Similarity examination of truncated virial equation of state correspondence to linear isothermal regularity (LIR) by applying square-well (SW) potential

Linear isotherm regularity works very well for fluids at high densities, and it has been shown that it is compatible with the EOSs based on statistical–mechanical theory. On the other hand, at low densities, the first few terms of virial EOS have the most contribution to express the deviations from ideal behavior. For finding similarities between dense and dilute states, experimental p–v–T data of 14 fluids (He, Ne, Ar, Kr, H₂, O₂, N₂, CO, NH₃, CH₃OH, CH₄, C₂H₄, C₂H₆ and C₃H₈) are examined. Comparing the thermal dependencies of the attraction and repulsion terms (A and B) of the LIR with the second and third virial coefficients (B ₂ and B ₃) in liquid and supercritical regions (0.7 < T _r < 3.0) shows a remarkable similarity. Square-well potential is applied to examination and comparison of theoretical results with experimental results. It is shown that in liquid and supercritical regions, (1) the short-range potential governs among particles in dense fluids, and the long-range interactions become important in the less dense fluid, (2) similar to Boyle temperature, T _B, in dilute state, there is a temperature as T′_B (in dense fluids) that the attractive forces and the repulsive forces acting on the dense-fluid particles balance out; thus, probably there is a maximum σ (molecular diameter) at nearly 2T _c (T′_B), and (3) in the liquid and supercritical regions (0.7 < T _r < 3.0), in the first-order approximation, there are no significant interactions higher than triple interactions in dense-fluid particles.