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On a Paradox in the Theory of Heat Conduction
Phys. Rev. 61, 643 – Published 1 May, 1942
DOI: https://doi.org/10.1103/PhysRev.61.643
Abstract
The classical theory of heat conduction leads to infinite values for the heat current and for the propagation of temperature at , if the initial conditions involve a discontinuity in the temperature distribution. These paradoxical results can be avoided if a method is applied which has been previously indicated by the author. In Section II the solution of a fundamental problem in gaseous heat conduction is given to a first approximation. This approximation holds for values of the distance from the discontinuity which are smaller than the mean free path, and for times which are smaller than the time required for a molecule to travel over a mean free path with the mean velocity. In Section III the new solution is compared with the classical one, and it is shown that all results of the latter which are devoid of physical sense disappear. Furthermore, it is indicated by graphical interpolation how the new solution changes into the classical one.
References (5)
- G. Jaffé, Ann. d. Physik 6, 195 (1930)
- M. v. Smoluchowski, Ann. d. Physik 33, 1559 (1910)
Omitted endnote
- Ph. Frank and R. v. Mises, Die Differential- und Integralgleichungen der Mechanik und Physik (Friedr. Vieweg & Sohn, A. G. Braunschweig, 1927), Vol. 2, p. 190
- L. B. Loeb, The Kinetic Theory of Gases (McGraw-Hill, New York, 1934), Sections 70 and 73