Linear correlation of heat of vaporization with surface tension of normal and quantum liquids: intrinsic conservation of degrees of freedom

For normal and quantum liquids, new results on a linear relation between the temperature scales Thv=ΔHv/R and Tref=f(γfρf,) are presented where ΔHv is the heat of vaporization, R is gas constant, γf and ρf are the surface tension and the liquid density at freezing temperature Tf, respectively. This relationship is well justified in terms of statistical mechanical results for the fact that both Tref and Thv are related to pair potential and pair correlation functions. In practice, we have determined that TrefTf1/2, is the corresponding parameter that links quantum liquids to normal liquids in the succeeding linear behavior. It applies quite well to linear hydrocarbons C1–C8, C2H4, H2, He, Ne, Ar, Kr, Xe, N2, C6H6, and C7H8 with a linear correlation coefficient of 0.9992. Variation of Tref and TrefTf1/2 with Λ, the de Boer constant, reveal that the role of Tf1/2 has to do, in general, with structure and, in particular, with quantum characters due to mass, size, and interaction energy effects. Such a distinction between Tref and Tf results in distinctions in quantum mechanical properties of the liquids. A particular T3/2 power-law arises, leading to a postulate for intrinsic conservation of degrees of freedom of solid–liquid interface equilibrated with its bulk phases.