AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Explanation of relationships between p, V and T in terms of a simple…
Full specification wording
Molecular kinetic theory model (A-level only): Explanation of relationships between p, V and T in terms of a simple molecular model.
A simple molecular model treats a gas as many identical molecules in random motion, colliding elastically with the container walls.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 2 of 5
- 3 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A simple molecular model treats a gas as many identical molecules in random motion, colliding elastically with the container walls. Pressure arises from the rate of change of momentum as molecules strike unit area of wall. Raising T increases mean molecular kinetic energy, so molecules hit the walls harder and more often, raising p at fixed V. Reducing V at fixed T packs the same molecules into less space, so wall collisions per second per unit area rise, raising p. At fixed p, heating a gas raises T and the molecules move faster, increasing the impulse per collision. To maintain constant pressure, the collision rate per unit area must decrease, which requires V to increase. Thus pV ∝ T for a fixed mass of ideal gas.
What earns the marks
- Pressure is explained as the force per unit area exerted by molecular collisions with the container walls, linked to rate of change of momentum.
- Temperature is linked to the mean kinetic energy of the molecules, so a higher T means faster molecules on average.
- At fixed V, increasing T increases both the frequency and the impulse of wall collisions, so p increases.
- At fixed T, decreasing V increases the number density of molecules, so the collision rate per unit area and p increase.
- At fixed p, increasing T increases the impulse per collision; therefore, V must increase so that the collision rate per unit area decreases, keeping pressure constant.
- A clear molecular account should refer to a fixed mass of gas and to random motion, not to macroscopic pushing or 'heat expanding' the gas.
Common mistakes and how to put them right
Saying molecules 'expand' when heated.
Put it right by stating that the molecules move faster and their mean kinetic energy increases, while molecular size stays essentially constant.
Explaining pressure as molecules 'pushing' continuously on the walls.
Put it right by describing discrete collisions and the rate of change of momentum at the wall.
Stating that at constant pressure, the collision rate remains constant when heated.
Put it right by noting that because impulse per collision increases, the collision rate per unit area must decrease to keep pressure constant.
Exam tips
- Always name the variable held constant before explaining how the other two change.
- Use the chain: temperature → mean kinetic energy → molecular speed → collision rate and impulse → pressure.
Try the lesson
The start of the Molecular kinetic theory model (A-level only): Explanation of relationships between p, V and T in terms of a simple molecular model. lesson, made from checked teaching notes for this specification point.
Have a go first
In the simple molecular kinetic theory model, a fixed mass of gas is held at constant temperature while its volume is reduced. What happens to the pressure of the gas?
Listen
A simple molecular model treats a gas as many identical molecules in random motion, colliding elastically with the container walls. Pressure arises from the rate of change of momentum as molecules strike unit area of wall. Raising T increases mean molecular kinetic energy, so molecules hit the walls harder and more often, raising p at fixed V. Reducing V at fixed T packs the same molecules into less space, so wall collisions per second per unit area rise, raising p. At fixed p, heating a gas raises T and the molecules move faster, increasing the impulse per collision. To maintain constant pressure, the collision rate per unit area must decrease, which requires V to increase. Thus pV ∝ T for a fixed mass of ideal gas. A strong answer earns marks for these points. Pressure is explained as the force per unit area exerted by molecular collisions with the container walls, linked to rate of change of momentum. Temperature is linked to the mean kinetic energy of the molecules, so a higher T means faster molecules on average. At fixed V, increasing T increases both the frequency and the impulse of wall collisions, so p increases. At fixed T, decreasing V increases the number density of molecules, so the collision rate per unit area and p increase. A common slip: Saying molecules 'expand' when heated. Instead, stating that the molecules move faster and their mean kinetic energy increases, while molecular size stays essentially constant. Exam tip: Always name the variable held constant before explaining how the other two change.
See it
Key words
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Kinetic theory model of gases
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Pressure from molecular collisions
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Absolute temperature and mean kinetic energy
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See every definition
- Kinetic theory model of gases
- A simple molecular model treats a gas as many identical molecules in random motion, colliding elastically with the container walls.
- Pressure from molecular collisions
- Pressure arises from the rate of change of momentum as molecules strike unit area of wall.
- Absolute temperature and mean kinetic energy
- Raising T increases mean molecular kinetic energy, so molecules hit the walls harder and more often.
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