By Ken Neubeck
A-10 Warthog КНИГИ ;ВОЕННАЯ ИСТОРИЯ Издательство: Squadron/Signal publicationsСерия: Mini 4Автор(ы): Ken NeubeckЯзык: EnglishГод издания: 1995Количество страниц: 52ISBN: 0-89747-335-3Формат: pdf (300 dpi) 1600x 2470Размер: 41.8 mbRapid 17
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This means that the fact of finding one molecule in a given state has no influence upon the probability of finding the second one in another given state, and is expressed by saying that the states of the molecules (in the case of thermal equilibrium of a monatomic ideal gas) are statistically uncorrelated. An elementary example of random events, which are also statistically uncorrelated, is given by the results of throwing a pair of dice; the fact that we obtain a certain number from one die does not influence the number which is shown by the other die, and the probability of getting a given combination (say, two from the first die and five from the 22 Basic Principles [Ch.
II and we have only to take j = i and sum from i = 1 to i = 3 in Eq. 7) to deduce i J~ 2! 9) Again the first term in the right-hand side will be macroscopically identified with the kinetic energy density, while the second term will be ascribed to the internal energy of the gas. 10) since the density of internal energy is obviously the product of the internal energy per unit mass times the mass density. , the sum of the three diagonal terms) of the stress tensor. In fact, Eqs. ) The spur divided by three gives the isotropic part of the stress tensor; it is therefore convenient to identify p = Pii/3 with the gas pressure, which is known to be isotropic, at least in the case of equilibrium (Pascal's principle; the identification is also correct for nonequilibrium situations in the case of a monatomic ideal gas, but is generally incorrect).
M. N. Kogan, Rarefied Gas Dynamics, Plenum Press, New York (1969). Reference 10 is also to be consulted for the Boltzmann equations describing gas mixtures and polyatomic gases. For recent developments in the justification of the Boltzmann equation see I 1. C. Cercignani, Transport Theory and Statistical Physics 2, 211 (1972); 12. 0. E. Lanford, III, in: Proceedings of the 1974 Battelle Rencontre on Dynamical Systems (J. ), Lecture Notes in Physics, Volume 35, Springer, Berlin (1975); 13. R. Illner and M.