N= volume of cylinder of length vt and area of cross-section
πd2×number of molecules per unit volume
or,
N=πd2nvt
Now, mean free path of a gas molecule,
λ=distance coveredNumber of collisions
λ=vtπd2nvt
The expression for mean free path has been obtained by assuming that all the gas molecules except the one under consideration, are at rest. In fact, all the gas molecules are in random motion, their velocities being governed by Maxwell's law of distribition of velocities. On taking the motion of all the gas molecules into consideration, the mean free path comes out to be:
λ=1√2πd2n
In the equation, substituting for n, we have
n=ρm=PKBT
hence
P is λ=kBT√2πd2P where d