Express the mean free path of a gas molecule in terms of the density o

1.	Express the mean free path of a gas molecule in terms of the density of the gas
Answer» In the usual notation, the mean free path of a gas molecule, \(\lambda\) = \(\frac{1}{\sqrt2\pi d^2(N/V)}\) Density, ρ, of the gas = \(\frac{mass}{volume}\) = \(\frac{mN}{V}\), where m is the molecular mass. ∴ \(\frac{N}{V}\) = \(\frac{ρ}{m}\) ∴ λ = \(\frac{m}{\sqrt2\pi d^2ρ}\)

Express the mean free path of a gas molecule in terms of the density of the gas

Answer»

In the usual notation, the mean free path of a gas molecule,

\(\lambda\) = \(\frac{1}{\sqrt2\pi d^2(N/V)}\)

Density, ρ, of the gas = \(\frac{mass}{volume}\)

= \(\frac{mN}{V}\), where m is the molecular mass.

∴ \(\frac{N}{V}\) = \(\frac{ρ}{m}\)

∴ λ = \(\frac{m}{\sqrt2\pi d^2ρ}\)