A new analytical expression for the free energy of hard-core fluids

A new potential function, which can in a simple and reasonable manner represent the molecular interaction of many kinds of hard-core fluids by varying the value of its parameter, is proposed. For prediction of thermodynamic properties of hard-core fluids such as the square-well (SW) and hard core Lennard-Jones (HCLJ), a simple perturbed equation of state (EOS) is derived by using the new potential function along with the Barker-Henderson perturbation theory. This method yields a simple and general analytical expression for each thermodynamic property of such fluids. The most important feature of these expressions is that they have no adjustable parameter and in some regions in which there is no simulation data for such hard-core fluids, such equation may be used to predict the needed data. The derived EOS in this work was successfully applied to predict thermodynamic properties of the SW and HCLJ fluids, for which the simulation data are available. The predicted results are in good agreement with both the computer simulation data and the well-known equations of state.