A vacuum chamber contains helium at pressure and temperature

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

A vacuum chamber contains helium at pressure

p = 2.0\times10^{-2}\,\mathrm{Pa}

and temperature

T = 300\,\mathrm{K}

. Treat the helium as an ideal gas of hard spheres of diameter

d = 0.21\,\mathrm{nm}

. ((a)) Find the number density and hence the mean free path, using

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

with

\sigma = \pi d^2

. ((b)) A vessel holds a mixture of

^{20}\mathrm{Ne}

(molar mass

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

) and

^{22}\mathrm{Ne}

(molar mass

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

) at a single temperature, with equal number densities of the two isotopes. The two isotopes escape through the same small hole, whose diameter is much smaller than the mean free path. Find the ratio of the number of

^{20}\mathrm{Ne}

atoms to the number of

^{22}\mathrm{Ne}

atoms escaping per second.

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