GCSE density, changes of state and specific heat: a guide

Density, changes of state and specific heat, explained

In a solid the particles are packed closely in a regular pattern and can only vibrate about fixed positions. In a liquid they are still close together but irregularly arranged, and they slide past one another. In a gas the particles are far apart, move quickly in random directions and are in no fixed arrangement. Density is the mass in each unit of volume, density = mass ÷ volume, in kilograms per cubic metre or grams per cubic centimetre. Solids and liquids are dense because their particles are close together, while gases are around a thousand times less dense because the same particles are spread over a much larger space. Changing state alters the spacing, so the density changes, but the number of particles, and therefore the mass, does not. Water is a well-known exception to the usual pattern: ice is slightly less dense than liquid water, which is why it floats.

Melting, evaporation (including boiling) and sublimation, where a solid turns directly to a gas, are physical changes and are reversible: freezing, condensing and a gas turning directly back to a solid (deposition) return the substance to how it began. No new substance is made and mass is conserved. Heating a substance increases its internal energy. When it is not changing state, the energy goes into making the particles move faster, which students see as a rising temperature. The amount needed depends on the mass, the substance and the temperature rise, and is found using the equation change in thermal energy = mass × specific heat capacity × change in temperature. Water’s specific heat capacity is high, about 4200 joules per kilogram per degree Celsius, which is why it takes a long time to warm up and a long time to cool down.

During a change of state the temperature stays constant, even though energy is still being supplied. On a heating curve this shows as a flat section. The energy is not making the particles move faster. It is being used to overcome the forces holding the particles together, so melting and evaporation take in energy and freezing and condensing give it out. The energy needed to change the state of 1 kg of a substance without a change in temperature is its specific latent heat, and the equation is energy = mass × specific latent heat. Evaporating is much more demanding than melting, because the particles have to be pulled completely apart.

Students also meet the idea that gas pressure comes from particles hitting the walls of the container. If the volume stays the same and the gas is heated, the particles move faster. They hit the walls more often and with more force, so the pressure increases. The programme of study asks for this link to be understood qualitatively, so the skill is explaining it in terms of particles, not calculating with it. It explains why a sealed can can burst in a fire and why car tyre pressure rises a little after a long drive.

Words your child will hear

Density

How much mass there is in each unit of volume. Water is about 1000 kg per cubic metre.

Specific heat capacity

The energy needed to raise the temperature of 1 kg of a substance by 1 °C.

Specific latent heat

The energy needed to change the state of 1 kg of a substance with no change in temperature.

Sublimation

A solid changing directly into a gas, without becoming a liquid first.

Evaporation

A liquid changing to a gas. It can happen at any temperature at the surface; boiling happens throughout the liquid at the boiling point.

Internal energy

The total of the kinetic and potential energy of all the particles in a substance.

Reversible change

A change that can be undone, and in which no new substance is made.

What the National Curriculum says

The programme of study for Key Stage 4 says:

• Students should be taught about relating models of arrangements and motions of the molecules in solid, liquid and gas phases to their densities
• Students should be taught about melting, evaporation, and sublimation as reversible changes
• Students should be taught about calculating energy changes involved on heating, using specific heat capacity; and those involved in changes of state, using specific latent heat
• Students should be taught about links between pressure and temperature of a gas at constant volume, related to the motion of its particles (qualitative)

Objectives from the National Curriculum in England, © Crown copyright, used under the Open Government Licence v3.0.

A worked example

Common mistakes and how to help

How to help at home

• Measure a density. Use kitchen scales for the mass of a small object that sinks, such as a stone, and a measuring jug of water to find its volume by how much the level rises (1 millilitre is 1 cubic centimetre). Divide mass by volume to get the density in grams per cubic centimetre and compare it with water at 1 g per cubic centimetre.
• Weigh an ice cube as it melts. Seal an ice cube in a small freezer bag and weigh it, leave it to melt, wipe the outside of the bag dry, then weigh it again. The mass is the same, because no particles have been added or lost. Put the bag back in the freezer to show the change is reversible, and ask your teenager what has changed instead.
• Watch the pressure change. Screw the lid tightly on an empty plastic bottle in a warm room, then put it in the freezer for twenty minutes. The sides often dent inwards, because the cooler air particles move more slowly and hit the walls less often and less hard, so the pressure inside falls below the pressure outside. Ask for that explanation in your teenager’s own words.
• Spot sublimation and evaporation. Washing hung out on a freezing day can freeze stiff and still dry slowly, because the ice turns straight into water vapour without melting: sublimation. Compare it with a puddle drying on a warm day, which is evaporation, and ask which changes reverse each one (deposition and condensation).

Related topics

Everything in Key Stage 4 science