A Level Physics Notes: Thermal Physics and Gases – 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.
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
