Specific Latent Heat Capacity | CIE International A Level Physics Revision Notes 2025

Defining latent heat capacity

Changes of state diagram

The example of changes of state between solids, liquids and gases

When a substance changes state, there is no temperature change
The energy supplied to change the state is called the specific latent heat and is defined as:

The thermal energy required to change the state of 1 kg of mass of a substance without any change of temperature

There are two types of latent heat:
- Specific latent heat of fusion (melting)
- Specific latent heat of vaporisation (boiling)
It is important to recognise the difference between latent heat and specific latent heat
- latent heat is the energy required to change a materials state
- specific latent heat is the energy required to change the state of 1 kg of a material

The changes of state with heat supplied against temperature. There is no change in temperature during changes of state.

The thermal energy required to convert 1 kg of solid to liquid with no change in temperature

The thermal energy required to convert 1 kg of liquid to gas with no change in temperature

The amount of energy Q required to melt or vaporise a mass of m with latent heat L is:

$Q = L m$

Where:
- Q = amount of thermal energy to change the state (J)
- L = latent heat of fusion or vaporisation (J kg^-1)
- m = mass of the substance changing state (kg)
The values of latent heat for water are:
- Specific latent heat of fusion = 330 kJ kg^-1
- Specific latent heat of vaporisation = 2.26 MJ kg^-1
Therefore, evaporating 1 kg of water requires roughly seven times more energy than melting the same amount of ice to form water
The reason for this is to do with intermolecular forces:
- When ice melts: energy is required to just increase the molecular separation until they can flow freely over each other
- When water boils: energy is required to completely separate the molecules until there are no longer forces of attraction between the molecules, hence this requires much more energy

The energy needed to boil a mass of 530 g of a liquid is 0.6 MJ.

Calculate the specific latent heat of the liquid and state whether it is the latent heat of vaporisation or fusion.

Step 1: Write the thermal energy required to change state equation

$Q = L m$

Step 2: Rearrange for latent heat

$L = \frac{Q}{m}$

Step 3: Substitute in the values

m = 530 g = 530 × 10^-3 kg

Q = 0.6 MJ = 0.6 × 10⁶ J

$L = \frac{0.6 \times 10^{6}}{530 \times 10^{- 3}} = 1.132 \times 10^{6} J k g^{- 1} = 1.1 M J k g^{- 1} (2 s . f .)$

L is the latent heat of vaporisation because the change in state is from liquid to gas (boiling)

Use these reminders to help you remember which type of latent heat is being referred to:

Latent heat of fusion = imagine ‘fusing’ the liquid molecules together to become a solid
Latent heat of vaporisation = “water vapour” is steam, so imagine vaporising the liquid molecules into a gas