Specific latent heat

Jonny Nelson introduces an animated explanation of latent heat

Changing the internal energy of a material will cause it to change temperature or change state. The thermal energy to:

curriculum-key-fact
The specific latent heat of a substance is the amount of energy needed to change the state of 1 kg of the substance without changing its temperature.

Each substance has two specific latent heats:

  • latent heat of fusion (the amount of energy needed to freeze or melt the substance at its melting point)
  • latent heat of vaporisation (the amount of energy needed to evaporate or condense the substance at its boiling point)

It usually takes more energy to boil a substance than to melt it, so the latent heat of vaporisation for a substance is usually greater than its latent heat of fusion. The table shows some typical values:

SubstanceSpecific latent heat of fusion (kJ/kg)Specific latent heat of vaporisation (kJ/kg)
Water3342,260
Lead22.4855
Oxygen13.9213

Calculating thermal energy changes

The thermal energy for a change in state is calculated using this equation:

thermal energy for a change in state = mass × specific latent heat

This is when:

  • thermal energy for a change in state is measured in joules (J)
  • mass is measured in kilograms (kg)
  • specific latent heat is measured in joules per kilogram (J/kg)

Question

Calculate the thermal energy needed to freeze 500 g of water at 0°C.

500 g = 500/1,000 = 0.5 kg

specific latent heat of fusion = 334 kJ/kg (from the table above)

specific latent heat of fusion = 334 × 1,000 = 334,000 J/kg

thermal energy = 0.5 × 334,000

= 1,670,000 J (167 kJ)

Measuring latent heat

Latent heat can be measured from a heating or cooling curveline graph. If a heater of known power is used, such as a 60 W immersion heater that provides 60 J/s, the temperature of a known mass of ice can be monitored each second. This will generate a graph that looks like this:

Graph measuring time against temperature, looking at the temperature changes between solid, liquid and gas for ice, water and steam.

The graph is horizontal at two places. These are where energy is being used to break the bonds between the particles to change the state, rather than increase the speed of the particles (and so to increase the temperature).

The longer the horizontal line, the more energy has been used to cause the change of state. The amount of energy represented by these horizontal lines is equal to the latent heat.

Examples

  • A heating curve shows that it takes a 60 W heater 30 minutes to boil a sample of water. Calculate the energy transferred to the water.

30 minutes = 30 × 60 = 1,800 s

energy transferred = power × time

energy transferred = 60 × 1,800

= 108,000 J

  • 50 g of water was used. Calculate the latent heat of vaporisation of water.

50 g = 50 ÷ 1,000 = 0.05 kg

latent heat of vaporisation = 10,800 ÷ 0.05

= 2,160,000 J/kg (2,160 kJ/kg)