An improved theoretical basis for the equation of state of pure fluids

The theoretical perturbation equation of state developed by McQuarrie and Katz is considered. The equation is where n, m, and A are Lennard-Jones parameters; T* is the reduced temperature; n* is a reduced density; x is the reduced radial distance; and ghs(x, n*) is the hard sphere radial distribution function for a system of diameter equal to sigma. An improved equation developed by Carnahan and Starling is used for the hard sphere compressibility factor. Instead of using tables of the hard sphere radial distribution function to evaluate the integral, the quadrature of the integral's Laplace transform is used for which an analytic form exists. A computer program was written to evaluate the quadrature numerically. The effective hard sphere diameter, ca, was determined from experimental methane data at temperature T0, which is the temperature for which (a2P/aT2)mv is zero. From the equation of state it is possible to calculate an effective hard sphere diameter over a range of temperature. This effective hard sphere diameter was determined over the temperature range of 200 to 2000°K. The hard sphere diameters which were calculated are compared with the effective hard sphere diameters predicted by Rowlinson and Barker and Henderson for the repulsive contribution of the intermolecular potential and with the experiment values. The deviation of the pressure of a linear van der Waals isochor from the actual experimental pressure was used to test the equation of state. It was found that the In T* term can not account for the deviation from a linear isochor observed experimentally. The diameter becomes negative for very large temperatures due to the in T* term, which originates from the Lennard-Jones potential. To predict the correct diameter and compressibility factor at very high temperatures a potential containing a hard core term is required