# Critical phenomena and phase transitions of condensable gases

A study of the phase transition of a condensable gas is conducted from the thermodynamic and microscopic points of view. The essential component of this study is the numerical solution of a set of recursion relations which yields the equation of state in the form of pressure and chemical potential isotherms. The thermodynamics of fluid systems is developed in some detail with particular reference to the thermodynamic description of phase transitions. The statistical mechanics of classical fluids is presented to give a traditional microscopic interpretation to the recursion relations. The classical mean field theory of fluids is presented both because of its simplicity and because it is the starting point for the recursion process. The renormalization group approach is briefly discussed as an introduction to the extended renormalization group technique here called the theory of condensable gases. The recursion relations of the theory are then presented in an heuristic manner. The numerical solutions of the recursion relations are described and presented in the form of pressure and chemical potential isotherms. The critical isotherm for the pressure is seen to reproduce the data for simple fluids over a large range of density and pressure quite well. The critical isotherm exponent $\delta$ was obtained from the chemical potential isotherm and found to be 4.76 $\pm$ 0.10 which is in good agreement with simple fluid data. The isotherms for T both above and below the critical isotherm are also presented. The coexistence curve is generated by equating chemical potentials and pressures for the two fluid phases. The agreement with simple fluid data is good for the low density to moderately high density range. In particular, the agreement in the critical region is quite good and yields an order parameter exponent $\beta$ of 0.338 $\pm$ 0.010.