Gas pressure starts with particle collisions
You will be able to: Connect particle momentum changes with the average force and pressure on a wall.
How can invisible particles push a piston?
A stream of tiny balls striking a wall pushes on it even though each impact is brief. Gas particles do the same: many impacts combine into a measurable average force. Start with one particle moving straight toward a wall.
A useful starting point: Momentum and direction →
Words and symbols before equations
- Momentum p
- Mass times velocity, p=mv, in kg·m/s; direction matters.
- Impulse Δp
- Change in momentum; Δ means final minus initial.
- Average force
- Momentum transferred divided by the time interval, in newtons.
- Pressure P
- Perpendicular force divided by area, P=F⊥/A, in pascals (Pa=N/m²).
What this picture assumes
Enlarged particle stream analogy: mass 0.01 kg each, fixed smooth wall, elastic normal impacts on area 0.02 m². Speed and arrival rate are independently controlled. This is not a sealed-gas model. Arrows show directions, not a spatial scale.
Connect the picture to the physics
Choose right as positive and a fixed wall on the right. A particle arriving with velocity +v and rebounding elastically with −v has Δp_particle=−2mv. The wall receives an equal and opposite impulse +2mv. Elastic means total kinetic energy is conserved in the collision; momentum of the particle alone is not conserved.
For a slanted collision with a smooth wall, only the perpendicular velocity component reverses. A 3–4–5 velocity triangle with normal component 3 m/s and tangential component 4 m/s has unchanged speed 5 m/s after reflection, but the normal momentum changes. Do not use the full speed in the normal impulse.
Add the normal impulses delivered during a time interval and divide by that interval to find average wall force. Dividing by wall area gives pressure. Gas has pressure throughout its volume, not just where it touches a solid wall. The stream model below isolates momentum transfer; it is not a complete gas temperature model.
A worked example, step by step
A 0.01 kg model particle hits a wall normally at 2 m/s and rebounds at the same speed. There are 10 such impacts per second on 0.02 m². Find average pressure.
- Particle momentum changes from +0.02 to −0.02 kg·m/s, so the wall receives +0.04 N·s per impact.
- In one second the wall receives 10×0.04=0.40 N·s. Average force is 0.40 N.
- P=0.40/0.02=20 Pa.
- This is a deliberately enlarged particle analogy; molecular masses are vastly smaller.
Pressure uses the force perpendicular to the surface. An elastic rebound changes momentum even when speed stays constant.
Does unchanged kinetic energy imply zero impulse?
Compare with an explanation
No. Momentum includes direction; reversing the normal velocity requires an impulse.
Predict. Change one thing. Explain.
Hold impact rate fixed and change normal speed. Explain why doubling this speed doubles the pressure in this stream model. In a sealed gas, the collision rate can also change, so the same factor argument does not automatically apply.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
10 impacts/s give average force 0.4 N on 0.02 m²: P=20 Pa. The arriving and rebounding dots are successive states of a particle, not two simultaneous particles.
Enlarged particle stream analogy: mass 0.01 kg each, fixed smooth wall, elastic normal impacts on area 0.02 m². Speed and arrival rate are independently controlled. This is not a sealed-gas model. Arrows show directions, not a spatial scale.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant particle, temperature or energy relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA 0.02 kg model particle approaches a smooth wall with normal velocity +3 m/s and tangential velocity +4 m/s. (a) State its velocity components after an elastic reflection. (b) Find the normal impulse on the wall. (c) Find the average force for 5 identical impacts per second. (d) Find pressure on area 0.03 m².
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Compare with the answer and four-point rubric
- 1 point: Normal −3 m/s, tangential +4 m/s.
- 1 point: Wall impulse +2(0.02)(3)=0.12 N·s along the outward push.
- 1 point: F_avg=5(0.12)=0.60 N.
- 1 point: P=0.60/0.03=20 Pa.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Why does a gas exert pressure?
Particles transfer momentum in collisions; many transfers produce average forces.
RECALL 2What reverses at a smooth fixed wall?
The normal velocity component; the tangential component is unchanged.
RECALL 3Can a particle alone conserve momentum in a wall collision?
No. The wall exerts an external impulse on that particle.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Gas pressure starts with particle collisions
- Normal elastic rebound: wall impulse = 2mv_normal.
- F_avg = total wall impulse / elapsed time.
- P = F_perpendicular / A; 1 Pa = 1 N/m².
Remember: Pressure uses the force perpendicular to the surface. An elastic rebound changes momentum even when speed stays constant.
Conditions: Enlarged particle stream analogy: mass 0.01 kg each, fixed smooth wall, elastic normal impacts on area 0.02 m². Speed and arrival rate are independently controlled. This is not a sealed-gas model. Arrows show directions, not a spatial scale.
Refresh Kid · AP Physics 2 Unit 1 (official Unit 9) · Objectives 9.1.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 9.1, objectives 9.1.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Refresh Kid calls this the first AP Physics 2 unit; College Board numbers it Unit 9, continuing after AP Physics 1. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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