Thermodynamic Properties of Nonideal Gases. I. Free-Energy Minimization Method

The thermodynamic properties of nonideal or interacting gases are studied using a thermodynamically consistent method which derives a state function for the gas from a separable Hamiltonian for the many-body system. The state function - the Helmholtz free energy - is a sum of translational, configurational, and internal components, and the statistical equilibrium state is calculated on a computer by minimizing the free energy in composition space at a given volume and temperature. A series of free-energy models is constructed to investigate the effects of various interactions. The effects on the equilibrium state of including Fermi-Dirac statistics in the translational free energy is shown to be small, while Coulomb and excluded-volume configurational terms produce large thermodynamic effects. The most important interaction effect, the modification of the internal partition function, is studied using a free-atom model and a confined-atom model which introduces volume- and temperature-dependent energy eigenvalues and partition-function sum terminations. The free-energy minimization method is shown to be a versatile and efficient tool for studying interacting gases, and provides quantitative estimates of the limits of validity of the various interaction models.