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Why is latent heat required for a system to change its state? (I.e. liquid water to ice) Why the "extra" energy?

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The second part of the question is nicely answer by Martin. To the first part: latent heat is not always required. There are a number of examples, the paramagnetic to ferromagnetic phase transition is one of them that do not require or give off any latent heat.

A general sign for latent heat is if you have coexistence of two phases. Water and ice can coexist at 0 degrees Celsius and it takes energy to convert one into the other without any temperature change.

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Forming bonds gives out energy, making bonds takes energy.

In a solid there are more (and stronger) bonds between molecules - so to melt a solid you have to put in energy to break these bonds and allow the molecules to move freely. Similarly a liquid gives off energy when it 'freezes' as the bonds are formed

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