A new equation of state for rigid spheres has been developed from an analysis of the reduced virial series. Comparisons with existing equations show that the new formula possesses superior ability to describe rigid-sphere behavior.

An equation of state is proposed for the mixture of hard spheres based on an averaging process over the two results of the solution of the Percus–Yevick integral equation for the mixture of hard spheres. Compressibility and other equilibrium properties of the binary mixtures of hard spheres are calculated and they are compared with the related machine-calculated (Monte Carlo and molecular dynamics) data. The comparison shows excellent agreement between the proposed equation of state and the machine-calculated data.

This investigation demonstrates the advantages of on improved expression for intermolecular repulsions in equotions of state. A highly accurate equation of state for the rigid-sphere fluid i s used as the model of repulsion behavior in real fluids. A method for general usage of this new rigid-sphere equation in reol fluid models is presented via reformulation of van der Wool's equation using the accurate new rigid-sphere equation to describe repulsion effects. To test this reformulation, properties of methane, ethane, propane, n-butane, isobutone, hydrogen sulfide, nitrogen, ethylene, acetylene, methyl chloride, cyclohexane, pentane and octane have been calculated. The advantage of using the accurate rigid-sphere equation was demonstrated by the generol improvement in calculated properties relative to the original van der Wools and Redlich-Kwong equations. Calculations of enthalpy departures for mixtures of nitrogen and methane, propane and methane, pentane and cyclohexane, and pentane and octane also indicated the desirability of using the accurate rigid-sphere equation to describe repulsion effects in mixtures. PURE FLUIDSSince van der Waals ( 1 ) proposed his theoretical model of the equation of state in 1873, the development of improved analytical models of the equation of state has proceeded along two routes, empirical and theoretical. Indeed, some empirical models have been based, in part, upon theoretical forms.The totally empirical models of the equation of state are generally employed to correlate experimental thermodynamic property data. They are, therefore, quite accurate in making interpolative calculations of the data from which they have been evaluated. Such evaluations are usually made by regression techniques requiring a considerable amount of experimental data to minimize errors in interpolative calculations. These equations of state generally are specific to a given material. They usually are not easily generalized (2) such that accurate calculations can be made for a material not included in the original correlation.On the other hand, theoretical or semitheoretical equations of state do not require vast amounts of experimental data for their evaluation. Using only a few characteristic bits of experimental data (for example, critical pressure, critical temperature, critical compressibility factor, latent heat of vaporization at the normal boiling point, etc.), these equations allow predictive calculations of properties at other temperatures and pressures. Such calculations naturally lack the accuracy of the regression-spawned equations of state. Yet, for calculating the properties of materials for which reliable experimental data are scarce, the theoretical and semitheoretical equations are definitely useful.Theoretical equations of state usually are developed using virial expansion theory ( 2 ) , distribution function This leads to a rigid-sphere repulsion term, plus something else which generally accounts for cohesion effects. Such a model corresponds to the general form of the van der Waals e...

The excess thermodynamic properties for a rigid-sphere fluid have been calculated with an accurate equation of state. Values of (PV / NkT), and (H − H°) / RT, (S − S°) / R, (G − G°) / RT, and (f / P) are reported for a wide range of fluid density.

Experimental results confirm that resins isolated from Boscan crude oil have a stabilizing effect on asphaltenes in Hamaca crude oil and in Boscan crude oil. A simple experimental technique, referred to as the filter drop spreading method, was used to detect the onset of flocculation quite accurately for crude oil mixtures and for mixtures of crude oils plus additives.