During a change of state the temperature does not change, so the equation uses the specific latent heat instead of a temperature change. The thermal energy for a change of state is found with:
thermal energy for a change of state = mass × specific latent heat
The thermal energy is in joules (J), the mass is in kilograms (kg) and the specific latent heat is in J/kg. There is no temperature term because the temperature stays constant while the state changes.
For water, the specific latent heat of fusion is 334000 J/kg and the specific latent heat of vaporisation is 2260000 J/kg. Melting 0.5 kg of ice at 0 °C needs 0.5 × 334000 = 167000 J. Boiling 1 kg of water at 100 °C needs 2260000 J. Vaporisation needs more energy than fusion for the same mass because the particles must be completely separated from each other, not just freed to move past each other.
The equation can be rearranged to give specific latent heat = thermal energy ÷ mass. If 600000 J melts 3 kg of a solid, then L = 600000 ÷ 3 = 200000 J/kg. Doubling the mass to 6 kg needs twice the energy, which is 1200000 J.