why is the latent heat of vaporisation greater than the latent heat of fusion?
Latent heat is the heat released or absorbed by a body or a thermodynamic system during a process that occurs without a change in temperature. A typical example is a change of state of matter, meaning a phase transition such as the melting of ice or the boiling of water.
Latent heat of fusion
The energy absorbed by the system under a phase transition of solid to liquid.
Latent heat of vaporization
The energy absorbed by the system under a phase transition of liquid to gas.
If you consider the phase transition of any substance it is from solid-liquid-gas.
We need some energy to convert a substance from solid to liquid. We need even more energy to convert it to a gas. For example from the amount of heat in room temperature a ice cube can be liquefied. But we need to give more heat than room temperature to boil it(to make vapour).
So now it is obvious that latent heat of fusion is lower than latent heat of vapourisation.
When you compare the difference in volume between gasses and liquids and liquids and solids we find that gasses exspand much more during this phasechange. This is because the speed of the molcules increases far more during vaporization then it does during melting. As such there is a corisponding increase in the latent heat.