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

Abstract

For normal and quantum liquids, new results on a linear relation between the temperature scales T hv=Δ H v/ R and T ref= f( γ f ρ f,) are presented where Δ H v is the heat of vaporization, R is gas constant, γ f and ρ f are the surface tension and the liquid density at freezing temperature T f, respectively. This relationship is well justified in terms of statistical mechanical results for the fact that both T ref and T hv are related to pair potential and pair correlation functions. In practice, we have determined that T ref T f 1/2, is the corresponding parameter that links quantum liquids to normal liquids in the succeeding linear behavior. It applies quite well to linear hydrocarbons C 1–C 8, C 2H 4, H 2, He, Ne, Ar, Kr, Xe, N 2, C 6H 6, and C 7H 8 with a linear correlation coefficient of 0.9992. Variation of T ref and T ref T f 1/2 with Λ, the de Boer constant, reveal that the role of T f 1/2 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 T ref and T f results in distinctions in quantum mechanical properties of the liquids. A particular T 3/2 power-law arises, leading to a postulate for intrinsic conservation of degrees of freedom of solid–liquid interface equilibrated with its bulk phases.