GCSE Combined Science Particle model and density revision

The particle model pictures matter as tiny moving particles. In a solid they are packed in a regular pattern and vibrate about fixed positions — a fixed shape and volume. In a liquid they are still close together but slide past one another, so the substance flows and takes its container's shape. In a gas the particles are far apart and fly in random directions at high speed, filling whatever space they are given and easily squeezed into less.

The six changes of state — melting, freezing, evaporating, boiling, condensing and sublimating — are physical changes: the particles themselves never change, only their arrangement, so the mass is exactly conserved. Internal energy is the account book of the particles: the sum of their kinetic stores (how fast they move or vibrate) and potential stores (the energy in their arrangements and the forces between them). Heating adds to both; a change of state spends the energy on the potential store alone, which is why the temperature holds steady while, say, ice melts.

Density is the mass packed into each unit of volume: ρ = m/V, with ρ in kg/m³ when m is in kilograms and V in cubic metres, or in g/cm³ for grams and cubic centimetres. The conversion: 1 g/cm³ = 1000 kg/m³ (a cubic metre holds a million cubic centimetres, and a kilogram is a thousand grams). Water sits at 1000 kg/m³; a cube of side 0.20 m with mass 21.6 kg has V = 0.20³ = 0.008 m³, so ρ = 21.6 ÷ 0.008 = 2700 kg/m³ — aluminium.

Required practical — density. For a regular solid (a cube or cuboid), measure each side with a ruler and compute the volume, then divide the balance-measured mass by it. For an irregular solid, lower it into a displacement can (or a measuring cylinder of water) and read the volume of water pushed out — a 178 g object that displaces 20 cm³ has ρ = 178 ÷ 20 = 8.9 g/cm³, the density of copper. For a liquid, weigh the empty measuring cylinder, add the liquid, read the volume at eye level, and subtract: 96 g of liquid filling 100 cm³ gives ρ = 0.96 g/cm³. Read the volume scale at the bottom of the meniscus and repeat for a mean.

During a change of state the temperature does not budge — yet you must keep supplying energy. The energy goes into changing the particle arrangement, not their speeds. The specific latent heat of fusion (L) is the energy needed to melt 1 kg of a substance at its melting point; the specific latent heat of vaporisation is the energy to boil 1 kg away. The equation is E = m L. Melting 0.25 kg of ice (L = 334 000 J/kg) takes E = 0.25 × 334 000 = 83 500 J.

Vaporisation's latent heat is always far larger than fusion's — breaking a liquid apart completely costs much more than loosening a solid. Water's values: 334 000 J/kg to melt, 2 260 000 J/kg to boil. That asymmetry is why a steam scald is vicious: when steam condenses on skin it releases its full latent heat — for 0.030 kg of steam that is 0.030 × 2 260 000 = 67 800 J delivered at 100 °C, on top of the cooling the water would do afterwards.

A gas presses on every wall of its container because its particles are colliding with it billions of times a second, each collision delivering a tiny push. The summed pushes per unit area are the gas pressure. Heating a gas in a sealed, rigid container makes the particles move faster, so they collide harder and more often — the pressure rises. That is the physics behind warnings never to incinerate a sealed aerosol can.

Squeeze the gas instead and the particles are crowded into a smaller volume, so they hit the walls more often — pressure rises. At constant temperature the link is exact: p₁V₁ = p₂V₂. A gas at 160 kPa occupying 3.0 m³, compressed to 1.2 m³, ends at p₂ = (160 × 3.0) ÷ 1.2 = 400 kPa. In the other direction, 120 kPa of gas expanding from 6.0 m³ to 9.0 m³ falls to (120 × 6.0) ÷ 9.0 = 80 kPa.

Doing work on a gas changes things once more. Push a syringe plunger quickly and your muscles transfer energy to the gas particles — their internal energy rises and so does the temperature. That is why a bike pump warms as you inflate a tyre, and why fast compressions break the constant-temperature rule that p₁V₁ = p₂V₂ relies on. Compress slowly, letting heat escape, and the relation holds.