Modified Lennard-Jones Potentials with a Reduced Temperature-Correction Parameter for Calculating Thermodynamic and Transport Properties: Noble Gases and Their Mixtures (He, Ne, Ar, Kr, and Xe)
The three-parameter Lennard-Jones potential function is proposed to calculate thermodynamic property (second virial coefficient) and transport properties (viscosity, thermal conductivity, and diffusion coefficient) of noble gases (He, Ne, Ar, Kr, and Xe) and their mixtures at low density. Empirical modification is made by introducing a reduced temperature-correction parameter to the Lennard-Jones potential function for this purpose. Potential parameters ( , , and ) are determined individually for each species when the second virial coefficient and viscosity data are fitted together within the experimental uncertainties. Calculated thermodynamic and transport properties are compared with experimental data by using a single set of parameters. The present study yields parameter sets that have more physical significance than those of second virial coefficient methods and is more discriminative than the existing transport property methods in most cases of pure gases and of gas mixtures. In particular, the proposed model is proved with better results than those of the two-parameter Lennard-Jones potential, Kihara Potential with group contribution concepts, and other existing methods. 1. Introduction Accurate representation of thermodynamic and transport properties is essential to process engineers to design and optimize equipment and chemical processes. Second virial coefficient is an important quantity which is useful in calculating vessel size from volumetric data, heating requirements from calorimetric data, and stage requirements from phase equilibrium data. Transport properties such as viscosity, thermal conductivity, and diffusion coefficient are critically important parameters in many engineering applications: for the determination of pipeline, heatexchanger and separation equipment size, mass transfer efficiency of reservoir of oils, and the power required to pump fluid [1]. The intermolecular forces are of great importance to scientists in a wide field of disciplines as information of these interactions provides the progress of collisions between molecules and determines the bulk properties of substances. Approximation of thermodynamic and transport properties from statistical mechanics requires a realistic intermolecular potential [2]. The theoretical basis in statistical mechanics for the virial equation is one of its attractions. The viral equation truncated after the second term is a popular tool to calculate accurate thermodynamic properties at low or moderate densities. A number of investigators have emphasized the determination of second
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