AQA GCSE Physics 8463: Particle model of matter – Revision Notes

These are condensed recall notes for section 4.3 Particle model of matter (4.3.1.1 to 4.3.3.3) of the AQA GCSE Physics (8463) specification, for teaching from September 2016 and exams from 2018 onwards. The topic is assessed on Paper 1, set at Foundation and Higher Tier. Section 4.3.3.3 is marked (HT only) and is labelled Higher tier only here.

For full explanations and worked examples, use the Particle model of matter study guide. Then test yourself with the Particle model of matter practice questions. The course hub is AQA GCSE Physics, the printable checklist lists every point, and the free diagnostics help you find gaps. For E = Pt and other electrical energy equations, see the Electricity revision notes.

The equations

Equation	Symbols	Units	Recall or given?
density = mass ÷ volume	ρ = m / V	kg/m³, kg, m³	Recall
change in thermal energy = mass × specific heat capacity × temperature change	ΔE = m c Δθ	J, kg, J/kg °C, °C	Given on equation sheet
energy for a change of state = mass × specific latent heat	E = m L	J, kg, J/kg	Given on equation sheet
pressure × volume = constant (fixed mass, constant temperature)	p V = constant	Pa, m³	Given on equation sheet

Unit traps: 1 cm³ = 1 × 10⁻⁶ m³; 1 g = 0.001 kg; 1 g/cm³ = 1000 kg/m³; 1 kPa = 1000 Pa.

Definitions to learn word for word

• Internal energy: the total kinetic energy and potential energy of all the particles (atoms and molecules) that make up a system.
• Specific heat capacity: the energy needed to raise the temperature of one kilogram of a substance by one degree Celsius.
• Latent heat: the energy needed for a substance to change state.
• Specific latent heat: the energy needed to change the state of one kilogram of a substance with no change in temperature.
• Specific latent heat of fusion: for solid to liquid. Of vaporisation: for liquid to vapour.
• Temperature of a gas: related to the average kinetic energy of its molecules.

4.3.1 States, density and changes of state

	Solid	Liquid	Gas
Spacing	Touching	Touching	Far apart
Arrangement	Regular	Irregular	Random
Motion	Vibrate in place	Slide past each other	Fast, random, all directions
Density	High	High	Very low

Why a gas is less dense: same mass of particles, far more space between them, so much bigger volume.

Changes of state: melting, freezing, boiling, evaporating, condensing, sublimating (solid → gas).

• Mass is conserved – same particles, rearranged.
• Physical change: reverse it and the material gets its original properties back. A chemical change does not.

Required practical 5 – method in steps

1. Regular solid: measure length, width and height (ruler, Vernier callipers or micrometer); V = l × w × h.
2. Irregular solid: displacement – rise in a measuring cylinder, or overflow from a eureka can collected in a measuring cylinder.
3. Liquid: mass of cylinder empty, then with a measured volume of liquid; subtract.
4. Measure mass on a balance; read volumes at eye level from the bottom of the meniscus.
5. Calculate ρ = m / V and convert to kg/m³.

Worked reminder: 0.60 kg in 2.4 × 10⁻⁴ m³ → ρ = 2500 kg/m³.

4.3.2 Internal energy and heating

Heating a system does one of two things:

1. Raises the temperature – particles gain kinetic energy. Use ΔE = m c Δθ.
2. Changes the state – particles gain potential energy; temperature stays constant. Use E = m L.

The rise in temperature depends on the mass, the material (its c) and the energy input.

Worked reminder: 7800 J raises a 1.0 kg metal block by 20 °C → c = 7800 ÷ (1.0 × 20) = 390 J/kg °C.

Heating graph (temperature against time, steady heating):

• Slope → one state warming (c applies).
• Flat → melting (first flat part) or boiling (second flat part) (L applies).
• Longer flat part → more energy needed for that change of state.
• Cooling graph → flat parts are condensing and freezing.

Two-stage calculation – method in steps

1. Split the process at each change of state.
2. Use ΔE = m c Δθ for each temperature change.
3. Use E = m L for each change of state.
4. Add the energies.

Worked reminder: boiling 0.050 kg of water at 100 °C with L = 2 260 000 J/kg → E = 0.050 × 2 260 000 = 113 000 J.

