Argon gas has number density

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Kinetic theory and transport in gases · Kinetic theory and transport in gases

Thermal Physics, Ch Collisions, mean free path and transport in gases

Problem

n = 1.8\times10^{25}\,\mathrm{m^{-3}}

. Treat its atoms as hard spheres of diameter

d = 0.36\,\mathrm{nm}

and the gas as ideal. ((a)) Find the mean free path of an argon atom, using the standard result

\lambda = 1/(\sqrt2\,n\sigma)

with

\sigma = \pi d^2

. ((b)) Two identical vessels, one holding

^{3}\mathrm{He}

(molar mass

3.016\,\mathrm{g\,mol^{-1}}

) and one holding

^{4}\mathrm{He}

(molar mass

4.003\,\mathrm{g\,mol^{-1}}

), are at the same temperature and the same number density. Each has an identical hole in its wall, of diameter much smaller than the mean free path. By what factor is the number of atoms escaping per second larger for the

^{3}\mathrm{He}

vessel?

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