Changes of state and 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 energy required for a particular change in temperature is given by the specific heat capacity and the mass of material
  • the energy required for a particular change in state is given by the specific latent heat and the mass of material
curriculum-key-fact
Specific latent heat is the amount of energy required to change the state of 1 kilogram (kg) of a material without changing its temperature.

As there are two boundaries, solid/liquid and liquid/gas, each material has two specific latent heats:

  • latent heat of fusion – the amount of energy needed to freeze or melt 1 kg of the material at its melting point
  • latent heat of vaporisation – the amount of energy needed to evaporate or condense 1 kg of the material at its boiling point

Some typical values for specific latent heat include:

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

An input of 334,000 joules (J) of energy is needed to change 1 kg of ice into 1 kg of water. The same amount of energy needs to be taken out of the liquid to freeze it.

Calculating thermal energy changes

The amount of thermal energy stored or released as the temperature of a system changes can be calculated using the equation:

energy required for a change of state = mass × specific latent heat

\Delta \text{E} = \text{m} \times \text{l}

This is when:

  • energy ( \Delta \text{E}) is measured in joules (J)
  • mass ( \text{m}) is measured in kilograms (kg)
  • specific latent heat ( \text{l}) is measured in joules per kilogram (J/kg)
Question

How much energy is needed to freeze 500 grams (g) of water from 0°C?

\text{E} = \text{ml}

= 0.5 × 334,000

\text{E} = 167,000 J

Measuring latent heat

Latent heat can be measured from a heating or cooling curve line 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 the places where the energy is not being used to increase the speed of the particles, increasing temperature, but is being used to break the bonds between the particles to change the state.

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 relates to the latent heat.

Example

If a horizontal line that shows boiling on a heating curve is 1 hour 3 minutes long, how much energy has a 60 watt (W) heater provided to the water?

63 minutes = 3,780 s

60 W means 60 J of energy is supplied every second

energy = power × time

energy = 60 × 3,780

energy = 226,800 J

Example two

If this energy had caused 100 g of water to evaporate, what is the latent heat of vaporisation of water?

226,800 J for 100 g is equivalent to 2,268,000 J for 1 kg.

The latent heat of vaporisation of water is 2,268,000 J/kg.