, 848 (1967)
E.J. Rhodes Jr., The velocity of sound in hydrogen when rotational degrees of freedom fail to be excited. Phys. Rev. 70(11), 932 (1946)
C. Sluijter, H. Knaap, J. Beenakker, Determination of rotational relaxation times of hydrogen isotopes by sound absorption measurements at low temperatures. I. Physica 30, 745 (1964)
E.S. Stewart, J.L. Stewart, Rotational dispersion in the velocity, attenuation, and reflection of ultrasonic waves in hydrogen and deuterium. J. Acoust. Soc. Am. 24, 194 (1952)
E.M. Lifshitz, L.P. Pitaevskii, Statistical Physics, 3rd Edition Part 1 (Pergamon Press, Oxford, 1980)
E.M. Lifshitz, L.P. Pitaevskii, Statistical Physics, Part 2 (Pergamon Press, Oxford, 1980)
A.A. Radzig, B.M. Smirnov, Reference Data on Atoms, Molecules, and Ions (Springer, Berlin/Heidelberg/New York/Tokyo, 1985)
C.G. Sluijter, R.M. Jonkman, Sound absorption measurements in para hydrogen at 170 ∘K. Physica 30, 1670 (1964)
H.J.M. Hanley, R.D. McCarty, H. Interman, The viscosity and thermal conductivity of dilute gaseous hydrogen from 15 to 5000 K. J. Res. Nat. Bur. Stand. Sect. A 74, 331 (1970)
M.J. Assael, S. Mixafendi, W.A. Wakeham, The viscosity of normal deuterium in the limit of zero density. J. Phys. Chem. Ref. Data 16, 189 (1987)
S.C. Saxena, W.K. Saxena, Thermal conductivity data for hydrogen and deuterium in the range 100–1100 degrees C. J. Phys. A 3, 309 (1970)
W.P. Mason (ed.), Physical Acoustics, Principles and Methods, vol. II-Part A (Academic, New York/London, 1965)
W.G. Vincenti, C.H. Kruger Jr., Introduction to Physical Gas Dynamics (Wiley, New York/London/Sydney, 1965)
S. Chapman, T.G. Cowling, The Mathematical Theory of Non-uniform Gases (Cambridge University Press, Cambridge, 1991)
B.C. Eu, Y.G. Ohr, Generalized hydrodynamics, bulk viscosity, and sound wave absorption and dispersion in dilute rigid molecular gases. Phys. Fluids 13(3), 744 (2001)
T. Arima, S. Taniguchi, T. Ruggeri, M. Sugiyama, Extended thermodynamics of real gases with dynamic pressure: an extension of Meixner’s theory. Phys. Lett. A 376, 2799 (2012)
G. Emanuel, Bulk viscosity of a dilute polyatomic gas. Phys. Fluids A 2(12), 2252 (1990)
W.E. Meador, G.A. Miner, L.W. Townsend, Bulk viscosity as a relaxation parameter: fact or fiction? Phys. Fluids A 8(1), 258 (1996)
G. Emanuel, Bulk viscosity as a relaxation parameter: fact or fiction? [Phys. Fluids 8, 258 (1996)]. Phys. Fluids A 8(7), 1984 (1996)
G. Emanuel, Bulk viscosity in the Navier-Stokes equations. Int. J. Eng. Sci. 36, 1313 (1998)
R.E. Graves, B.M. Argrow, Bulk viscosity: past to present. J. Thermophys. Heat Transf. 13(3), 337 (1999)
S.R. de Groot, P. Mazur, Non-equilibrium Thermodynamics (North-Holland, Amsterdam, 1963)
H.J. Bauer, Phenomenological theory of the relaxation phenomena in gases, in Physical Acoustics II Part A, ed. by W.P. Mason (Academic, New York/London, 1965), pp. 47–131
T. Arima, S. Taniguchi, T. Ruggeri, M. Sugiyama, Dispersion relation for sound in rarefied polyatomic gases based on extended thermodynamics. Continuum Mech. Thermodyn. 25, 727 (2013)
T. Arima, S. Taniguchi, T. Ruggeri, M. Sugiyama, A study of linear waves based on extended thermodynamics for rarefied polyatomic gases. Acta Appl. Math. 132, 15 (2014)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Ruggeri, T., Sugiyama, M. (2015). Linear Wave in a Polyatomic Gas. In: Rational Extended Thermodynamics beyond the Monatomic Gas. Springer, Cham. https://doi.org/10.1007/978-3-319-13341-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-13341-6_7
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13340-9
Online ISBN: 978-3-319-13341-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)