The key idea
Use particle arrangement, motion and energy to explain the properties of solids, liquids and gases. Then connect that model to gas-pressure calculations, keeping the amount of gas and the stated temperature conditions fixed.
Understand it · 01
Explain a state using arrangement and motion
A solid keeps its shape because its particles remain close together and vibrate around fixed positions. Heating increases the energy associated with their motion; it does not make each particle larger. In the simple school model a solid is often drawn as a regular array. Real materials can have more complicated arrangements, so treat the drawing as a useful model of restricted movement, not a photograph of every solid.
A liquid keeps approximately the same volume but takes the shape of its container because neighbouring particles can rearrange. A gas fills its container because widely separated particles move freely in random directions. Both liquids and gases flow. Gases compress much more easily because the large spaces between particles can become smaller; squeezing a gas does not normally shrink the particles themselves.
Understand it · 02
Build a particle explanation of gas pressure
Gas particles exert forces on the walls when collisions change their momentum. Many impacts over an area produce a measurable pressure. To explain a pressure change, identify what is held constant before describing the collisions. For a sealed, rigid container, heating increases average particle kinetic energy. Collisions with the wall become more frequent and the average momentum change per collision is greater, so pressure increases.
That explanation changes if the container can expand. A freely moving piston may allow volume to increase while the external pressure remains constant. It would then be wrong to insist that pressure must rise whenever temperature rises. Temperature describes average particle energy, while internal energy also depends on how much material is present and on interactions between its particles.
Understand it · 03
Separate the visible particle from the invisible cause
Brownian motion is the irregular movement of a small suspended particle, such as a smoke particle. Under a microscope you see the smoke particle, not the individual air molecules. Unequal impacts from moving air molecules repeatedly change the visible particle’s direction. The motion supports the model of matter as particles that are themselves moving continuously.
Diffusion is a different observation: particles spread through random motion, producing a net movement from a region of higher concentration to lower concentration. There is no deliberate journey towards empty space. Individual particles move in many directions; the overall concentration difference becomes smaller. A warmer gas generally diffuses faster because its particles have a higher average speed.
Understand it · 04
Use Boyle’s law only for the specified conditions
For a fixed amount of gas at constant temperature, pressure multiplied by volume remains constant: p₁V₁ = p₂V₂. A smaller volume means particles reach the walls more frequently, even though their average kinetic energy is unchanged. Doubling the pressure therefore halves the volume in this model; pressure is inversely proportional to volume, not proportional to the amount by which volume decreases.
Write the two states in a small table before substituting. Pressure units must match each other and volume units must match each other; they need not both be converted to SI for this ratio calculation. Use absolute gas pressure. If a question supplies a gauge pressure above atmospheric pressure, add the stated atmospheric pressure before applying the relationship.
Key definitions
- Brownian motion
- The random movement of microscopic particles (such as smoke) caused by collisions with fast-moving, invisible air molecules — evidence that gases consist of moving particles.
- Gas pressure
- The force per unit area on the container walls caused by gas particles colliding with the walls and changing momentum.
- Absolute zero
- −273 °C, the temperature at which particles have their minimum possible kinetic energy.
Equations, units & conditions
Boyle's law (fixed mass, constant temperature)
p₁V₁ = p₂V₂
Worked examples, step by step
Example 1
A sealed gas has volume 600 cm³ at a pressure of 100 kPa. It is compressed to 150 cm³ at constant temperature. Calculate the new pressure.
Follow the method
- Boyle's law: p₁V₁ = p₂V₂.
- 100 × 600 = p₂ × 150.
- p₂ = 60,000 ÷ 150.
p₂ = 400 kPa
Practice questions with worked solutions
Try each question on paper before opening the solution. These are original academy questions; the suggested marks are a self-checking guide, not an official exam-board mark scheme. Difficulty labels describe this practice set, not predicted grades.
Starter · 3 suggested marks
1. Compress a fixed gas
A fixed amount of gas occupies 240 cm³ at 90 kPa. Find its volume at 144 kPa when its temperature is unchanged.
Show solution and self-check: question 1
- Use p₁V₁ = p₂V₂.
- V₂ = (90 × 240) ÷ 144 = 150 cm³.
150 cm³
Self-check · one mark per point
- Identify the constant-temperature relationship.
- Substitute matching pressure and volume units.
- Calculate 150 cm³.
Build · 3 suggested marks
2. Explain Brownian motion
A smoke particle moves unpredictably when viewed under a microscope. Explain the cause and what this tells us about air.
Show solution and self-check: question 2
- Air consists of molecules moving randomly.
- The smoke particle receives unequal impacts from these molecules.
- The impacts change its motion in unpredictable directions.
Random, unequal collisions from moving air molecules cause the smoke particle’s motion.
Self-check · one mark per point
- Identify invisible moving air molecules.
- State unequal collisions with the visible smoke particle.
- Connect the collisions to random changes in its motion.
Common mistakes & how to avoid them
- Saying particles expand when heated. The particles stay the same size — they move faster and move further apart. Only the substance expands.
- Explaining gas pressure without collisions. The mark scheme wants: particles collide with the walls, exert a force on the wall, and pressure = force per unit area.
- Describing Brownian motion as smoke particles 'moving because they are hot'. They move because air molecules — too small to see — collide with them unevenly.
- Explaining pressure rise on heating with 'particles push harder' only. Full marks: particles move faster, collide with the walls more often and with more force.
