Two distinct approaches are used to derive a unique and exact analytical expression for the heat of vaporization with respect to the nanocavity energy formation and the molecular hard-core diameter. This expression provides a new method to compare different models of cavity formation in the liquids as well as to predict the effective molecular hard-core diameter at different temperatures and pressures. The effective hard-core diameters and cavity formation energies of liquid Ar, Xe and CH4 are calculated at various temperatures and pressures using different cavity formation models and they are compared. It is found that the effective hard-core diameter generally decreases with increase of temperature as expected and it increases with increase of pressure.
