Is more energy required to melt one gram of ice at 0 or to boil one gram of water at 100?

The energy required to melt one gram of ice at 0 degrees is given by:

where m is the mass of the ice and  is the latent heat of fusion of ice. Substituting, we find


The energy required to boil one gram of water at 100 degrees is given by:
 
where m is the mass of the water and  is the latent heat of evaporation of the water. Substituting, we find


Therefore, it is required more energy to boil one gram of water at 100 degrees than to melt one gram of ice at 0 degrees.

This is what a calorimeter is used for simpler ex, to measure calories in food.