Theory of the Two- and One-Dimensional Rigid Sphere Fluids

The approximate theory of the three-dimensional hard sphere fluid developed by Reiss, Frisch, and Lebowitz has given astonishingly good predictions with little labor. In an attempt to investigate the reason for this result we adduce, in this paper, further evidence for the internal consistency of the approximations of this theory. Thus it is noted that the same equation of state of hard sphere fluid is obtained when one used the ``integral condition'' as when the ``infinity condition'' is used. We have then applied the theory to study the thermodynamic properties, in particular the equation of state, of the rigid sphere fluid in two and one dimensions. The approximate equation of state of the two-dimensional rigid sphere fluid is in good agreement over the range of fluid densities with the results of the machine Monte Carlo calculations by Jacobson and Wood and dynamical machine calculations of Wainwright and Alder. The exact Tonks' equation of state of the one-dimensional rigid sphere fluid is derived in a particularly simple manner.