A vessel holds nitrogen gas (

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

^{14}\mathrm{N_2}

, molecular mass

28.0\,\mathrm{u}

) at a pressure of

250\,\mathrm{Pa}

and a temperature of

320\,\mathrm{K}

. The gas is ideal. A hole of area

0.050\,\mathrm{mm^2}

is opened in the wall; the hole is much smaller than the mean free path, so molecules pass through it one at a time without colliding, and outside the vessel there is a vacuum. Take

1\,\mathrm{u} = 1.661\times10^{-27}\,\mathrm{kg}

. ((a)) Calculate the root-mean-square speed and the mean speed of a molecule in the vessel. ((b)) Calculate the number of molecules leaving through the hole per second. ((c)) The vessel is emptied and refilled with a mixture containing equal numbers of

^{14}\mathrm{N_2}

(

28.0\,\mathrm{u}

) and

^{15}\mathrm{N_2}

(

30.0\,\mathrm{u}

) at the same pressure and temperature. Find the ratio of the rate at which

^{14}\mathrm{N_2}

molecules leave to the rate at which

^{15}\mathrm{N_2}

molecules leave.

Browse the problem library