Welcome to practical physicsPracticle physics - practical activities designed for use in the classroom with 11 to 19 year olds

Time for air molecules to cross a room

Once they understand the thinking behind estimates of mean free path, s, students 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 500T metres. The number of collisions it makes in that time is 500T / s which is 5 x 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 x 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.