ABSTRACT
In this Boltzmann was guided by Liouville’s theorem in classical mechanics. See Lectures on Gas Theory, pp. 274-290 and also p. 443. To obtain the result, we must also invoke a relationship between pressure and energy density. At first sight this is surprising. For a more detailed discussion see Rushbrooke, Statistical Mechanics, p. 27. Max Planck, The Theory of Heat Radiation, Dover Edition, 1959, p. 118. A. E. Guggenheim, Research, 2, 450 (1949). A. Einstein, Annafen der Physik, 22, 180 (1907). The question of Gibbs’ paradox arises at this point. See The Scientific Papers of J. Willard Gibbs, Dover Edition, vol. I, 1961, p. 166. Eu can be deduced from equation (142), p. 121. Notice, however, that in calculating Ea here I have assumed one particle only per translational energy level. For particles of spin i (e.g. electrons) there are two spin states associated with each translational level and these, in the absence of a magnetic field, would in general have the same energy. For particles of different spin there would be different numbers of spin states. This does not alter the argument but it does alter the numerical coefficients involved. F. London, Super-fluids, vol. 2, John Wiley and Sons, Inc., New York 1954. This discussion is based on an article in Physics World, August 1995 by D. Meacher and P. Ruprecht. For a discussion of the conditions under which a composite particle is a boson, see Elements of Statistical Mechanics by ter Haar, Butterworth, 1995, Chapter 4.9. J. C. Maxwell, Theory of Heat, Longman, Green and Co., London 1883, p. 328. L. Brillouin, Science and Information Theory, Academic Press Inc., New York 1956. L. Boltzmann, Lectures on Gas Theory, p. 444.
