The mean free path of a gas, lambda, is defined as the average distance traveled

Question

The mean free path of a gas, lambda, is defined as the average distance traveled by molecules between collisions. A commonly used formula for estimating lambda of an ideal gas is: lambda = C mu/rho Squareroot RT where mu is the viscosity of the gas. rho is the density of air. T is the temperature in Kelvin, and C is an experimentally determined constant. Calculate the mean free path of air (in units of nm) at 25 degree C and standard atmospheric pressure if the viscosity of air is 1.8003 times 10^-5 N-s/m^2, the density of air is 1.169 kg/m^3 the constant C is equal to 1.3.

Explanation / Answer

Use the formula given above -

lemda = (C*mu) / [rho*sqrt(RT)]

Given that -

C = 1.3, mu = 1.8003x10^-5 N-s/m^2, rho = 1.169 kg/m^3, R = 0.287 kJ/KG-K = 287 kJ/KG-K,

T = 273+25 = 298 K

So, lemda = (1.3x1.8003x10^-5) / [1.169*sqrt(287*298)] = (2.34039x10^-5) / [1.169*292.4] = 6.846x10^-8 m.

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