An accurate investigation of second virial coefficient with Morse-Morse Spline Van der Waals potential and its utilization in the study of real systems Elif Somuncu * , Bahtiyar A. Mamedov Department of Physics, Faculty of Arts and Sciences, Gaziosmanpas ¸a University, Tokat, Turkey article info Article history: Received 9 May 2019 Received in revised form 21 July 2019 Accepted 24 July 2019 Available online 25 July 2019 Keywords: Virial equation of state Second virial coefficient Morse-morse spline Van der Waals potential abstract The fundamental investigations of virial coefficients with various potentials have many applications in thermodynamics and natural sciences. An analytical approach for the calculation of the second virial coefficient with Morse-Morse Spline Van der Waals (MMSV) potential is presented in this study. The method is based on the series expansion of the exponential function and binomial function, exponential integral function, gamma function, Meijer function, and hypergeometric function. The assessment of the second virial coefficient with MMSV potential is performed mostly using a numerical approach that accounts for significant parameters and ensures the required results. This simple general formula is more suitable for simulations of all thermodynamic quantities. As an example of application of the analytical expression, calculations have been performed forSF 6 molecule. The obtained results agree well with that obtained from the numerical approach, which make possible the proposed analytical formula to be useful for evaluation of other properties of gases. © 2019 Published by Elsevier B.V. 1. Introduction It is widely known that the virial equation of state consists of virial coefficients is invaluable in most areas of natural sciences and engineering [1e3]. The virial coefficients based on intermolecular potential provide the determination of important thermodynamic properties of gases such as internal energy, entropy, heat capacities, and the speed of sound [4,5]. The evaluation of the second virial coefficient over MMSV potential is fundamental and efficient nu- merical approach of thermodynamic and transport properties of hexafluoride gaseous [6,7]. MMSV potential, which has established by Aziz et al. [7], is appeared to have the best predictive ability for hexafluoride gaseous data. The MMSV potential comprised of the C 6 ,C 8 ,C 10 dispersion coefficients provides satisfactory results of second virial coefficient, diffusion coefficients, viscosity, thermal conductivity and nuclear magnetic resonance (NMR) system data [8e10]. None of the potential functions formerly suggested in the literature has predicted these properties at the same time. Note that, in the literature the numerical approach [10] has been reported for the evaluation of second virial coefficient with MMSV potential. Therefore, the obtained explicit analytical formulae for the second virial coefficient with MMSV potential have prime importance in the evaluation of the thermodynamic and transport properties of gases. In this study, a new analytical formula for the computation of the second virial coefficient with MMSV potential is suggested firstly, which considerably improved its ability during analytical evaluations in important cases. 2. Theory and basic formulae The virial equation of state of gases may be expressed Z ¼ PV nRT ¼ 1 þ B 2 ðT Þ n V þ B 3 ðT Þ n 2 V 2 þ ::: (1) whereB 2 ðT Þ and B 3 ðT Þis called second and third virial coefficients, respectively [11]. The coefficients depend on intermolecular po- tential and temperature. The second virial coefficient may be written * Corresponding author. E-mail addresses: elf_smnc@hotmail.com (E. Somuncu), bamamedov@yahoo. com (B.A. Mamedov). Contents lists available at ScienceDirect Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid https://doi.org/10.1016/j.fluid.2019.112255 0378-3812/© 2019 Published by Elsevier B.V. Fluid Phase Equilibria 499 (2019) 112255