Reciprocal System Research Society

I just noticed that the ratio of heat of vaporization of water (540 cal/g) to the heat of fusion (80 cal/g) is an unusual ratio (27/4). Larson explains the derivation of specific heat but this particular ratio is dimensionless and doesnt require the interregional ratio. I would venture an explanation, paraphrasing Larson, as follows: A liquid has escaped the time region in one dimension of space. To become a gas it must escape two more dimensions of space. Larson also says that thermal motion cannot cross the time boundary until "its magnitude is sufficient to overcome the progression of the natural reference system without assistance from the gravitational motion" The molecule must reach unit speed distributed over three dimensions therefore 3 squared times 3, or 27 possible motions. Because we are analyzing energy rather than mass we take the reciprocal. It would be interesting to see if this ratio of 27/4 applies to other substances. I suppose if it doesnt then this explanation is complete nonsense. Nevertheless it is interesting.

Heat of vaporization and heat of fusion are temperature and pressure dependent. A compound's ability to change phase depends on its surrounding environment. In general compounds won't follow this ratio but I wonder if they will at a certain temperature and pressure combination?