Abstract
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.
Similar content being viewed by others
References
I. Müller,Z. Phys. 198:329 (1967).
I.-S. Liu and I. Müller,Arch. Rat. Mech. Anal. 83:285 (1983).
L. S. García-Colín and G. Fuentes,J. Stau Phys. 29:387 (1982).
L. S. García-Colín, M. Lopez de Haro, R. F. Rodriguez, J. Casas-Vázquez, and D. Jou,J. Slat. Phys. 37:465 (1984).
H. Grad,Commun. Pure Appl. Math. 2:331 (1949).
H. Grad,Principles of the Kinetic Theory of Gases, Handbuch der Physik, Vol. XII, S. Flügge, ed. (Springer-Verlag, Berlin, 1958), p. 205.
H. Grad,Commun. Pure Appl. Math. 2:325 (1949).
S. K. Ma,J. Stau Phys. 31:107 (1983).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Banach, Z. On the fundamentals of extended thermodynamics (ET) of a one-dimensional rarefied gas. J Stat Phys 48, 813–837 (1987). https://doi.org/10.1007/BF01019698
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01019698