What you'll learn
This revision guide covers the particle model of matter as specified in the AQA GCSE Physics specification. You'll understand how particles arrange themselves in solids, liquids and gases, calculate density using standard equations, and explain energy changes during state transitions. These concepts form the foundation for understanding thermal physics and are regularly tested in both Paper 1 and combined science exams.
Key terms and definitions
Density — the mass per unit volume of a substance, measured in kg/m³ or g/cm³
State of matter — the physical form a substance takes (solid, liquid or gas) determined by particle arrangement and energy
Internal energy — the total kinetic energy and potential energy of all particles in a system
Specific latent heat — the energy required to change the state of 1 kg of a substance without changing its temperature
Latent heat of fusion — the energy needed to change 1 kg of a substance from solid to liquid at its melting point
Latent heat of vaporisation — the energy needed to change 1 kg of a substance from liquid to gas at its boiling point
Brownian motion — the random movement of particles suspended in a fluid, caused by collisions with fast-moving fluid molecules
Sublimation — the direct change of state from solid to gas without passing through the liquid state
Core concepts
The particle model and states of matter
The particle model explains the properties of solids, liquids and gases by describing how particles are arranged and how they move.
Solids:
- Particles arranged in a regular, fixed pattern
- Strong forces of attraction hold particles in fixed positions
- Particles vibrate about fixed points but cannot move from place to place
- Solids have fixed shape and volume
- Generally have the highest density of the three states
Liquids:
- Particles close together but randomly arranged
- Weaker forces of attraction allow particles to move past each other
- Particles can flow and move throughout the liquid
- Liquids have fixed volume but take the shape of their container
- Density usually slightly less than the solid form (water is an exception)
Gases:
- Particles far apart with no regular arrangement
- Almost no forces of attraction between particles
- Particles move rapidly and randomly in all directions
- Gases have no fixed shape or volume and fill their container
- Much lower density than solids or liquids
The particle model is a simplification—it assumes particles are solid spheres with no forces between them in gases, which isn't completely accurate but works well for GCSE-level explanations.
Density calculations
Density relates the mass and volume of a substance. The equation you must know is:
ρ = m/V
Where:
- ρ (rho) = density in kg/m³ or g/cm³
- m = mass in kg or g
- V = volume in m³ or cm³
Unit conversions you need to know:
- 1 m³ = 1,000,000 cm³ (10⁶ cm³)
- 1 g/cm³ = 1000 kg/m³
- To convert cm³ to m³, divide by 1,000,000
- To convert g to kg, divide by 1000
Measuring density experimentally:
For a regular solid (e.g., cube, cylinder):
- Measure mass using a balance
- Calculate volume using length measurements (V = l × w × h for a cuboid)
- Use ρ = m/V
For an irregular solid:
- Measure mass using a balance
- Fill a eureka can to the spout, allow excess water to drain
- Place object in water and collect displaced water in a measuring cylinder
- Volume of object = volume of water displaced
- Use ρ = m/V
For a liquid:
- Measure mass of empty measuring cylinder
- Pour liquid into cylinder and record volume
- Measure total mass of cylinder plus liquid
- Mass of liquid = total mass − mass of cylinder
- Use ρ = m/V
Changes of state
When substances change state, the process is physical not chemical — no new substances are formed and the change is reversible.
The six changes of state:
- Melting — solid to liquid (requires heating)
- Freezing — liquid to solid (requires cooling)
- Evaporation/boiling — liquid to gas (requires heating)
- Condensation — gas to liquid (requires cooling)
- Sublimation — solid to gas (requires heating)
- Deposition — gas to solid (requires cooling)
During a change of state:
- Temperature remains constant even though energy is being transferred
- The energy supplied changes the internal energy by altering the potential energy of particles
- Particles gain or lose potential energy as bonds break or form
- Kinetic energy of particles stays the same (hence constant temperature)
- Mass is conserved — the number of particles doesn't change
Internal energy and temperature
Internal energy is the sum of:
- Kinetic energy of particles (related to their movement and temperature)
- Potential energy of particles (related to their positions and forces between them)
When you heat a substance:
- If it's not changing state: kinetic energy increases, temperature rises
- If it's changing state: potential energy increases, temperature stays constant
Temperature is a measure of the average kinetic energy of particles. A higher temperature means particles are moving faster on average.
Specific latent heat
Energy is required to change state because you must overcome forces between particles without increasing their kinetic energy (temperature).
The equation for energy changes during state transitions is:
E = m × L
Where:
- E = energy transferred in joules (J)
- m = mass in kilograms (kg)
- L = specific latent heat in J/kg
Two types of specific latent heat:
Specific latent heat of fusion (Lf) — for melting/freezing
- Energy to change between solid and liquid
- For water: Lf = 334,000 J/kg or 334 kJ/kg
Specific latent heat of vaporisation (Lv) — for boiling/condensing
- Energy to change between liquid and gas
- For water: Lv = 2,260,000 J/kg or 2260 kJ/kg
The latent heat of vaporisation is much larger than latent heat of fusion because:
- All bonds between particles must be broken (not just some)
- Particles must be separated much further apart
- More work is done against attractive forces
Heating and cooling curves
Temperature-time graphs during heating show:
- Sloped sections: temperature increasing, substance in one state, kinetic energy increasing
- Flat (horizontal) sections: temperature constant, change of state occurring, potential energy increasing
For water being heated from ice:
- Ice warming: temperature rises from below 0°C to 0°C
- Melting: temperature stays at 0°C while ice becomes water
- Water warming: temperature rises from 0°C to 100°C
- Boiling: temperature stays at 100°C while water becomes steam
- Steam warming: temperature rises above 100°C
The length of flat sections depends on:
- Mass of substance (more mass = longer time)
- Specific latent heat (higher value = longer time)
- Rate of energy supply (higher rate = shorter time)
Gas pressure and particle collisions
Gas pressure is caused by particles colliding with container walls. Each collision exerts a tiny force, and billions of collisions per second create a steady pressure.
