By Daniel V. Schroeder

This article appears at thermodynamics and statistical mechanics. half I introduces options of thermodynamics and statistical mechanics from a unified view. elements II and III discover additional purposes of classical thermodynamics and statistical mechanics. all through, the emphasis is on real-world purposes.

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**Extra resources for An Introduction to Thermal Physics**

**Example text**

These functional remains bounded for 0 ~ t ~ T. If we add the assumption that the fourth moment of ~ exists, then we can prove a uniqueness theorem. 23) where gives: Rr is the maximum value of the density in lo,TI. Hence Eq. 25) where Mr CT = Q(O) exp{ l4b(ET + RT) + 12K + MT I T} is the maximum value of Tr~ O,T. It is now easy to prove the following Uniqueness theorem. Let f be the solution, whose existence is guaranteed by the previous theorem. If Q(O) exists, then so does Q(T) in lo,TI and the solution of Eq.

14) where, again, the constant HT depends only on the initial data anc T. When the boundedness assumption stated in Eq. £.. 16) where m is a positive constant. 20) ~(t) ~ HT where the constants ET and HT do not depend on m. Then using the same weak compactness criterion used by ARKERYD 1321 in his first proof and and the equicontinuity in time of sequence fm, we arrive at the following. Existence theorem: there exists a solution f of Eq. 7), where the kernel B(6, ~~-~*I) of the collision term Q(f, f) satisfies Eq.

44) M. H. L. LEBOWITZ and E. W. MONTROLL, eds. North Holland, Amsterdam (1983) 45) C. TREUSDELL - "On the pressures and the flux of energy in a gas according to· Maxwell's Kinetic theory, II", Journal of Rational Mechanics and Analysis, ~. 55-128 (1956) 46) V. S. GALKIN - Prikladnaya Matematika i Mechanika, 20, 445-446 (1956) (In Russian) 47) V. S. GALKIN - "On a class of solutions of Grad's moment equations", PMM 22, 532- 536 (1958) 48) V. S. GALKIN - "One-dimensional unsteady solution of the equation for the kinetic moments of a monatomic gas", PMM 28, 226-229 (1964) 49) V.