How much heat is required to convert 500 g of ice at 0°C to water at 0°C? The latent heat of fusion of ice is 330 J g⁻¹.

Given: mass of ice m = 500 g at 0 °C, to become water at 0 °C

latent heat of fusion L = 330 J g⁻¹

The temperature does not change, so only the latent heat term applies: Q = m L = 500 × 330 = 165 000 J

Heat required = 165 000 J (165 kJ)

Ice at 0 °C becoming water at 0 °C is a pure change of STATE — the thermometer never moves. So the formula is Q = mL alone, with no mcΔθ term.

Since Δθ = 0, anyone who reaches for Q = mcΔθ here gets zero, which should be the signal that latent heat is what the question is about. The energy is going into breaking the rigid structure of the ice, not into speeding up its molecules.

Note L = 330 J g⁻¹ in this paper, where others use 336. Take the value given.