Must-know distinctions

Pair	Difference
Specific heat capacity vs specific latent heat	c: temperature changes, no change of state. L: state changes, no temperature change
Fusion vs vaporisation	Fusion: solid ↔ liquid. Vaporisation: liquid ↔ vapour
Internal energy vs temperature	Internal energy is total KE + PE of all particles; temperature relates to average KE
Physical vs chemical change	Physical: reversible, original properties recovered. Chemical: new substances
Gas heated at constant volume vs gas expanded at constant temperature	Pressure rises (faster molecules) vs pressure falls (fewer hits per unit area each second)

4.3.3 Gas pressure

• Molecules in constant random motion collide with the walls, exerting a force.
• Pressure produces a net force at right angles to the container wall (or any surface).
• Heat at constant volume: molecules faster → hit walls more often and harder → pressure rises.
• Increase volume at constant temperature: same speed, but molecules hit each unit area of wall less often → pressure falls.
• p₁V₁ = p₂V₂ for a fixed mass of gas at constant temperature. Keep units consistent on both sides.

pV calculation – method in steps

1. Check the mass of gas is fixed and the temperature is constant.
2. Write p₁V₁ = p₂V₂.
3. Substitute, keeping the same units for both pressures and for both volumes.
4. Rearrange for the unknown. Sense check: if the volume went down, the pressure must have gone up.

Worked reminder: 200 kPa in 0.050 m³, compressed to 0.020 m³ → p₂ = 200 × 0.050 ÷ 0.020 = 500 kPa.

Higher tier only (4.3.3.3): work is the transfer of energy by a force. Doing work on a gas (such as pushing a bicycle pump) increases its internal energy, which can raise its temperature.

Quick self-test

1. A block of mass 0.60 kg has a volume of 2.4 × 10⁻⁴ m³. Calculate its density.
2. Convert 350 cm³ to m³.
3. Oil has a density of 900 kg/m³. Calculate the mass of 0.0020 m³ of oil.
4. Name the change of state from solid straight to gas.
5. Define internal energy.
6. How much energy raises 2.0 kg of aluminium by 15 °C? (c = 900 J/kg °C)
7. How much energy melts 0.50 kg of ice at 0 °C? (L = 334 000 J/kg)
8. What is happening on a flat section of a heating graph?
9. A fixed mass of gas at 100 kPa has a volume of 0.60 m³. It expands to 1.5 m³ at constant temperature. Find the new pressure.
10. Why does the pressure in a sealed rigid can rise when it is heated?
11. Higher tier only. Why does a bicycle pump get warm when you use it?
12. 12 600 J is supplied to 0.30 kg of water (c = 4200 J/kg °C). Calculate the temperature rise.

Answers

1. ρ = 0.60 ÷ 2.4 × 10⁻⁴ = 2500 kg/m³
2. 3.5 × 10⁻⁴ m³
3. m = ρV = 900 × 0.0020 = 1.8 kg
4. Sublimation
5. The total kinetic and potential energy of all the particles in the system.
6. ΔE = 2.0 × 900 × 15 = 27 000 J
7. E = 0.50 × 334 000 = 167 000 J
8. A change of state: energy increases internal energy but the temperature stays constant.
9. p₂ = 100 × 0.60 ÷ 1.5 = 40 kPa
10. The molecules move faster, so they hit the walls more often and with more force.
11. Work is done on the gas, which increases its internal energy and so its temperature.
12. Δθ = 12 600 ÷ (0.30 × 4200) = 10 °C

Where marks are usually lost

• Leaving volume in cm³ while giving density in kg/m³.
• Writing that mass decreases when water boils or ice melts.
• Defining internal energy as “the heat in an object” or as kinetic energy only.
• Using an end temperature in place of Δθ.
• Using c on a flat part of a heating graph, or L on a sloping part.
• Forgetting to add both stages in a heat-then-change-state calculation.
• Saying the particles themselves get bigger when a substance is heated.
• In gas pressure answers, giving “more collisions” without “per second” or “more often”.
• Applying pV = constant when the temperature is not constant.

Official syllabus

AQA GCSE Physics (8463) specification, for teaching from September 2016 onwards, for exams in 2018 onwards (Version 1.1, 30 September 2019), published by AQA. These notes cover section 4.3 Particle model of matter.