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

[bon]

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?

 

[bon]

anyone...?