Statistical physics near the critical point: An analysis of some free energy function models

This dissertation describes the fundamental statistical thermodynamics of a simple fluid near the critical point. Various free energy function models are analyzed. A theory of particulate interactive effects developed by Professor John A. White of The American University, and based on renormalization group concepts, is applied using numerical methods. Results for pressure-density isotherms, density-temperature coexistence curves, and specific heat near the critical point are presented. The paper is divided into six sections: (1) Introduction. Fundamental thermodynamics is presented in terms of the free energy function. (2) Basic theory. A model of intermolecular interactions is described which accounts for short range attractive forces using increasingly long correlation lengths based on renormalization group methods. (3) Specific heat. The theory of the specific heat near the critical point is developed for the liquid-gas two-phase region. (4) The iterative algorithm. A computer model in FORTRAN has been developed which numerically calculates thermodynamic parameters. (5) Numerical results. The numerical output of the iterative algorithms is compared to experimental data for: pressure-density isotherms, density-temperature coexistence curves, and specific heat. (6) Summary and conclusions. An assessment of the relationship of the theory to experimental data is made.