Enthalpy/entropy compensation is a general issue of intermolecular binding processes when the interaction between the partners can be roughly modelled with a single harmonic potential. Whereas linear H/S correlations are wished for by experimentalists, and often graphically justified, no inflexible law of thermodynamics supports the latter statement. On the contrary, the non-directional Ford's approach suggests logarithmic H/S relationships, which can be linearized only over narrow enthalpy/entropy ranges. Predictions covering larger domains require mathematical mapping obeying specific boundary conditions which are not compatible with linear plots. The analysis of solvent-free melting processes operating in six different classes of organic and inorganic materials shows that reciprocal Hill plots are acceptable functions for correlating melting enthalpies and entropies. The combination of H/S compensation with the observed linear dependence of the cohesive free energy densities with respect to the melting temperature eventually provides an unprecedented interdependence between melting temperatures and molar volumes. This procedure is exploited for the prediction of melting temperatures in substituted cyanobiphenyls.