Understand the why
Questions, explained
Start with the short answer, then follow the reasoning. Each explanation has a permanent link you can share with a classmate or return to when revising.
How do you describe the three states of matter for full marks?
Describe both arrangement and motion: solid particles vibrate around fixed positions; liquid particles remain close but rearrange; gas particles are widely separated and move randomly. Link those features to the stated property rather than listing them without explanation.
A question about compressibility needs a different link from a question about shape. Gas particles have large spaces between them, so decreasing those spaces reduces the volume considerably. Liquid particles are already close together, making the liquid difficult to compress. However, they can move past neighbours, explaining flow and a changing shape. In a solid, restricted movement maintains shape. A neat lattice is a simplified representation; real solids need not all have a perfectly regular arrangement.
Explain liquid behaviour
Why can water flow through a pipe but resist compression?
- Its particles can rearrange and slide past one another, allowing flow.
- The particles are close together, leaving little empty space to reduce.
Motion explains flow; close spacing explains low compressibility.
Why does gas pressure increase with temperature?
For a fixed amount of gas in a rigid container, heating increases pressure because faster particles collide with the walls more often and transfer more momentum per collision. If the container expands, temperature can rise without the same pressure increase.
The words “rigid” and “sealed” supply essential conditions. Sealed means the amount of gas cannot change; rigid means the volume cannot change. Temperature rises when average particle kinetic energy increases. Each collision changes particle momentum and therefore exerts a force on the wall. Many such collisions create pressure. If a piston moves outwards instead, increased wall separation can reduce collision frequency enough to keep pressure approximately constant. Always identify what the apparatus allows to change before predicting the outcome.
What does Brownian motion prove?
Brownian motion provides evidence that invisible molecules move continuously and collide with suspended particles. The visible smoke or pollen particle changes direction because impacts are unequal. It is the suspended particle, rather than individual air molecules, that a microscope reveals.
Imagine a relatively large smoke particle surrounded by many much smaller air molecules. At one moment their combined impacts are stronger from one side, and a moment later the imbalance is different. The resulting irregular path does not require the smoke particle to propel itself. Avoid describing the motion as a regular vibration or as a smooth upward drift caused by warm air. Convection can move a whole region of fluid, whereas Brownian motion is the irregular microscopic motion of individual suspended particles.
What graph shows that gas pressure is inversely proportional to volume?
For a fixed amount of gas at constant temperature, pressure against volume is a downward curve, while pressure against reciprocal volume is a straight line through the origin in the ideal model. This follows from pV being constant, so p is proportional to 1/V.
A decreasing graph alone does not establish inverse proportionality. To test the model, multiply each pressure by its corresponding volume and compare the products, or calculate 1/V for a straight-line plot. Use absolute pressure, with any atmospheric contribution included where necessary. Allow the gas to return to the chosen temperature after compression: doing the reading immediately can introduce a temperature change. The axes on the reciprocal plot must state reciprocal volume units rather than simply repeating the original volume label.
Check inverse proportionality
A gas has p = 120 kPa at V = 200 cm³ and p = 160 kPa at V = 150 cm³. Are these readings consistent with Boyle’s law?
- First product: 120 × 200 = 24 000 kPa cm³.
- Second product: 160 × 150 = 24 000 kPa cm³.
Yes: pV is the same for both readings.
What is the difference between diffusion and Brownian motion?
Diffusion is the overall spreading of particles from a region of higher concentration to lower concentration. Brownian motion is the irregular movement of a suspended particle caused by molecular collisions. Both support random particle motion, but they describe different observations.
A perfume smell spreading through still air is an example of diffusion. Individual perfume molecules travel in many directions and collide, yet the concentration becomes more uniform overall. A microscope view of one smoke particle zigzagging is an example of Brownian motion. Neither process means that each particle chooses a destination or moves steadily towards the least crowded point. Air currents may also transport perfume rapidly; a real room can involve convection as well as diffusion, so distinguish a clean model from mixed everyday processes.
Do particles get bigger when a substance is heated?
Ordinary thermal expansion increases average separation between particles; it does not mean the particles themselves grow larger. In solids their vibrations become more energetic, while in gases their average speed increases. State the material and constraints when explaining an observed size change.
A metal rail expands slightly when heated because its structure responds to increased particle motion by adopting a greater average spacing. A gas in a freely moving piston can expand much more noticeably because its particles are already far apart. A gas in a rigid vessel cannot expand, so its pressure changes instead. Draw equal-sized dots before and after heating and change their spacing where expansion occurs. This avoids suggesting that atoms inflate like balloons, which is not the model used for these questions.
Your learning checklist
Use these goals to check your understanding. Requirements vary by specification, tier and exam year; the official references below define your full course.
- Describe the arrangement, separation and motion of particles in solids, liquids and gases
- Explain the properties of each state using the particle model
- Describe Brownian motion as evidence for moving particles
- Explain gas pressure in terms of particle collisions with the container walls
- Relate temperature to the average kinetic energy of particles
Sources & how to cite these notes
Original explanations, illustrations and practice by Dr Desouky Physics Academy. Official specifications guide the course scope; questions and suggested marks on this page are our own revision material.
- Cambridge IGCSE Physics 0625 — 2026–2028 syllabus
- Pearson Edexcel International GCSE Physics 4PH1 — specification
Reference this page
Dr Desouky Physics Academy. IGCSE Physics: The particle model of matter. Updated 2026-09-25. https://www.drdesouky.com/revision/igcse-physics/particle-model-of-matter
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