Journal of Statistical Physics

, Volume 48, Issue 3–4, pp 813–837 | Cite as

On the fundamentals of extended thermodynamics (ET) of a one-dimensional rarefied gas

  • Zbigniew Banach


Extended thermodynamics (ET) of degreer for a one-dimensional rarefied gas based, by definition, on a finite set Ar={a0, a2,..., ar} of the firstr−1(3⩽r) direct internal moments of the one-point distribution functionf is carefully investigated. With the aid of the second axiom of thermodynamics, the new representation forf, depending in a local and nonlinear way onA r , is explicitly derived. It is demonstrated that in ET of degreer an infinite sequence {br+1, br+2,...} ofhigher order Hermite coefficients, which normally drops out of Grad's proposition forf fashioned by mathematical apparatus such as the Hermite polynomials, cannot be considered negligible in the case when nonlinear constitutive functions are established. Using Ma's kinetic equation corresponding to a one-dimensional rarefied gas as well as the generalized representation forf, collision productions in the nonconservative moment equations are then calculated for a special choice of the rate of collisions between particles.

Key words

Extended thermodynamics (ET) one-dimensional rarefied gases Ma's kinetic equation hierarchy of moment equations truncation of the hierarchy Grad's moment procedure and its generalization 


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Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • Zbigniew Banach
    • 1
  1. 1.Institute of Fundamental Technological Research, Department of Fluid MechanicsPolish Academy of SciencesWarsawPoland

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