Particle motion in gases and pressure

What you'll learn

This revision guide covers how gas particles move and create pressure, a key topic in AQA GCSE Physics Paper 1. You'll understand the kinetic theory model of gases, learn how temperature and volume affect gas pressure, and apply these concepts to calculations and real-world scenarios. This content links directly to the Particle Model of Matter section of your specification.

Key terms and definitions

Kinetic theory — a model that explains the physical properties of matter in terms of the movement of particles

Gas pressure — the force per unit area that gas particles exert on the walls of their container when they collide with it

Absolute zero — the lowest possible temperature (0 K or -273°C) at which particles have minimum kinetic energy

Kelvin scale — a temperature scale starting at absolute zero where 0°C = 273 K and temperature intervals are the same as Celsius

Random motion — the unpredictable movement of gas particles in all directions at varying speeds

Collisions — impacts between gas particles and container walls (or other particles) that are perfectly elastic at GCSE level

Atmospheric pressure — the pressure exerted by the weight of air in the Earth's atmosphere, approximately 100,000 Pa (100 kPa) at sea level

Brownian motion — the random movement of larger particles suspended in a fluid caused by collisions with smaller, invisible molecules

Core concepts

The kinetic theory model of gases

Gas particles are in constant, rapid motion. According to kinetic theory:

• Gas particles move randomly in all directions at high speeds
• The particles are very small compared to the spaces between them
• Particles collide with each other and with container walls
• These collisions are elastic — no kinetic energy is lost overall
• There are negligible forces of attraction between gas particles (unlike liquids and solids)

The higher the temperature, the faster the particles move on average. This means particles have more kinetic energy in their kinetic energy stores.

When gas particles collide with container walls, they exert a force on the walls. Since pressure equals force divided by area (P = F/A), these collisions create gas pressure. More frequent or more forceful collisions increase the pressure.

How temperature affects gas pressure

When you heat a gas in a fixed volume container:

• Particles gain energy in their kinetic energy stores
• Particles move faster on average
• Faster-moving particles collide with walls more frequently
• Each collision exerts a greater force (due to increased momentum change)
• Therefore gas pressure increases

This relationship is directly proportional when temperature is measured in kelvin. If you double the absolute temperature (in K), you double the pressure, provided the volume stays constant.

Converting between Celsius and Kelvin:

Temperature in K = Temperature in °C + 273

For example:

• 20°C = 293 K
• 100°C = 373 K
• -73°C = 200 K

At absolute zero (0 K or -273°C), particles would have minimum kinetic energy and stop moving (in theory — in practice, quantum effects prevent this, but that's beyond GCSE). This is the lowest possible temperature.

How volume affects gas pressure

When you compress a gas (reduce its volume) at constant temperature:

• The same number of particles occupy a smaller space
• Particles travel shorter distances between collisions with walls
• Collisions with walls happen more frequently
• Therefore gas pressure increases

This relationship is inversely proportional. If you halve the volume, you double the pressure (assuming temperature and the amount of gas remain constant).

For a fixed mass of gas at constant temperature:

P₁V₁ = P₂V₂

Where:

• P₁ = initial pressure (Pa)
• V₁ = initial volume (m³)
• P₂ = final pressure (Pa)
• V₂ = final volume (m³)

This is sometimes called Boyle's Law, though you don't need to name it for AQA GCSE.

Pressure in different contexts

Standard atmospheric pressure at sea level is approximately:

• 100,000 Pa (pascals)
• 100 kPa (kilopascals)
• 1 atmosphere (atm)

Gas pressure can be measured in different units:

• Pascals (Pa) — the SI unit, 1 Pa = 1 N/m²
• Kilopascals (kPa) — 1 kPa = 1000 Pa
• Atmospheres (atm) — based on average atmospheric pressure

In real-world applications:

• Car tyres are inflated to approximately 200-250 kPa (2-2.5 times atmospheric pressure)
• Scuba diving cylinders can contain gas at 20,000 kPa (200 atm) or higher
• Weather systems involve pressure differences — high pressure brings settled weather, low pressure brings clouds and rain

Doing work on a gas

When you compress a gas, you do work on it. This transfers energy to the gas particles' kinetic energy stores.

If the gas is compressed quickly (so heat cannot escape):

• Work done on the gas increases its internal energy
• Temperature increases
• Pressure increases (both because of the reduced volume AND the increased temperature)

This principle explains:

• Why a bicycle pump gets warm when you inflate a tyre rapidly
• How diesel engines ignite fuel by compression alone
• Why meteorites heat up when entering the atmosphere (air compression ahead of the meteorite)

The equation for work done is:

Work done = Force × Distance (in the direction of the force)

When a piston compresses gas in a cylinder, the force is provided by gas pressure acting on the piston area.

Evidence for particle motion: Brownian motion

Brownian motion provides direct evidence that particles are constantly moving.

