How to use pV = constant
For a fixed mass of gas kept at a constant temperature, pressure × volume stays the same. Squash the gas into half the volume and its pressure doubles. On the equation sheet it is written as pV = constant, which you use as:
p1 × V1 = p2 × V2
- p is pressure in pascals (Pa)
- V is volume in cubic metres (m³)
- The 1s are the values before the change; the 2s are the values after.
Gas in a syringe at 100 kPa and 600 cm³ is pushed into 200 cm³. The new pressure is (100,000 × 0.0006) ÷ 0.0002 = 300,000 Pa, or 300 kPa: a third of the volume, three times the pressure.
Because the same units appear on both sides, you can leave pressures in kPa and volumes in cm³ if every value uses them. The answer then comes out in those units too. The solver converts to SI so the working matches the mark scheme either way.
This equation is in GCSE Physics (separate science) only, not Combined Science, and is tested on both tiers. In particle terms, a smaller volume means the particles hit the container walls more often, so the pressure rises.
Common mistakes that cost marks
- Mixing units between the two sides. If p₁ is in kPa, p₂ comes out in kPa. Don't mix kPa with Pa, or cm³ with m³.
- Multiplying instead of dividing. A smaller volume must give a bigger pressure. Check your answer goes the right way.
- Using it when the temperature changes. pV = constant only works at constant temperature.
- Confusing p for pressure with p for momentum. Here p is pressure in pascals.
Practice questions
Try each one on paper first, then reveal the worked answer.
Q1A gas has a pressure of 100 kPa and a volume of 600 cm³. It is compressed to 200 cm³ at constant temperature. Calculate the new pressure.[3 marks]
- p₁V₁ = p₂V₂, so p₂ = p₁V₁ ÷ V₂
- p₂ = (100 × 600) ÷ 200
- p₂ = 300 kPa (300,000 Pa)
Q2A gas at 1.0 × 10⁵ Pa occupies 0.030 m³. Its pressure is increased to 1.5 × 10⁵ Pa at constant temperature. Calculate its new volume.[3 marks]
- V₂ = p₁V₁ ÷ p₂
- V₂ = (100,000 × 0.030) ÷ 150,000 = 3000 ÷ 150,000
- V₂ = 0.020 m³
Q3The air in a sealed syringe has a volume of 50 cm³ at 100 kPa. The plunger is pushed in until the volume is 20 cm³. The temperature stays the same. Calculate the new pressure.[3 marks]
- p₂ = p₁V₁ ÷ V₂
- p₂ = (100 × 50) ÷ 20 = 5000 ÷ 20
- p₂ = 250 kPa
Endless practice
A new question every time, marked instantly. Work it out on paper, then type your answer.
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Frequently asked questions
What does pV = constant mean?
For a fixed mass of gas at constant temperature, pressure × volume stays the same. If the volume halves, the pressure doubles.
What units should I use for pV = constant?
Pascals and cubic metres are the SI units. You can use kPa and cm³ instead, as long as every value uses the same units; the answer comes out in those units.
Why does pressure increase when volume decreases?
The gas particles have less space, so they hit the walls of the container more often. More collisions each second means a bigger force on the walls, so the pressure rises.
Is pV = constant in Combined Science?
No. In AQA it is in GCSE Physics (separate science) only, in the particle model topic, and appears on both Foundation and Higher papers.