Use specific heat capacity, and explain melting and boiling using latent heat

What this dot point is asking

SEAB wants you to use the specific heat capacity formula to find the energy needed to change an object's temperature, to describe the changes of state (melting, boiling, freezing, condensing), and to explain why the temperature stays constant during a change of state using the idea of latent heat. The big idea is that energy raises temperature in one state, but during melting or boiling that energy instead changes the state.

The answer

Specific heat capacity

Some materials heat up easily, others need a lot of energy. The specific heat capacity, $c$, is the energy needed to raise the temperature of one kilogram of a substance by one degree Celsius.

The formula linking the energy supplied to the temperature change is:

where $E$ is the energy in joules, $m$ is the mass in kilograms, $c$ is the specific heat capacity, and $\Delta\theta$ is the temperature change. Water has a high specific heat capacity ($4200\ \text{J kg}^{-1}\,^\circ\text{C}^{-1}$), which is why it takes a long time to heat a kettle and why the sea warms up slowly.

Changes of state

Matter exists as solid, liquid or gas. Adding or removing energy changes the state:

• Melting: solid to liquid (adding energy).
• Boiling (or evaporating): liquid to gas (adding energy).
• Condensing: gas to liquid (removing energy).
• Freezing (solidifying): liquid to solid (removing energy).

Why temperature stays constant during a change of state

Here is the surprising part. While a pure substance melts or boils, its temperature stays constant even though energy is still being supplied. For example, a mixture of ice and water stays at $0\ ^\circ\text{C}$ until all the ice has melted.

This is because the energy supplied is not raising the temperature. Instead it is used to break the bonds between the particles so they can move further apart (from solid to liquid, or liquid to gas). Only once the change of state is complete does the temperature start to rise again.

Latent heat

The energy needed to change the state of a substance without changing its temperature is called latent heat ("latent" means hidden):

• The latent heat of fusion is the energy to melt a solid into a liquid.
• The latent heat of vaporisation is the energy to boil a liquid into a gas.

This hidden energy is given back when the substance condenses or freezes, which is why steam can scald badly: it releases a lot of latent heat as it condenses on your skin.

Examples in context

Example 1. Sweating to cool down. When sweat evaporates from your skin, it takes its latent heat of vaporisation from your body. Removing that energy cools you down. This is why a breeze, which speeds up evaporation, feels cooling on a hot day.

Example 2. Using water as a coolant. Car engines and power stations use water to carry away heat because its high specific heat capacity lets it absorb a lot of energy for only a small temperature rise. The same property means coastal areas have milder weather, as the sea heats and cools slowly.

Try this

• Cue. Find the energy to heat $0.20\ \text{kg}$ of water by $30\ ^\circ\text{C}$, with $c = 4200\ \text{J kg}^{-1}\,^\circ\text{C}^{-1}$. [2 marks] $E = mc\,\Delta\theta = 0.20 \times 4200 \times 30 = 25\,200\ \text{J}$.

• Cue. Explain why the temperature of boiling water stays at $100\ ^\circ\text{C}$ even as heating continues. [2 marks] The energy supplied is used as latent heat to turn liquid into gas, breaking the bonds between particles, rather than raising the temperature.

• Cue. Name the change of state and whether energy is added or removed: water vapour forming droplets on a cold window. [2 marks] Condensing (gas to liquid); energy is removed (given out) to the cold window.