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.... My perhaps naive approach is to
describe the process non-mathematically as
1. Add/remove energy to/from the water
2. Some of the energy goes to changing the entropy of the water
3. Some of the energy goes to changing the temperature of the water
I would then like to give this a more formal mathematical expression. Importantly, I would like it be valid for a phase change, during which all of the energy goes to changing the entropy, and none to changing the temperature.