Question

Explain what is meant by mean free path of a gas and
derive an expression for it. & fole​

Answer 1

basically, mean free path is the average distance travelled by a particle between successive collisions.

i.e., mean free path = length of path covered by particle/number of collisions

Let diameter of particle is d, moves with speed v . let $n_v$ is number of particle per unit volume.

after time t, length of path covered by particle is vt. see figure, effective collision area , A = πd²

so, volume of interaction , V = A × average length of path covered by particle.

= πd²(v't) , where v' is average relative velocity. i.e., v' = √2v

so, V = πd²√2vt

then, mean free path = vt/πd²√2vt$n_v$

= 1/√2πd²$n_v$

now, put $n_v$ = NP/RT, where N is Avogadro's number, P is pressure, R is universal gas constant and T is temperature.

so, $\boxed{\lambda=\frac{RT}{\sqrt{2}\pi d^2NP}}$

Answer 2

Answer:

Concept of mean free path

The mean free path λ of a gas molecule is its average path length between collisions and is given by, λ = \frac {1}{\sqrt{2} \pi d^2 \frac NV}