1. J. E. Mayer and M. G. Mayer,Statistical Mechanics(John Wiley & Sons, Inc., New York, 1940).
2. We have followed, with slight modifications, the terminology of H. L. Friedman [Ionic Solution Theory(Interscience Publishers, Inc., New York, 1962)]
3. and T. L. Hill [Statistical Mechanics(McGraw Hill Book Company, Inc., New York, 1956)]. Thetotalfree energy per particle and chemical potential are, respectively, F+kT[32 ln(h2∕2πmkT)+ln ρ−1) and μ+kT[ln ρ+32 ln(h2∕2πmkT)], wheremis the particle mass andhis Planck’s constant.
4. In the following we shall take it for granted thatz,F, μ, andPare intensive variables, i.e., that they depend onNandVonly in the combination ρ = N∕V. If one does not wish to accept this fact as proved, then one can still carry through the following analysis, although with a great deal of further complication. We mention this because if one were willing to cope with the further complication, one could go a long way towards proving that the above thermodynamic quantities are indeed intensive.
5. T. L. Hill, reference 2, Sec. 28.