AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
A simple algebraic approach involving conservation of momentum is required.
Full specification wording
Molecular kinetic theory model (A-level only): A simple algebraic approach involving conservation of momentum is required.
In the molecular kinetic theory model, gas pressure arises from countless molecular collisions with the container walls.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 4 of 5
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
In the molecular kinetic theory model, gas pressure arises from countless molecular collisions with the container walls. To analyse one collision, treat the wall and a molecule as an isolated system: total momentum is conserved. For a molecule of mass m moving at velocity component u perpendicular to a wall, an elastic collision reverses that component, so its momentum change is −2mu. The wall gains +2mu. Over time Δt, the total momentum transferred to the wall is the impulse Δp. The average force exerted is this momentum transferred divided by Δt (F = Δp/Δt). Summing over N molecules and dividing by wall area A gives pressure p = (1/3)ρc̄², where ρ is density and c̄² is the mean square speed.
What earns the marks
- State that the wall–molecule system is isolated during the collision, so total momentum is conserved.
- For a molecule of mass m with perpendicular velocity component u, show the momentum change of the molecule is −2mu and therefore the wall gains +2mu.
- Relate the total momentum transferred to the wall in time Δt to the average force using F = Δp/Δt.
- Combine the single-collision result with the number of molecules and collisions per unit time, then divide by the wall area to obtain a pressure expression such as p = (1/3)ρc̄².
- Keep the algebra symbolic and clearly define each symbol, including m, u, N, Δt and A, before substituting any values.
Common mistakes and how to put them right
Treating the molecule's momentum change as mu rather than 2mu.
Put it right by writing the change as final minus initial, giving −2mu.
Forgetting that momentum is a vector and adding speeds or momenta without direction.
Put it right by resolving velocities perpendicular to the wall and assigning signs consistently.
Confusing force with momentum or pressure with force.
Put it right by using force equals rate of change of momentum, then dividing force by area to find pressure.
Exam tips
- Begin by drawing a labelled diagram showing one molecule approaching a wall with velocity component u and rebounding with −u.
- Write the conservation-of-momentum statement explicitly before doing any algebra; examiners look for the physical principle, not just the final formula.
- Check units at the end: momentum in kg m s⁻¹, force in N, pressure in Pa or N m⁻².
Try the lesson
The start of the Molecular kinetic theory model (A-level only): A simple algebraic approach involving conservation of momentum is required. lesson, made from checked teaching notes for this specification point.
Have a go first
A gas molecule of mass m travels at speed v and strikes a wall of its container head-on, rebounding with speed v in the opposite direction. According to the principle of conservation of momentum, what is the magnitude of the momentum transferred to the wall?
Listen
In the molecular kinetic theory model, gas pressure arises from countless molecular collisions with the container walls. To analyse one collision, treat the wall and a molecule as an isolated system: total momentum is conserved. For a molecule of mass m moving at velocity component u perpendicular to a wall, an elastic collision reverses that component, so its momentum change is −2mu. The wall gains +2mu. Over time Δt, the total momentum transferred to the wall is the impulse Δp. The average force exerted is this momentum transferred divided by Δt (F = Δp/Δt). Summing over N molecules and dividing by wall area A gives pressure p = (1/3)ρc̄², where ρ is density and c̄² is the mean square speed. A strong answer earns marks for these points. State that the wall–molecule system is isolated during the collision, so total momentum is conserved. For a molecule of mass m with perpendicular velocity component u, show the momentum change of the molecule is −2mu and therefore the wall gains +2mu. Relate the total momentum transferred to the wall in time Δt to the average force using F = Δp/Δt. Combine the single-collision result with the number of molecules and collisions per unit time, then divide by the wall area to obtain a pressure expression such as p = (1/3)ρc̄². A common slip: Treating the molecule's momentum change as mu rather than 2mu: the velocity component reverses, so the change is twice the initial magnitude. Instead, writing the change as final minus initial, giving −2mu. Exam tip: Begin by drawing a labelled diagram showing one molecule approaching a wall with velocity component u and rebounding with −u.
Key words
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Conservation of momentum
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Elastic collision
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Average force
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Pressure
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See every definition
- Conservation of momentum
- The wall and a molecule are treated as an isolated system during the collision, so total momentum is conserved.
- Elastic collision
- A collision in which the velocity component perpendicular to the wall reverses, so the molecule's momentum change is −2mu and the wall gains +2mu.
- Average force
- The total momentum transferred to the wall in time Δt divided by Δt, given by F = Δp/Δt.
- Pressure
- Obtained by summing over N molecules and dividing by wall area A, giving p = (1/3)ρc̄², where ρ is density and c̄² is the mean square speed.
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