Robert Brown (1827) observed pollen grains suspended in water jiggling randomly under a microscope. Later scientists explained this:

• Large pollen grains (visible under microscope) move randomly
• This motion is caused by collisions with tiny water molecules (too small to see)
• Water molecules move randomly and constantly
• Collisions are uneven — more molecules hit one side than the other at any instant
• This creates an unbalanced force, causing the visible particle to change direction randomly

You can observe similar effects with:

• Smoke particles in air (using a smoke cell and microscope)
• Dust particles in a beam of sunlight

Brownian motion demonstrates:

• Molecules in liquids and gases move randomly
• Molecules move constantly (even when we can't see them)
• The kinetic theory model is correct

Worked examples

Example 1: Temperature and pressure relationship

Question: A gas cylinder has a pressure of 150 kPa at a temperature of 27°C. The cylinder is heated to 177°C. Calculate the new pressure, assuming the volume remains constant. [3 marks]

Solution:

Step 1: Convert temperatures to kelvin

• Initial temperature: T₁ = 27 + 273 = 300 K
• Final temperature: T₂ = 177 + 273 = 450 K

Step 2: Apply the relationship (for constant volume, P/T = constant) P₁/T₁ = P₂/T₂

Step 3: Rearrange and calculate P₂ = P₁ × (T₂/T₁) = 150 × (450/300) = 150 × 1.5 = 225 kPa

Answer: 225 kPa [1 mark for converting to kelvin, 1 mark for correct method, 1 mark for answer with unit]

Example 2: Volume and pressure relationship

Question: A syringe contains 60 cm³ of air at atmospheric pressure (100 kPa). The plunger is pushed in until the volume is 20 cm³. Calculate the new pressure, assuming temperature stays constant. [3 marks]

Solution:

Step 1: Write down what you know

• P₁ = 100 kPa, V₁ = 60 cm³
• V₂ = 20 cm³, P₂ = ?

Step 2: Apply P₁V₁ = P₂V₂

Step 3: Rearrange for P₂ P₂ = (P₁V₁)/V₂ = (100 × 60)/20 = 6000/20 = 300 kPa

Answer: 300 kPa [1 mark for selecting correct relationship, 1 mark for correct rearrangement, 1 mark for answer with unit]

Note: You can use cm³ or m³ as long as you're consistent on both sides.

Example 3: Explaining pressure increase

Question: Explain, in terms of particles, why the pressure inside a sealed container increases when the temperature increases. [3 marks]

Solution:

Mark scheme would award marks for points such as:

• When temperature increases, particles gain kinetic energy / move faster [1 mark]
• Particles collide with container walls more frequently [1 mark]
• Each collision exerts a greater force (or particles have greater momentum) [1 mark]
• Therefore the overall force on the walls increases, so pressure increases [1 mark]

(Maximum 3 marks available, so any 3 distinct points from above)

Key exam technique: Use particle language ("particles move faster") not vague terms ("the gas gets more energetic"). Link particle behaviour explicitly to pressure.

Common mistakes and how to avoid them

• Forgetting to convert Celsius to Kelvin in calculations — Always add 273 when using temperature in calculations involving gas laws. Using °C instead of K will give completely wrong answers.

• Saying pressure increases because "particles expand" or "get bigger" — Particles themselves don't change size or expand. They move faster and further apart. Use precise language: "particles move faster" and "collide more frequently/forcefully."

• Confusing the effects of temperature and volume — Make sure you clearly identify which factor is changing. Temperature increase = particles move faster. Volume decrease = particles have less space to move in. Both increase pressure but for different reasons.

• Mixing up units without converting — If pressure is in kPa in your question, keep it in kPa throughout. If you need to convert (e.g., to Pa), do so carefully: 1 kPa = 1000 Pa.

• Forgetting that P₁V₁ = P₂V₂ only works at constant temperature — This equation assumes temperature doesn't change. If temperature changes too, you need to consider both effects or you'll need the more complex combined gas law (usually not required at GCSE unless clearly supported in the question).

• Not explaining collisions with container walls — When explaining pressure, you must mention that particles collide with (or exert force on) the container walls. Particles colliding with each other doesn't create pressure on the container.

Exam technique for "Particle motion in gases and pressure"

• "Explain" questions require particle-level detail — Describe what particles are doing (moving faster, colliding more frequently) and link this explicitly to the observable effect (increased pressure). Aim for 2-3 distinct points for 2-3 marks.

• Show your working in calculations — Even if you know P₁V₁ = P₂V₂, write it down. Show the rearrangement. State your answer with units. This protects you if you make an arithmetic error — you can still get method marks (typically 2 out of 3 marks).

• Read the question carefully for what's kept constant — Questions will specify "at constant temperature" or "in a sealed container of fixed volume." This tells you which relationship to use. Underline these key phrases.

• Use scientific terminology accurately — Write "kinetic energy stores" not just "energy," "directly proportional" not "increases with," "collisions" not "hits." Examiners reward precise physics language, especially in longer answer questions worth 4-6 marks.

Quick revision summary

Gas particles move randomly and constantly. When they collide with container walls, they create pressure. Increasing temperature makes particles move faster, causing more frequent and forceful collisions, thus increasing pressure (at constant volume). Decreasing volume at constant temperature also increases pressure because particles collide with walls more frequently. The relationship P₁V₁ = P₂V₂ applies when temperature is constant. Always convert temperatures to kelvin (K = °C + 273) for gas law calculations. Brownian motion provides observable evidence for constant particle movement.