Towards new thermodynamic regularities for dense fluids based on the effective attraction pair potential via the perturbation theory

Abstract

In the present work, several new thermodynamic linear isotherm regularities for the dense fluids have been derived for the first time. For this purpose, the thermodynamic perturbation theory (TPT) employing only the attractive effective pair potential (AEPP) as u(r)=−εeff (σeff/r)m was used, where σeff which is the effective hard core diameter, is temperature dependent and m>0. Based on the derived regularities, the isotherm (Z−Z(0))v2 is a linear function of ρ2, ρ and 1/ρ, depends on the values of m=12, 9 and 6, respectively where Z−Z(0) is the difference between the experimental compressibility factor of the real fluid (Z) and that of the reference fluid (Z(0)). Also, Z−Z(0) is a linear function of ρ2 when the value of m=3 and is linear in terms of ρ1/3 for m=1. The latter linearity is similar to the results obtained using the Yukawa effective pair potential along with TPT. It is worthy to note that the observed regularities are only due to the contribution of the effective intermolecular attraction in the fluid. We have noticed that the effective hard core diameter depends on the range of attraction from of the effective pair potential, in such a way that it increases when the range of attraction is longer. The experimental data have been used to check the validity of the derived regularities for eleven fluids namely, Ar, Kr, H2, N2, NH3, CH4, C2H6, C3H8, C6H6, CH3OH and CO2. The most important outcome of this study is that different types of the regularities in the dense fluids may be derived by using the perturbation theory with a suitable reference fluid with temperature dependency for the σeff.