What you'll learn
This revision guide covers everything you need to know about the relationship between pressure and volume in gases for AQA GCSE Physics. You'll understand how gas particles behave when compressed or expanded, apply Boyle's Law to solve calculations, and interpret pressure-volume graphs. This topic links directly to particle theory and appears regularly in both Paper 1 and combined science exams.
Key terms and definitions
Pressure — the force exerted per unit area, measured in pascals (Pa) or atmospheres (atm), caused by gas particles colliding with container walls
Volume — the space occupied by a gas, measured in cubic metres (m³), cubic centimetres (cm³), or litres (L)
Boyle's Law — the principle stating that for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume
Inversely proportional — a relationship where one quantity increases as the other decreases by the same factor, such that their product remains constant
Constant temperature — a condition where thermal energy remains unchanged, ensuring gas particle speeds stay the same during pressure-volume changes
Atmospheric pressure — the pressure exerted by the Earth's atmosphere, approximately 100,000 Pa or 1 × 10⁵ Pa at sea level
Compression — reducing the volume of a gas by applying force, which increases the pressure if temperature remains constant
Expansion — increasing the volume available to a gas, which decreases the pressure if temperature remains constant
Core concepts
How gas pressure is created
Gas particles move randomly in all directions at high speeds. When these particles collide with the walls of their container, they exert a force. Pressure results from the combined effect of billions of these collisions per second.
The magnitude of gas pressure depends on:
- Number of collisions per second — more frequent collisions create higher pressure
- Force of each collision — faster-moving particles hit harder, increasing pressure
- Surface area — the same force spread over a larger area produces lower pressure
At constant temperature, particle speed remains unchanged. Any pressure changes must therefore result from changes in collision frequency, which depends on how tightly packed the particles are.
The relationship between pressure and volume
When you compress a gas (reduce its volume) while keeping temperature constant:
- Particles occupy a smaller space
- The same number of particles collide with a smaller wall area
- Collision frequency increases
- Pressure increases
When you allow a gas to expand (increase its volume) at constant temperature:
- Particles spread out over a larger space
- Collisions with walls become less frequent
- Pressure decreases
This inverse relationship is fundamental to understanding gas behaviour. If you halve the volume, you double the pressure. If you triple the volume, you reduce the pressure to one-third of its original value.
Boyle's Law equation
For a fixed mass of gas at constant temperature:
p₁V₁ = p₂V₂
Where:
- p₁ = initial pressure (Pa)
- V₁ = initial volume (m³, cm³, or L)
- p₂ = final pressure (Pa)
- V₂ = final volume (m³, cm³, or L)
This equation tells us that the product of pressure and volume remains constant. You can rearrange it to find any unknown variable:
- To find final pressure: p₂ = (p₁V₁)/V₂
- To find final volume: V₂ = (p₁V₁)/p₂
- To find initial pressure: p₁ = (p₂V₂)/V₁
- To find initial volume: V₁ = (p₂V₂)/p₁
Critical requirement: Units for volume must be the same on both sides of the equation (both in m³, both in cm³, or both in L). Pressure units must also match on both sides.
Graphical representations
Pressure-volume graph (rectangular hyperbola)
When you plot pressure (y-axis) against volume (x-axis), you get a curve called a rectangular hyperbola. Key features:
- The curve never touches either axis
- As volume approaches zero, pressure approaches infinity
- As volume increases towards infinity, pressure approaches zero
- The curve shows the inverse relationship clearly
Pressure × Volume graph (straight horizontal line)
When you plot the product pV (y-axis) against either pressure or volume (x-axis), you get a horizontal straight line. This demonstrates that pV remains constant, which is another way of expressing Boyle's Law.
1/Volume graph (straight line through origin)
If you plot pressure (y-axis) against 1/V (x-axis), you get a straight line passing through the origin. This shows direct proportionality between pressure and inverse volume (p ∝ 1/V).
Required practical considerations
The AQA specification includes investigating the relationship between pressure and volume as part of required practical skills. Key experimental points:
Method
- Use a sealed syringe with trapped air
- Apply force to compress the gas, reducing volume
- Measure volume from syringe markings
- Measure pressure using a pressure gauge
- Keep temperature constant by working slowly and waiting between readings
- Take readings over a wide range of volumes
Variables
- Independent variable: volume of gas
- Dependent variable: pressure of gas
- Control variables: temperature, mass of gas
Safety
- Ensure apparatus is secure to prevent sudden release
- Wear eye protection
- Don't over-compress the syringe
Analysis
- Calculate p × V for each data pair to show it's constant
- Plot pressure against volume to show inverse relationship
- Plot pressure against 1/volume to show direct proportionality
Real-world applications
Understanding Boyle's Law helps explain everyday phenomena:
Breathing
- Diaphragm contracts, increasing chest volume
- Lung pressure decreases below atmospheric pressure
- Air rushes in from higher to lower pressure
- Diaphragm relaxes, decreasing chest volume
- Lung pressure increases above atmospheric pressure
- Air is pushed out
Syringes
- Pulling plunger increases volume
- Pressure inside decreases
- Atmospheric pressure pushes liquid in
- Pushing plunger decreases volume
- Pressure inside increases
- Liquid is forced out
Scuba diving
- Air in lungs is compressed at depth (high pressure, small volume)
- Ascending too quickly allows air to expand rapidly
- Can cause serious injury called "the bends"
- Divers must ascend slowly to allow gradual decompression
Bicycle pumps
- Pushing handle decreases air volume
- Pressure increases significantly
- High-pressure air forced into tyre
- Valve prevents backflow
Worked examples
Example 1: Basic Boyle's Law calculation
Question: A gas has a volume of 2.0 m³ at a pressure of 100,000 Pa. What is its volume when the pressure is increased to 250,000 Pa at constant temperature?
