Paper 1 Q10 — Kinetic theory: apply, don’t recall

Kinetic theory of gases — the factor of ⅓ comes from 3D averaging, not this special case

What the examiners said

“This question proved challenging. The most common incorrect answer was option C, indicating a recalled version of the proof rather than an application of the proof to the specific case in the question, where all N molecules are travelling perpendicular to the shaded wall.”

Try the question (reconstruction)

In a special model, all N molecules (mass m, speed c) move perpendicular to one wall of a cube (side L), bouncing back and forth elastically. What is the pressure on that wall?

Examiner report: “Candidates recalled the ⅓ result instead of applying the derivation to this all-perpendicular case.”

Explore — where does the ⅓ come from?

Toggle between the standard gas (motion in x, y, z) and this special case (all along x). Watch what fraction of the molecular energy actually pushes on the shaded wall.

The ⅓ in p = ⅓(Nm/V)⟨c²⟩ is purely the price of sharing motion across three axes. Remove the sharing and the ⅓ vanishes.

Original reconstruction inspired by the misconceptions described in the Singapore-Cambridge GCE A-Level H2 Physics 9749 November 2023 Examiner Report. Not the actual examination question. For classroom exploration.

Made by lookang, using Claude Fable 5. More resources: iwant2study.org