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Extended thermodynamics of classical and degenerate ideal gases. (English) Zbl 0554.76014

Extended thermodynamics is a phenomenological theory of dilute gases using the thirteen fields of mass, momentum, energy densities, stress deviator, and heat flux. Whereas ordinary thermodynamics is a 5-field theory with a state space containing derivatives of these five fields, extended thermodynamics uses a state space which only contains the required thirteen fields themselves, and it needs additional balance equations being guessed from the kinetic theory of gases. Besides the entropy principle and hyperbolicity of the field equations the principle of material objectivity is used which here indeed states only the isotropy of the material.
The dissipation inequality is exploited correctly by using Lagrange parameters whereas the decomposition of the entropy flux density into its convective and non-convective part is not induced by the phenomenological theory. The concept of absolute temperature is a confusing one because the authors do not distinguish between equilibrium and non-equilibrium temperature, and they do not say anything about how temperature is measured. Although the fundamentals are not totally convincing the constitutive equation of the classical and quantum ideal gas is derived except to only one constant for adjusting. Heat flux density and entropy flux density are calculated up to third order. A comparison between the results of extended and ordinary thermodynamics is given.
Reviewer: W.Muschik

MSC:

76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
76N15 Gas dynamics (general theory)
80A05 Foundations of thermodynamics and heat transfer
82B40 Kinetic theory of gases in equilibrium statistical mechanics

Citations:

Zbl 0554.76015
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References:

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