I have read many times that the reason temperature stays constant when heating a substance through a change of state is because most of the joules of energy put into the substance go into the potential energy store of the substance (to help the molecules/atoms move further apart from each other even though they have attractive forces towards each other) whilst barely any of the joules of energy put into the substance go into increasing the kinetic energy of the molecules (i.e. by making them vibrate more). (Of course, when the substance is not being heated through a change of state, a greater proportion of the total energy put in goes into the kinetic energy store of the molecules whilst a smaller proportion (than during a change of state) goes into the potential energy store of the molecules: this is what the specific heat capacity reflects, from my understanding.) But no sources I've found explain the reverse situation: where temperature stays constant whilst cooling a substance through a change of state. So I wanted to check if the argument for this would be the reverse argument, as you would expect: during a change of state, you are still taking a total number of joules out of the substance per second in order for it to freeze/condense, but a very large proportion of those joules taken out comes from the potential energy store of the substance (since the molecules/atoms are quite suddenly getting quite a lot closer together again during the change of state) and only a tiny proportion of those joules taken out come from the vibrational/kinetic store of the molecules of the substance, so since this vibrational level is what we measure as heat, the temperature does not go down much. So is this argument correct, please?
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