Answer to Question #142896 in Molecular Physics | Thermodynamics for sridhar

Question

Equation of Mean free path of molecules in a polyatomic gas

Answer 1

The Kinetic theory of gases assumes that molecules are continuously colliding with each other and they move with constant speeds and in straight lines between two collisions. Hence, a molecule follows a zigzag pattern/path, each of which is known as a free path.

The average distance travelled by the molecule between two collisions is known as the Mean Free Path and the number of collisions increases if the gas is denser or the molecules are larger in size.

If the molecules of a gas are spheres having a diameter(d), and one molecule is moving with an average speed(v) and the number of molecules per unit volume is "$n_v$", then the mean free path ($\mu$) can be calculated by using the formula;

$\mu = \dfrac{1}{\sqrt{2}πd^2n_v}$

but $n_v = \dfrac{nN_a}{V} = \dfrac{N_aP}{RT}$

$\mu = \dfrac{RT}{\sqrt{2}πd^2N_aP}$