What you'll learn
This revision guide covers the particle model of matter as tested in WJEC GCSE Physics. You'll learn how particles behave in solids, liquids and gases, how to calculate density and specific heat capacity, and how energy transfers affect the state and temperature of substances. This topic accounts for approximately 10% of your final exam and appears in both Foundation and Higher tier papers.
Key terms and definitions
Density — the mass per unit volume of a substance, measured in kg/m³ or g/cm³
Internal energy — the total kinetic energy and potential energy of all the particles in a system
Specific heat capacity — the energy required to raise the temperature of 1 kg of a substance by 1°C (or 1 K), measured in J/kg°C
Specific latent heat — the energy required to change the state of 1 kg of a substance without changing its temperature, measured in J/kg
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 molecules
Absolute zero — the lowest possible temperature (0 K or -273°C) where particles have minimum kinetic energy
Core concepts
States of matter and particle arrangement
The particle model explains the properties of solids, liquids and gases based on particle arrangement, movement and energy.
Solids:
- Particles arranged in a regular, fixed pattern
- Strong forces of attraction between particles
- Particles vibrate about fixed positions
- Fixed shape and volume
- High density
Liquids:
- Particles close together but not in fixed positions
- Moderate forces of attraction between particles
- Particles can move past each other
- Fixed volume but take the shape of their container
- Generally high density (slightly lower than solids)
Gases:
- Particles far apart with no regular arrangement
- Very weak forces of attraction between particles
- Particles move rapidly in random directions
- No fixed shape or volume (fill their container)
- Low density
Changes of state
When substances change state, the arrangement and energy of particles changes, but the mass remains constant.
Key state changes:
- Melting: solid → liquid (energy absorbed)
- Freezing: liquid → solid (energy released)
- Boiling/evaporation: liquid → gas (energy absorbed)
- Condensation: gas → liquid (energy released)
- Sublimation: solid → gas (energy absorbed)
During a change of state:
- Temperature remains constant
- Energy supplied changes the potential energy of particles (breaks or forms bonds)
- The kinetic energy of particles does not change
- Mass is conserved
Density calculations
Density links mass and volume. Higher density means more mass packed into a given volume.
The density equation:
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:
- 1 g/cm³ = 1000 kg/m³
- 1 m³ = 1,000,000 cm³
Measuring density:
For regular solids:
- Measure mass using a balance
- Calculate volume using length × width × height
- Use ρ = m/V
For irregular solids:
- Measure mass using a balance
- Measure volume using displacement in a measuring cylinder (final volume - initial volume)
- Use ρ = m/V
For liquids:
- Measure mass of empty measuring cylinder
- Pour liquid in and measure total mass
- Calculate liquid mass (total - cylinder)
- Read volume from scale
- Use ρ = m/V
Internal energy and temperature
Internal energy is the sum of:
- Kinetic energy of particles (due to their movement)
- Potential energy of particles (due to their positions and bonds)
When a substance is heated:
- Internal energy increases
- This can increase temperature (kinetic energy increases)
- Or cause a change of state (potential energy increases)
Temperature is a measure of the average kinetic energy of particles. Higher temperature means particles move faster on average.
The Kelvin scale is the absolute temperature scale:
- Temperature in K = temperature in °C + 273
- At absolute zero (0 K or -273°C), particles have minimum kinetic energy
- They still vibrate slightly due to quantum effects
Specific heat capacity
Different materials require different amounts of energy to change temperature. This is determined by their specific heat capacity.
The specific heat capacity equation:
ΔE = mcΔθ
Where:
- ΔE = change in thermal energy in J (joules)
- m = mass in kg
- c = specific heat capacity in J/kg°C
- Δθ (delta theta) = temperature change in °C
Typical values:
- Water: 4200 J/kg°C (very high - water stores lots of energy)
- Aluminium: 900 J/kg°C
- Copper: 385 J/kg°C
- Lead: 130 J/kg°C
Water's high specific heat capacity makes it useful for:
- Cooling systems in cars and power stations
- Storage heaters
- Moderating coastal climates
Specific latent heat
Energy is needed to change state even though temperature stays constant. This energy breaks or forms bonds between particles.
The specific latent heat equation:
E = mL
Where:
- E = energy in J
- m = mass in kg
- L = specific latent heat in J/kg
Two types of latent heat:
Specific latent heat of fusion (Lf):
- For melting/freezing
- Energy changes potential energy by separating/bringing together particles
- Lower values than vaporisation
Specific latent heat of vaporisation (Lv):
- For boiling/condensing
- Much larger energy needed to completely separate particles
- Water: Lv = 2,260,000 J/kg (very high)
Gas pressure and temperature
Gas particles move randomly and collide with container walls, creating pressure.
