RMS/Mean Free Path
Properties of Matter

Time for air molecules to cross a room

Teaching Guidance for 14-16 PRACTICAL PHYISCS

Once students understand the thinking behind estimates of mean free path, s , they can estimate the time for air molecules to cross a room. Assume there are no convection currents.

In time T seconds the straightened-out path of a molecule of air is 500 T metres. The number of collisions it makes in that time is 500 T / s which is 5 × 109  x T collisions. The average progress from start to finish will be sN which is the length of the room, say 6 m.

Hence 6 = √( 5 × 109  x T) x 10-7. And so the time for an air molecule to cross the room is 720 000 seconds, more than a week!

The same kind of story applies to neutrons diffusing from the inner regions of a nuclear reactor. Also for the particles of light (photons) cannoning their way out from the inner layers of the Sun.

RMS/Mean Free Path
can be analysed using the quantity RMS Speed
is used in analyses relating to Brownian Motion
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