I guess that it would need several characteristics
+ It would have to conduct heat really well so that you could get the heat into it very quickly.
+ It would have be able to freeze at temperatures that were not too cold and boil at temperatures that were not too hot (things that freeze at very cold temperatures often go straight from solid to gas when you try to melt them).
+ It probably wouldn’t have a crystal structure, since crystals take a bit more energy to break up than amorphous (i.e. non-crystals) materials.
+ It would have a low ‘specific heat’, which is a measure of how much energy it take to make or break bonds in the material. (A frozen material is one that has bonds between the different molecules).
What that material is: I don’t know, but I’m sure that it would be possible to work out with a list of the specific heat capacities and thermal conductivities of different materials. If you find out, let me know!
There are two easy ways to change state, heating and cooling (which Tim has covered very well) and compressing things (like liquids in an aerosol can).
The fastest way to melt something that I could imagine would be to have something that is normally liquid and squash it up until it is a solid – then when you release it, it will melt.
Have you ever seen walking on custard? Or tried to punch a bowl of cornflour in water? This seems to be something changing very quickly from liquid to solid and then back again (melting).
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