Explain, using the kinetic molecular model, why the pressure of an ideal gas remains constant when its volume is decreased and its temperature is simultaneously reduced.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A fixed mass of ideal gas is compressed slowly in a thermally insulated container. A student then carefully reduces the thermal insulation and allows heat to escape, so that the temperature of the gas falls back to its original value. The student observes that the pressure returns to exactly its original value as well.
Model answer (4 marks)
1. Reducing the volume increases the collision frequency of the gas molecules with the walls, which would raise the pressure.
2. Lowering the temperature decreases the average kinetic energy and speed of the molecules, which would lower the pressure.
3. In this case the volume and temperature are reduced by the same factor, so the increased collision frequency is exactly offset by the reduced force per collision.
4. Consequently the pressure remains unchanged, in agreement with the ideal‑gas law P=nRT/V when T and V change proportionally.
2. Lowering the temperature decreases the average kinetic energy and speed of the molecules, which would lower the pressure.
3. In this case the volume and temperature are reduced by the same factor, so the increased collision frequency is exactly offset by the reduced force per collision.
4. Consequently the pressure remains unchanged, in agreement with the ideal‑gas law P=nRT/V when T and V change proportionally.
Examiner tips
- Use the kinetic‑molecular explanation of collision frequency and force per collision.
- Show the two opposing effects and state that they cancel.
- Mention the ideal gas law to confirm the result.
- Keep the answer concise and use correct terminology.
Mark scheme (4 marks)
- Decreasing the volume alone would increase the frequency of molecular collisions with the walls, tending to increase pressure.
- Decreasing the temperature alone would reduce the average kinetic energy (and hence average speed) of the molecules, tending to decrease pressure.
- The two effects exactly cancel: the increase in collision frequency due to reduced volume is offset by the decrease in force per collision due to reduced temperature.
- This is consistent with the ideal gas law: if the temperature and volume are both reduced by the same factor, the pressure P = nRT/V remains unchanged.
Key terms in this question
kinetic molecular model · pressure
Related
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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