Time for air molecules to cross a room
Teaching Guidance for 14-16
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 s √ N 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.