Latent Heat
Heat for a phase change, Q = mL, with the specific latent heats of common substances.
167000 J · L = 334 kJ/kg · the temperature does not change while this heat flows
Latent heat is the energy a substance absorbs to change state while its temperature stays fixed: Q = mL. Melting half a kilogram of ice needs 0.5 × 334 = 167 kJ, and the ice stays at 0 °C for the entire time that heat is flowing in.
Heat that does not raise the temperature
Put a thermometer in a beaker of melting ice and it reads 0 °C throughout, even with a flame underneath. The energy going in is not speeding the molecules up — it is breaking the bonds holding them in the solid structure. Only once every last piece has melted does the temperature start to climb again. That is what latent means: hidden, in the sense that it does not show on a thermometer.
This is why a heating curve has flat sections. Between phase changes, heat raises temperature and Q = mcΔT applies. During a phase change, temperature holds still and Q = mL applies instead. A problem that spans both — ice at −10 °C to steam at 110 °C — needs the curve broken into five separate stages, each with its own equation.
Why water’s values are so large
Water takes 334 kJ/kg to melt and 2260 kJ/kg to boil, both unusually high because hydrogen bonding holds the molecules together strongly. The consequences are everywhere: sweating cools effectively because evaporating water carries away a great deal of heat, steam burns are far worse than hot-water burns because condensing steam releases that 2260 kJ/kg into the skin, and coastal climates are mild because the sea absorbs and releases enormous amounts of heat with little temperature change.
m in kilograms, L the specific latent heat in kJ/kg; no temperature term appears because there is no temperature change
- 1 Identify which phase change is happening. Melting and freezing use the latent heat of fusion; boiling and condensing use the latent heat of vaporisation.
- 2 Look up the specific latent heat. For water, fusion is 334 kJ/kg and vaporisation is 2260 kJ/kg.
- 3 Put the mass in kilograms. 500 g becomes 0.5 kg.
- 4 Multiply. 0.5 × 334 = 167 kJ, or 167 000 J.
- 5 Check whether heat goes in or comes out. Melting and boiling absorb that energy; freezing and condensing release exactly the same amount.
Specific latent heats
In kJ/kg, at each substance’s normal transition temperature.
| Substance | Fusion (melting) | Vaporisation (boiling) |
|---|---|---|
| Water | 334 | 2260 |
| Ethanol | 108 | 841 |
| Ammonia | 332 | 1369 |
| Lead | 23 | 871 |
| Aluminium | 397 | 10500 |
The mistakes to avoid
The commonest is including a ΔT. There is no temperature change during a phase transition, so Q = mL has no temperature term — reaching for Q = mcΔT out of habit gives an answer that does not mean anything. The second is using the wrong latent heat: fusion for melting, vaporisation for boiling, and vaporisation is far larger for most substances.
The third is forgetting that the process is symmetric. Freezing a kilogram of water releases the same 334 kJ that melting it absorbs, which is why spraying orchards with water protects the fruit from frost — the water freezing gives up heat that keeps the surroundings at 0 °C rather than colder. And for a multi-stage problem, the total is the sum of every stage: heating the ice, melting it, heating the water, boiling it, then heating the steam.