Pressure increases when:
- Temperature increases (particles move faster, collide harder and more frequently)
- Volume decreases (more collisions per second with walls)
- More particles added (more collisions)
For a fixed mass of gas at constant volume:
- Pressure is directly proportional to absolute temperature (in Kelvin)
- p ∝ T
- p₁/T₁ = p₂/T₂
This explains why:
- Aerosol cans warn against heating (pressure builds up)
- Car tyres should be checked when cold
- Brownian motion can be observed: smoke particles move randomly when viewed under a microscope due to collisions with invisible air molecules
Worked examples
Example 1: Density calculation
Question: A metal cube has sides of length 2.0 cm and a mass of 62 g. Calculate its density in g/cm³. [3 marks]
Solution:
Step 1: Calculate volume
- V = length × width × height
- V = 2.0 × 2.0 × 2.0 = 8.0 cm³ [1 mark]
Step 2: Use density equation
- ρ = m/V [1 mark]
- ρ = 62/8.0
- ρ = 7.75 g/cm³ [1 mark]
Mark scheme notes: Must show working, include units, give answer to 2-3 significant figures.
Example 2: Specific heat capacity
Question: A student heats 2.0 kg of water from 20°C to 100°C using an electric kettle. The specific heat capacity of water is 4200 J/kg°C. Calculate the energy transferred to the water. [3 marks]
Solution:
Step 1: Identify values
- m = 2.0 kg
- c = 4200 J/kg°C
- Δθ = 100 - 20 = 80°C [1 mark]
Step 2: Use equation
- ΔE = mcΔθ [1 mark]
- ΔE = 2.0 × 4200 × 80
- ΔE = 672,000 J or 672 kJ [1 mark]
Mark scheme notes: Remember to calculate temperature change. Must show substitution into equation.
Example 3: Specific latent heat
Question: A student boils 0.50 kg of water. The specific latent heat of vaporisation of water is 2,260,000 J/kg. Calculate the energy needed to turn the water into steam at 100°C. [2 marks]
Solution:
Step 1: Use equation
- E = mL [1 mark]
- E = 0.50 × 2,260,000
- E = 1,130,000 J or 1.13 MJ [1 mark]
Mark scheme notes: Temperature doesn't change during boiling, so don't use ΔE = mcΔθ.
Common mistakes and how to avoid them
Confusing mass and weight when calculating density — Always use mass in kg or g, not weight in N. Use a balance, not a force meter.
Using the wrong temperature units — For specific heat capacity, °C is acceptable. For gas pressure calculations, you must convert to Kelvin (K = °C + 273).
Forgetting to calculate temperature change — In ΔE = mcΔθ, you need Δθ (final temperature - initial temperature), not just the final temperature.
Using the wrong latent heat equation during state changes — When temperature is constant, use E = mL, not ΔE = mcΔθ. The temperature staying constant is the key indicator.
Incorrect unit conversions for density — Remember 1 g/cm³ = 1000 kg/m³. Check which units the question asks for.
Stating particles stop moving at absolute zero — At 0 K, particles have minimum energy but still vibrate slightly. They don't become completely stationary.
Exam technique for "Particle Model of Matter"
Command word "calculate" requires you to show your working clearly. Write the equation, substitute values with units, then give your final answer. Even if your final answer is wrong, you can gain method marks for correct working.
For 3-mark calculations expect: 1 mark for correct equation/rearrangement, 1 mark for correct substitution, 1 mark for correct answer with units. Always include units in your final answer.
Describing particle behaviour — Use precise scientific language: "particles vibrate/move," not "molecules bounce." State changes in arrangement, movement and energy. For 4-6 mark questions, structure your answer with comparison points about both states.
Required practicals appear regularly. You must know how to measure density of regular solids, irregular solids and liquids. Be able to describe the method, identify variables and suggest improvements.
Quick revision summary
The particle model explains properties of solids, liquids and gases based on arrangement, movement and forces between particles. Density (ρ = m/V) measures mass per unit volume. Internal energy is the sum of kinetic and potential energy of all particles. During temperature changes use ΔE = mcΔθ; during state changes use E = mL. Temperature in Kelvin relates to average kinetic energy; absolute zero is 0 K (-273°C). Gas pressure increases with temperature due to faster-moving particles creating more frequent, harder collisions.