A sealed tube of length contains still air at room temperature; there are no draughts…
PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Kinetic theory and transport in gases · Statistical foundations and the equilibrium ensembles
Thermal Physics, Ch Probability, random walks and the statistics of large numbers
Problem
A sealed tube of length 3.0cm contains still air at room temperature; there are no draughts or convection currents, so transport along the tube is by diffusion alone. A few carbon monoxide molecules are released at one end. Model such a molecule as a one-dimensional random walker that takes an independent step of fixed length equal to its mean free path λ=65nm once every collision time τ=λ/vˉ, with mean speed vˉ=470ms−1.
((a)) Estimate the diffusion coefficient D of carbon monoxide in air from this walk.
((b)) Estimate the time for the root-mean-square displacement of a released molecule to reach the far end of the tube, 3.0cm away.