For normal and quantum liquids, new results on a linear relation between the temperature scales T-hv = Delta H-v/R and T-ref =f(gamma(f) rho(f),) are presented when Delta H-v is the heat of vaporization, R is gas constant, gamma(f) and rho(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 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 C-1-C-8, C2H4, H-2, He, Ne, Ar, Kr, Xe, N-2, C6H6, and C7H8 with a linear correlation coefficient of 0.9992. Variation of T-ref and TrefTf1/2 With Lambda, the de Beer 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.