Equation of state for pure fluids at critical temperature

In this paper, we employ the concept of probability for creating a cavity with diameter d in fluid along with the perturbation and variation approach, and develop an equation of state (EOS) for a hard sphere (HS) and Lennard-Jones (LJ) fluids. A suitable axiomatic form for surface tension S(r) is assumed for the pure fluid, with r as a variable. The function S(r) has an arbitrary parameter m. S(r)=A+B(d/r)/[1+m(d/r)]. We use the condition in terms of radial distribution function G(λ d, η) containing the self-consistent parameter λ and the condition of continuity at r=d/2 to determine A and B. A different EOS can be obtained with a suitable choice of m and the EOS has a lower root-mean-square deviation than that of Barker-Henderson BH2 for LJ fluids.