Increasing the Pressure of a Gas
Revise Increasing the Pressure of a Gas for GCSE Physics with this free worksheet and full mark scheme — Higher-tier exam-style questions with worked answers for AQA, Edexcel and OCR. A separate (triple) physics topic: doing work on a gas by compressing it transfers energy to its particles and can raise its temperature.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
This is a Higher tier only topic, so there's no Foundation paper — only the Higher worksheet and mark scheme below.
Topic overview
For a fixed mass of gas at constant temperature, the pressure and volume are inversely proportional. This is a Triple-only and Higher-only topic.
The equation is pressure × volume = constant, written pV = constant. So p₁V₁ = p₂V₂ can be used to compare two situations. If the volume is halved at constant temperature, the pressure doubles.
The explanation is molecular. Reducing the volume means the molecules have less space, so they hit the walls more frequently. The frequency of collisions rises even though their speed is unchanged, because the temperature is constant, and more frequent collisions mean a higher pressure.
Revision notes
The relationship
For a fixed mass of gas at constant temperature, pressure × volume = constant.
So p₁V₁ = p₂V₂. Pressure and volume are inversely proportional: if one doubles the other halves. A graph of pressure against volume is a curve; pressure against 1/volume is a straight line.
The molecular explanation
Reducing the volume gives the molecules less space to move in.
They therefore collide with the walls more frequently. Because the temperature is constant, their average speed is unchanged, so it is the increased frequency of collisions alone that raises the pressure.
Using the equation
Substitute the known values into p₁V₁ = p₂V₂ and rearrange for the unknown.
The units of pressure and of volume must be the same on both sides, though they need not be SI units — any consistent pair works because the relationship is a ratio.
Key points
- pV = constant for a fixed mass at constant temperature.
- Pressure and volume are inversely proportional.
- p₁V₁ = p₂V₂ compares two situations.
- Halving the volume doubles the pressure.
- Less space means more frequent collisions.
- Molecular speed is unchanged at constant temperature.
Worked examples
Example 1
A gas has a volume of 0.5 m³ at a pressure of 200 kPa. It is compressed to 0.2 m³ at constant temperature. Calculate the new pressure. [3 marks]
Model answer
Using p₁V₁ = p₂V₂: 200 × 0.5 = p₂ × 0.2 (1 mark). 100 = 0.2p₂ (1 mark). p₂ = 100 ÷ 0.2 = 500 kPa (1 mark).
Example 2
Explain, in terms of molecules, why reducing the volume of a gas at constant temperature increases its pressure. [3 marks]
Model answer
The molecules have less space to move in (1 mark), so they collide with the walls of the container more frequently (1 mark). Since the temperature is constant their average speed is unchanged, so the increased frequency of collisions alone raises the pressure (1 mark).
Example 3
State what happens to the pressure of a fixed mass of gas if its volume is doubled at constant temperature. [2 marks]
Model answer
The pressure halves (1 mark), because pressure and volume are inversely proportional at constant temperature (1 mark).
Common mistakes
Saying the molecules speed up when compressed.
At constant temperature their average speed is unchanged; only the collision frequency rises.
Treating pressure and volume as directly proportional.
They are inversely proportional — one rises as the other falls.
Using different units on each side.
The units must match on both sides of p₁V₁ = p₂V₂.
Forgetting the constant temperature condition.
The relationship only holds at constant temperature for a fixed mass.
Exam tips
- State the constant temperature and fixed mass conditions.
- Say collision frequency, not molecular speed, in the explanation.
- Keep units consistent on both sides of the equation.
- Remember this is Triple-only AND Higher-only.
Key terms
- Inversely proportional
- One quantity doubling as the other halves.
- Constant temperature
- The condition required for pV = constant.
- Collision frequency
- How often molecules strike the walls.
- Fixed mass
- A sealed quantity of gas with no particles added or removed.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.