Unobviously a poor metaphor.
energy to heat 1kg from -100°C to -5°C: 200kJ
energy to melt 1kg from -5°C (as ice) to 0°C (as water): 345kJ
Water has lots of extremely non-linear behaviours!!!
Do you have a better idea? Either another example or a better way to tell it so it becomes true?
I guess I could start somewhere closer to 0°K, but that wouldn't mean much I guess?
Maybe it is more like water spilling over the top of an earthen dam. It only takes incrementally more water to happen, but is very bad for the structure of the dam and things downstream.
Is caused by a special property of water? Or is it just the discontinuity arising from taking 0°C ice to 0°C water?
If it's the latter it applies to all solid to liquid transitions (entropy of fusion).