Factors affecting gas pressure:
Increasing temperature (constant volume):
- Particles gain kinetic energy and move faster
- Collisions are more frequent and more forceful
- Pressure increases
Decreasing volume (constant temperature):
- Same number of particles in smaller space
- Particles collide with walls more frequently
- Pressure increases
Adding more gas (constant volume and temperature):
- More particles present
- More frequent collisions with walls
- Pressure increases
This particle explanation is required in exam answers — you must link pressure to particle movement and collisions.
Worked examples
Example 1: Density calculation with unit conversion
Question: A metal cube has sides of length 4.0 cm and a mass of 550 g. Calculate the density of the metal in both g/cm³ and kg/m³. (4 marks)
Solution:
Step 1: Calculate volume V = l³ = 4.0³ = 64 cm³ ✓
Step 2: Calculate density in g/cm³ ρ = m/V = 550/64 = 8.59 g/cm³ (8.6 g/cm³ to 2 s.f.) ✓
Step 3: Convert to kg/m³ Method: multiply g/cm³ by 1000 ρ = 8.59 × 1000 = 8590 kg/m³ (8600 kg/m³ to 2 s.f.) ✓
Alternative method: convert units first m = 550 g = 0.55 kg V = 64 cm³ = 64/1,000,000 = 0.000064 m³ ρ = 0.55/0.000064 = 8594 kg/m³ ✓
Example 2: Specific latent heat calculation
Question: Calculate the energy required to boil 2.5 kg of water at 100°C. The specific latent heat of vaporisation of water is 2,260,000 J/kg. (3 marks)
Solution:
Step 1: Write the equation E = m × L ✓
Step 2: Substitute values E = 2.5 × 2,260,000 ✓
Step 3: Calculate and state unit E = 5,650,000 J (or 5.65 MJ or 5650 kJ) ✓
Mark scheme notes: 1 mark for correct equation, 1 mark for correct substitution, 1 mark for correct answer with unit. Accept answer in J, kJ or MJ.
Example 3: Explaining changes of state
Question: Explain, in terms of particles and energy, why the temperature of ice remains at 0°C while it is melting. (4 marks)
Model answer:
Energy is being supplied to the ice ✓
This energy breaks bonds/overcomes forces between particles ✓
The energy increases the potential energy of the particles (not kinetic energy) ✓
Temperature is related to kinetic energy of particles, which isn't changing, so temperature stays constant ✓
Mark scheme notes: Look for clear references to energy changing potential energy not kinetic energy, and linking temperature to kinetic energy. Alternative acceptable phrases: "energy used to overcome attractive forces" or "energy stored as potential energy."
Common mistakes and how to avoid them
Confusing mass and weight in density calculations — Always use mass (kg or g), never weight (N). Mass is measured with a balance, weight with a newton-meter.
Incorrect unit conversions — Remember 1 g/cm³ = 1000 kg/m³ (multiply by 1000, not divide). Write out conversions step-by-step in exams to avoid errors.
Saying particles expand when heated — Particles themselves don't change size. The spacing between particles increases, causing substances to expand. Use precise language: "particles move further apart" not "particles get bigger."
Thinking temperature increases during state changes — Temperature stays constant during melting, boiling, freezing and condensing. Energy is changing potential energy of particles, not kinetic energy.
Forgetting to explain pressure in terms of particle collisions — When asked to explain gas pressure, you must mention particles colliding with container walls creating forces. Simply saying "particles move faster" is incomplete.
Muddling latent heat of fusion and vaporisation — Fusion relates to melting/freezing (solid↔liquid), vaporisation relates to boiling/condensing (liquid↔gas). The values are very different, so using the wrong one gives an incorrect answer by a factor of about 7 for water.
Exam technique for "Particle model of matter: states and changes of state"
"Describe" and "Explain" questions have different requirements — Describe means state what happens (e.g., "temperature stays constant"). Explain means give reasons using particle theory (e.g., "temperature stays constant because energy is breaking bonds, changing potential energy not kinetic energy, and temperature depends on kinetic energy").
Show working for all calculations — Even if you can do density or latent heat calculations mentally, write out the equation, substitution and answer with unit. This gains you method marks if your final answer is wrong. Each step typically earns 1 mark.
Use standard form or prefixes for large numbers — Rather than writing 2,260,000 J in an answer, use 2.26 MJ or 2.26 × 10⁶ J. This reduces errors and is clearer.
Draw particle diagrams when helpful — If a question asks you to compare solids, liquids and gases, a simple diagram showing particle arrangement can earn marks and helps structure your written answer. Ensure particles in solids are touching and regularly arranged, particles in liquids are touching but random, and particles in gases are far apart.
Quick revision summary
The particle model explains properties of solids (fixed arrangement, vibrating particles), liquids (touching but moving particles) and gases (widely-spaced, fast-moving particles). Density = mass/volume, with careful attention to units. During state changes, temperature remains constant as energy changes particle potential energy by overcoming forces between particles. Specific latent heat calculations use E = m × L, with vaporisation requiring more energy than fusion. Gas pressure results from particle collisions with container walls, increasing with temperature or particle concentration.