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Dynamic pressure in relativistic thermodynamics. (English) Zbl 0885.76088

Summary: While in classical monatomic ideal gases the dynamic pressure (i.e. the non-equilibrium contribution to the pressure) is equal to zero, this is not true in relativistic thermodynamics. Indeed, thermodynamics and kinetic theory of relativistic gases indicate that there is a nonvanishing bulk viscosity. However, the bulk viscosity is small, of \({\mathcal O} ({1\over c^4})\) in a nondegenerate gas. We confirm this and proceed to show that there is also an \({\mathcal O} ({1\over c^2})\) contribution to the dynamic pressure due to a nonhomogeneous temperature field or, equivalently, to heating. In the nonrelativistic limit this new contribution is much larger than the one due to bulk viscosity.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
80A10 Classical and relativistic thermodynamics
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References:

[1] W. Israel , Relativistic Kinetic Theory of a Simple Gas , J. Math. Phys. , Vol. 4 , 1963 , pp. 1163 - 1181 . MR 165921
[2] S.R. De Groot , W.A. Van Leeuwen and Ch.G. Van Weert , Relativistic kinetic theory . North-Holland , Amsterdam , 1980 . MR 635279
[3] I. Müller and T. Ruggeri , Extended thermodynamics . Springer Tracts in Natural Philosophy , Vol. 37 , Springer , New York , 1993 . MR 1269783 | Zbl 0801.35141 · Zbl 0801.35141
[4] S. Weinberg , Entropy Generation and the Survival of Protogalaxies in an Expanding Universe . Astrophys. J. , Vol. 168 , 1971 , pp. 175 - 194 .
[5] I-Shih Liu , I. Müller and T. Ruggeri , Relativistic Thermodynamics of Gases , Ann. Physics (N.Y.) , Vol. 169 , 1986 , pp. 191 - 219 . MR 846050
[6] W. Dreyer and W. Weiss , The Classical Limit of Relativistic Extended Thermodynamics , Ann. Itist. Henry Poincaré , Vol. 45 , 1986 , pp. 401 - 418 . Numdam | MR 880745 | Zbl 0614.76124 · Zbl 0614.76124
[7] G.M. Kremer , Extended Thermodynamics of Ideal Gases with 14 Fields , Ann. Inst. Henry Poincaré , Vol. 45 , 1986 , pp. 419 - 440 . Numdam | MR 880746 | Zbl 0618.76075 · Zbl 0618.76075
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