Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 103

where is the concentration of themolecules inside thevessel and is the

concentration of themolecules in the chamber. Disregarding the thickness

of the walls of the vessel, we canwrite the conditionthat thenumber of

molecules entering thevessel per second isequal to thenumber ofmolecules

whereAis the area of the hole,and we used theresult of Problem4.14 for

the number ofmoleculesstriking a unitarea persecond. Actually, the only

importantpointhere isthat thisnumber isproportional to the product of

concentration and average velocity.Therefore,

The average velocity So,from(S.4.16.3), wehave

Substituting(S.4.16.4) into(S.4.16.1), weobtain

4.17 Hole in Wall (Princeton)

a) If the diameter of thehole is large compared to the meanfree path in
bothgases, wehaveregular hydrodynamicflow ofmolecules inwhich the
pressures are thesame inboth parts. If the diameter of thehole (and
thickness of thepartition) issmall compared to the meanfree path,there
are practically nocollisionswithin thehole and themoleculesthermalize
far from thehole(usuallythroughcollisionswith the walls).

b) In case there are twoindependenteffusiveflowsfrom I

to II and from II to I. Thenumber ofparticles and goingthrough

the hole fromparts I and IIare, respectively(seeProblem 4.14),

leaving it: