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For example, let us say we are measuring water. The energy gained during vaporization requires 2260 Joules/gram, while the energy gained during melting is only 334 Joules/gram. Is this because the particles during melting are close together, and the particles of vaporization are far apart?

If I were to rephrase the question above, why is the latent heat of vaporization of water greater than the latent heat of fusion of water?

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The reason is that occasionally there are much more differences between the liquid phase and the gaseous phase of a system than the differences between the liquid and solid phases of the same system. In the liquid phase although the translation symmetry doesn't exists in contrast to the solid phase, the molecules are yet close enough to each other that the interactions among them is significant(however they are relatively weaker than in the solid phase and so the melting's latent heat is non-zero). But in the gaseous phase the typical distance between molecules are much more larger than the solid and liquid phase and hence the interactions among them are by far weaker than the liquid phase and therefore the vaporizing's latent heat is significantly larger than the one in the melting process.

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