Why does it take more energy to evaporate water than to melt ice?

The energy required to completely separate the molecules, moving from liquid to gas, is much greater that if you were just to reduce their separation, solid to liquid. Hence the reason why the latent heat of vaporization is greater that the latent heat of fusion.

It takes longer to boil water than to melt ice because of the difference in the amount of heat required to overcome the forces of attraction by keeping the temperature constant during this time. ... This is the reason it takes longer in boiling than in melting.

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