Solution:
Write down what you know:
- p₁ = 100,000 Pa
- V₁ = 2.0 m³
- p₂ = 250,000 Pa
- V₂ = ?
Use Boyle's Law: p₁V₁ = p₂V₂
Rearrange to find V₂: V₂ = (p₁V₁)/p₂
Substitute values: V₂ = (100,000 × 2.0)/250,000
Calculate: V₂ = 200,000/250,000 = 0.8 m³
Check your answer makes sense: Pressure increased, so volume should decrease ✓
Answer: 0.8 m³ (2 marks — 1 for correct rearrangement, 1 for correct answer with unit)
Example 2: Converting units
Question: A sealed syringe contains 60 cm³ of air at atmospheric pressure (1.0 × 10⁵ Pa). The plunger is pushed in until the volume is 40 cm³. Calculate the new pressure, assuming temperature remains constant.
Solution:
Write down what you know:
- p₁ = 1.0 × 10⁵ Pa
- V₁ = 60 cm³
- V₂ = 40 cm³
- p₂ = ?
Note: volumes are already in the same units (both cm³), so no conversion needed
Use Boyle's Law: p₁V₁ = p₂V₂
Rearrange to find p₂: p₂ = (p₁V₁)/V₂
Substitute values: p₂ = (1.0 × 10⁵ × 60)/40
Calculate: p₂ = (6.0 × 10⁶)/40 = 1.5 × 10⁵ Pa
Check your answer makes sense: Volume decreased, so pressure should increase ✓
Answer: 1.5 × 10⁵ Pa (3 marks — 1 for correct equation, 1 for substitution, 1 for answer with unit)
Example 3: Multi-step problem
Question: A balloon contains 3000 cm³ of helium at a pressure of 120,000 Pa.
(a) Calculate the pressure if the volume is reduced to 2000 cm³ at constant temperature. [3 marks]
(b) Explain in terms of particles why the pressure changes. [3 marks]
Solution:
(a) p₁ = 120,000 Pa, V₁ = 3000 cm³, V₂ = 2000 cm³
p₁V₁ = p₂V₂
p₂ = (p₁V₁)/V₂ = (120,000 × 3000)/2000
p₂ = 360,000,000/2000 = 180,000 Pa
Answer: 180,000 Pa
Mark scheme:
- Correct use of p₁V₁ = p₂V₂ or rearranged form (1 mark)
- Correct substitution (1 mark)
- Correct answer with unit (1 mark)
(b) When volume decreases, the same number of particles occupy a smaller space. Particles collide more frequently with the container walls. More frequent collisions result in greater pressure.
Mark scheme:
- Same number of particles in smaller space/particles closer together (1 mark)
- Increased collision frequency with walls (1 mark)
- More frequent collisions cause higher pressure (1 mark)
Common mistakes and how to avoid them
Using different units for volume on each side of the equation — Always check V₁ and V₂ are in the same units before calculating. Convert cm³ to m³ if necessary (divide by 1,000,000), or litres to m³ (divide by 1000).
Forgetting to check if the answer makes physical sense — When volume increases, pressure must decrease. When volume decreases, pressure must increase. If your answer contradicts this, you've made an error.
Assuming Boyle's Law applies when temperature changes — The law only works at constant temperature. If a question mentions temperature change, Boyle's Law alone cannot be used.
Confusing direct and inverse proportionality — Remember: pressure is inversely proportional to volume (p ∝ 1/V), not directly proportional. Doubling volume halves pressure; it doesn't double it.
Explaining pressure changes without mentioning collision frequency — Stating "particles are closer together" isn't enough. You must explain that closer particles lead to more frequent wall collisions, which increases pressure.
Not including units in final answers — Physics answers without units lose marks. Always write Pa for pressure and m³, cm³, or L for volume.
Exam technique for "Pressure and volume of gases (Boyle's Law)"
Command word "calculate" means you must show your working, substitute numbers into the equation, and give your answer with the correct unit. Just writing the answer gets no marks if working is wrong. Typical calculation questions are worth 2-3 marks.
Command word "explain" requires you to link cause and effect using particle theory. State what happens to the particles, describe the change in collision frequency, and link this to pressure change. Each distinct point earns one mark, usually 2-3 marks total.
Check the information given carefully — Questions often provide more data than needed to test if you can identify relevant values. For Boyle's Law, you need only four variables (p₁, V₁, p₂, V₂) and must know three to find the fourth.
Use standard form for very large or very small numbers — Atmospheric pressure (100,000 Pa) is better written as 1.0 × 10⁵ Pa in calculations to avoid errors with zeros.
Quick revision summary
Boyle's Law states that pressure and volume are inversely proportional for a fixed mass of gas at constant temperature: p₁V₁ = p₂V₂. Gas pressure results from particle collisions with container walls. Compressing a gas decreases volume, increases collision frequency, and raises pressure. Expanding a gas increases volume, decreases collision frequency, and lowers pressure. Always use matching units and check answers make physical sense. Graphs show either a curved inverse relationship (p vs V) or a straight horizontal line (pV vs V or p).