Carbon dioxide fills a flask at and

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

Carbon dioxide fills a flask at

p = 1.01\times10^{5}\,\mathrm{Pa}

and

T = 293\,\mathrm{K}

. Treat it as an ideal gas of hard spheres of diameter

d = 0.46\,\mathrm{nm}

. ((a)) Find the mean free path of a

\mathrm{CO_2}

molecule, using

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

with

\sigma = \pi d^2

. ((b)) A single small hole, of diameter much smaller than the mean free path, is opened in the flask. The gas contains both

^{12}\mathrm{C}^{16}\mathrm{O_2}

(molar mass

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

) and

^{13}\mathrm{C}^{16}\mathrm{O_2}

(molar mass

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

). If the two species have equal number densities inside the flask, by what factor does the lighter one leave more rapidly?

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