How to Calculate Latent Heat

This finds the heat needed for a change of state, such as ice melting or water boiling.

$m$ is the mass and $L$ the latent heat. The latent heat of fusion of ice is 334 J/g and the latent heat of vaporisation of water is 2257 J/g. This is separate from the heat $Q = mc\Delta T$ needed to change the temperature.

Heat that does not raise the temperature

Add heat to ice at 0°C and it stays at 0°C until every last piece has melted. The heat is not raising the temperature but breaking apart the bonds between molecules. Heat that never shows on a thermometer is called latent. It is why a drink with ice in it stays cold.

Example

Melt 100 g of ice at 0°C and heat the water to 100°C. Melting takes $100 \times 334 = 33400$ J and heating takes $100 \times 4.2 \times 100 = 42000$ J, giving 75400 J in total, or 18.0 kcal. Simply melting the ice costs as much heat as raising the water from 0°C to 80°C.

Vaporisation costs far more

The latent heat of vaporisation of water is 2257 J/g, nearly seven times the heat of fusion. This is why evaporating sweat cools the body so effectively, and why a kettle takes so long to boil dry.

Notes

Latent heat and specific heat are different things. Latent heat is the heat of changing state; specific heat is the heat of changing the temperature by one kelvin.