## Mean Free Path

In an ideal gas the molecules never collide since they are all assumed to have zero volume. In fact, obviously the molecules do have volume and collisions occur many times per second. We can estimate the average distance gas molecules travel between collisions. This distance is called the mean free path.

Considerspherical molecules with diameterin a volumeand suppose for simplicity that only one molecule is moving. The molecules collide whenever the distance between their centres is less thanDraw a cylinder radiuswith axis parallel to the path of the molecule. The molecule collides with any other molecule whose centre is inside this cylinder. In a short timea molecule with speedtravels a distance

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The volume of the cylinder isThere aremolecules per unit volume so the numberwith centres in the cylinder isso the number of collisions per unit time is

The average time between collisions is the reciprocal of this:and the mean free path

Taking into account that all the molecules are moving introduces another factor ofso in fact