Specific Latent Heat

Two ways that heating can affect a substance

Transferring energy to a substance increases its internal energy, but the result is not always a rise in temperature. The energy can instead cause a change of state.

If a substance remains in one state, such as liquid water being warmed, its particles gain kinetic energy and move more rapidly on average. Its temperature rises. The property that connects the energy transferred with the resulting temperature change is specific heat capacity.

Specific heat capacity is the energy required to raise the temperature of 1 kg of a substance by 1 °C, without changing its state. Its unit is joules per kilogram per degree Celsius, written J/(kg °C).

Energy during a change of state

At the melting point or boiling point, continued energy transfer can change the state instead of raising the temperature. The transferred energy changes the particles’ potential energy as forces of attraction between them are overcome. It does not increase their average kinetic energy, so the temperature remains constant while the change takes place.

This energy may appear to be “hidden” because a thermometer records no temperature rise. It is therefore called latent heat. The word specific means that the quantity is given for each kilogram of the substance.

Specific latent heat is the energy required to change the state of 1 kg of a substance without changing its temperature. It is measured in joules per kilogram, J/kg.

Data for Temperature as energy is supplied

Once the whole sample has changed state, further energy supplied can again increase the particles’ average kinetic energy, so the temperature starts to rise. This explains the sloping and horizontal sections of the heating curve.

The reverse changes also involve latent heat. During freezing or condensation, energy is transferred from the substance to the surroundings as attractions form. The temperature remains constant until that change of state is complete. The specific latent heat gives the magnitude of the energy transferred per kilogram, whether the change is forwards or backwards.

Fusion and vaporisation

There are two named types of specific latent heat:

• Specific latent heat of fusion applies to a change between a solid and a liquid. Energy is supplied during melting and released during freezing.
• Specific latent heat of vaporisation applies to a change between a liquid and a gas. Energy is supplied during vaporisation and released during condensation.

“Fusion” must not be taken to mean only melting, and “vaporisation” must not be taken to mean only boiling: each specific latent heat also applies to the reverse change.

Specific heat capacity compared with specific latent heat

The key question is whether the substance’s temperature changes or its state changes.

For a temperature change with no change of state,

$$\Delta E = mc\Delta \theta$$

where $c$ is specific heat capacity in J/(kg °C) and $\Delta\theta$ is the temperature change in °C.

For a change of state with no change in temperature,

$$E=mL$$

where $L$ is specific latent heat in J/kg. The correct value of $L$ must match the state change: $L_f$ for fusion or $L_v$ for vaporisation.

Specific heat capacity therefore describes how difficult it is to change a substance’s temperature. Specific latent heat describes how much energy per kilogram is transferred when changing its state at constant temperature.