Effusion Physics Problem: Calculating Final Temperature of Gas in a Vessel

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The discussion revolves around calculating the final temperature of gas in a vessel after effusion through a small hole into a vacuum. The user has derived the mean kinetic energy of the effused molecules as 2kT and is attempting to relate this to the final temperature Tf of the gas in the box. They suggest that Tf can be expressed as Tf = p/nk, leading to the conclusion that Tf = 4/3 T. The user seeks confirmation on the correctness of this approach and result. The conversation highlights the application of kinetic theory and Maxwellian distribution in solving effusion problems.
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Homework Statement



A vessel contains gas at temp T (monatomic). Maxwellian distribution of speeds.

Molecules diffuse via small hole into vacuum. Box opened for short time and catches some molecules. Calc. final temp of gas in box.

Homework Equations





The Attempt at a Solution



So i worked out mean ke of effused molecules to be 2kT

Let Tf be temp of gas in box

can i then just say Tf = p/nk

But p = 1/2 n m <v^2>

Therefore, using my result, Tf = 4/3 T? Is this right?
 
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