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.
Consider
spherical molecules with diameter
in a volume
and suppose for simplicity that only one molecule is moving. The molecules collide whenever the distance between their centres is less than
Draw 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 time
a molecule with speed
travels a distance
|
The volume of the cylinder is
There are
molecules per unit volume so the number
with centres in the cylinder is
so 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 of
so in fact