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Latent heat

Heat and matter · level 6, lesson 1 of 6

A question to start

Heat a pan of ice from −20 °C on a steady flame, and take its temperature every minute. The temperature climbs, then sits at 0 °C for a long time, then climbs again, then sits at 100 °C. Where does the heat go while the temperature is stuck?

The idea

While a substance is changing state, the heat goes into pulling its particles apart, not into making them move faster. So the temperature stays the same until the change is complete. This hidden energy is latent heat:

\[Q = mL,\]

where \(L\) is the specific latent heat, the energy per kilogram to change state.

For water \(L\), kJ per kg
Melting ice (fusion) 334
Boiling water (vaporisation) 2,260
Ice straight to vapour (sublimation) about 2,830

Boiling takes almost seven times as much energy as melting: pulling the particles right apart, into a gas, is much harder than letting them slide.

meltingboiling0 °C100 °C heat put in

Worked examples

1. Melting. 2 kg of ice at 0 °C into water at 0 °C: \(Q = 2 \times 334{,}000 = 668{,}000\) J.

2. Boiling. 0.5 kg of water at 100 °C into steam: \(Q = 0.5 \times 2{,}260{,}000 = 1.13\times10^6\) J.

3. Sweat. Evaporating 0.1 kg of sweat takes about \(0.1 \times 2{,}400{,}000 = 240{,}000\) J from your skin (evaporating at skin temperature takes a little more than at 100 °C). That is how sweating cools you.

Try it

  1. Why does the temperature stay at 0 °C while ice melts?
  2. How much energy melts 5 kg of ice at 0 °C?
  3. A 2,000 W kettle boils at 100 °C. How long does it take to boil away 0.2 kg of water?
  4. Why does steam at 100 °C burn worse than water at 100 °C?
Answers
  1. The heat is going into separating the particles, not making them move faster.
  2. \(5 \times 334{,}000 = 1.67\times10^6\) J.
  3. \(0.2 \times 2{,}260{,}000/2000 = 226\) s.
  4. As steam condenses on your skin it gives out its latent heat, 2,260 kJ per kg, as well as cooling.

Common mistake

"Turning up the heat makes boiling water hotter." It boils faster, not hotter. The extra heat makes more steam; the water stays at its boiling point.

Where it leads