Correlation examination of truncated virial equation of state correspondence to linear isothermal regularity (LIR)

According to LIR, (Z-1) v2 varies linearly with respect to ρ2, where Z = p / ρRT is thecompression factor and ρ = 1 / v is the molar density. It was shown that LIR works fordensities greater than the Boyle density (pB ~ 1.8pc, where ρc is the critical density) and fortemperatures below about twice the Boyle temperature (TB c ~ 2.5 2.7TTc ) [1-2]. On the otherhand, the second and third viral coefficients emerge in analytical EOSs based on statisticalmechanicalperturbation theory for hard spheres and LJ fluids [3-6]. By considering thesefacts, it seems that there is a correlation between dilute and dense EOSs. In this paper wepresent a new method that shows the similarity and correlation of dilute and dense states.