Cell Model of a Fluid. II. Thermodynamic Properties of the System

In Paper I of this series (preceding paper) the model was formulated mathematically and the solution derived in the form of an infinite series. The convergence and analyticity of the solution were investigated. It was then applied to one-, two-, and three-dimensional systems with nearest-neighbor interactions, and low-temperature series for these systems were obtained. In the present article the thermodynamics of the model are investigated. The series solution of the partition function derived in Paper I is applied to systems with interaction potentials of increasing complexity. The validity of the model is established by showing that in the appropriate limits it leads correctly to the ideal gas and the Tonks equation of state. It is shown that the model is capable of portraying phase transitions and gives realistic results thermodynamically. Finally various finite one-, two-, and three-dimensional systems are analyzed numerically by high-speed computer and their thermodynamic properties and pair-correlation functions are examined. Interesting conclusions emerge concerning the range of order in such systems and the probable critical temperatures.