Density packs mass into volume

Density tells you how much mass is squeezed into a given volume. A dense material has a lot of mass in a small space.

The symbol ρ is the Greek letter "rho". Density can also be quoted in g/cm³ — just keep your units consistent.

Why solids are densest

The particle model explains why the same substance is usually densest as a solid and least dense as a gas:

• Solid — particles in a regular pattern, touching, only vibrating in fixed positions. Most particles per volume → highest density.
• Liquid — particles close together but random, able to move/flow past each other. Slightly less dense than the solid.
• Gas — particles far apart, random and moving fast. Very few particles per volume → lowest density.

Required practical: find density with a balance and ρ = m ÷ V. For a regular solid, measure sides and calculate the volume. For a liquid, read its volume directly from a measuring cylinder. For an irregular solid, use a eureka (displacement) can — the volume of water pushed out equals the object's volume.

Spot the gas

Your turn — density

Why is a litre of steel so heavy?

Name the state

Tap the state that matches each particle description.

Where does the energy go when water boils?

Melting, boiling and back again

Adding or removing energy moves a substance between states. Each change has a name:

Key idea: changes of state are physical, not chemical. No new substance is made, the mass is conserved, and you can always get the original substance back by reversing the change (e.g. freeze the water and you have ice again).

Watch out — particles don't change size. When something melts, boils or expands, the particles themselves stay exactly the same size and number. What changes is only their spacing and how they move — they spread out and move more freely, they do not grow or shrink.

Internal energy of a substance

The internal energy of a substance is the total energy of all its particles. It is made of two parts:

• Kinetic energy — because the particles are moving/vibrating (linked to temperature).
• Potential energy — stored in the forces and spacing between the particles (linked to the state).

Heating a substance raises its internal energy. That extra energy does one of two jobs:

• raise the temperature (more particle kinetic energy), or
• change the state (more particle potential energy, at constant temperature).

Don't confuse internal energy with temperature. Internal energy = total kinetic + total potential energy of all the particles. Temperature only tracks the kinetic part. So on a plateau the temperature is fixed, yet the internal energy is still rising (the potential part is going up).

Why the graph goes flat

Heat ice steadily and plot temperature against time (or energy supplied). The two flat sections are the changes of state — the temperature stays constant while particles gain potential energy and the forces between them are overcome.

Analogy — the "unlocking" energy: on a flat plateau the energy isn't speeding the particles up, it's spent unlocking them from one another (pulling them apart against their attractions). That's why the thermometer pauses — kinetic energy isn't changing, only potential energy is.

Reading the flat part

Temperature or state?

Tap an event, then tap whether the supplied energy raises the temperature or changes the state.

Physical or chemical?

Raising the temperature

When energy raises the temperature (the sloped parts of the graph), use the specific heat capacity equation:

The specific heat capacity c is the energy to raise 1 kg of a substance by 1 °C. Water's is high (4200 J/kg°C).

Analogy — water is a "thermal sponge". A high specific heat capacity means a substance soaks up a lot of energy for only a small temperature rise (and gives it back slowly when cooling). That is why water is slow to heat and slow to cool — handy for car radiators and central-heating systems, and why coastal climates are milder.

Your turn — heating

Changing state takes energy too

To change state at constant temperature (the flat parts of the graph) you need the specific latent heat L — the energy to change the state of 1 kg of a substance with no temperature change:

• Latent heat of fusion — melting or freezing (solid ⇄ liquid).
• Latent heat of vaporisation — boiling or condensing (liquid ⇄ gas).

Your turn — latent heat

Where does the energy go when water boils?

Why does squashed air push back harder?

How a gas pushes on its walls

Both courses: how particle motion causes gas pressure is in Physics and Combined Science Trilogy; the p V = constant section that follows is Physics only.

Gas particles move quickly and randomly. Each time one collides with a wall it bounces off and gives the wall a tiny push. Billions of collisions every second add up to a steady pressure on the container.

Analogy — drumming on the walls: picture thousands of tiny rubber balls thrown nonstop at the inside of a box. No single ball does much, but the constant drumming of all of them keeps a steady outward push — that push, per unit area, is the gas pressure.

Raise the temperature at constant volume and the particles move faster, so they hit the walls harder and more often — the pressure rises.

Heating a sealed gas

Squeeze it, and pressure rises

For a fixed mass of gas at constant temperature, pressure and volume are linked:

Squeeze the gas into a smaller volume and the same particles hit the walls more often, so the pressure rises. Also (higher tier), doing work on a gas (e.g. quickly pushing a bike pump) transfers energy to it and can raise its temperature.

Analogy — same balls, half the room. The number of particles never changes. Halve the volume and you crowd exactly the same particles into half the space, so each square metre of wall is hit twice as often — double the volume, halve the pressure; halve the volume, double the pressure. That's why p × V stays constant.

Your turn — p₁V₁ = p₂V₂

Why does squashed air push back harder?

The equations to know

You've covered the key ideas in AQA 4.3 — density & the states of matter, changes of state & internal energy, specific heat capacity, latent heat, and gas pressure. Press Finish to see your score.