Latent heat

When a substance melts or boils, the energy supplied breaks the bonds between its particles instead of raising the temperature, so the temperature stays the same: the flat parts of a heating curve. The energy needed to change the state of 1 kg is the specific latent heat, L, and the energy for any mass is E = mL.

Key facts

  • Energy to change state: E = mL (L = specific latent heat, J/kg).
  • Water: L (fusion) = 334,000 J/kg; L (vaporisation) = 2,260,000 J/kg.
  • During melting or boiling the temperature stays constant (flat parts of a heating curve).

Worked examples

Example 1

While water is boiling, where does the energy supplied go?

  1. While water boils, its temperature stays at 100°C.
  2. So the energy is not raising the temperature.
  3. It goes into separating the particles: the latent heat.

Answer: into breaking the bonds between particles (latent heat), not raising the temperature

Example 2

A heating curve for ice shows a flat part at 0°C, even though the ice is still being heated. Why?

  1. At 0°C the ice is changing into water.
  2. The energy supplied goes into separating the particles, not into making them move faster.
  3. So the temperature stays at 0°C until all the ice has melted. This energy is the latent heat.

Answer: the ice is melting: the energy breaks the bonds between the particles instead of raising the temperature (latent heat)

Example 3

Water at 20°C is heated steadily until it has been boiling for 5 minutes. Describe the shape of its temperature–time graph.

  1. While the water warms up, the energy raises its temperature, so the line rises.
  2. At 100°C the water boils: the energy now separates the particles instead, so the line is flat.

Answer: A line rising from 20°C to 100°C, then a flat line at 100°C while it boils.

Example 4

Liquid stearic acid is left to cool. Its temperature stays at 69°C for several minutes. What is happening, and why does the temperature not fall?

  1. A flat part on a cooling curve shows a change of state.
  2. As the liquid freezes, bonds form between the particles and energy is released.
  3. That energy makes up for the energy lost to the room, so the temperature stays at the freezing point until it is all solid.

Answer: It is freezing: as bonds form between the particles, energy is released, which keeps the temperature at 69°C until it is all solid.

Example 5

How much energy is needed to melt 0.7 kg of ice on a car windscreen at 0°C? (Specific latent heat of fusion of ice = 334,000 J/kg.)

  1. Melting needs latent heat, with no temperature change.
  2. Use E = mL.
  3. E = 0.7 × 334,000 = 233,800 J

Answer: 233,800 J

Example 6

How much energy is needed to boil away 0.20 kg of water that is already at 100°C? (specific latent heat of vaporisation: 2,260,000 J/kg)

  1. The temperature does not change while it boils: E = m × L
  2. E = 0.20 × 2,260,000 = 452,000 J

Answer: 452,000 J (452 kJ)

Example 7

How much energy is needed to boil away 1 kg of water already at 100°C? (Specific latent heat of vaporisation of water = 2,260,000 J/kg.) Give your answer in MJ.

  1. Boiling needs latent heat, with no temperature change.
  2. Use E = mL.
  3. E = 1 × 2,260,000 = 2,260,000 J = 2.26 MJ

Answer: 2.26 MJ