# Thermal effusion problem - typical qualifier

1. Dec 14, 2009

### StarTiger

1. The problem statement, all variables and given/known data

Part a: A thin walled vessel of volume V, kept at constant temperature T, contains a gas which slowly leaks through a small hole of area A. The outside pressure is negligible (assume zero), so no leakage back into the vessel is possible. Find an expression for the pressure "inside the gas" as a function of time.

Part b: Repeat the calculation for an ideal gas, this time "without correct Boltzmann counting", ie assume that z(T,V,N) = Z^N.
Show that entropy is not extensive.

2. Relevant equations

Statistical physics.

3. The attempt at a solution

I'm fairly sure I've solved part A, but I am a bit stumped on how to approach B.
Perhaps I tackled A using the wrong model and that's what has left me stumped.
For A,
I took dN/dt = - PA / ((2*pi*m*k*T)^(1/2)) (from flux expression)
and dN = d(PV/kT) =(V/kT) dP
so -DP/dt=kT/V[(-AP/(2pi*mkT)^1/2]
so dP/dt = -kTAP/(V(2pi*mkT)^.5)

and from here I solve for P(t).

Set -V(2pi*mkT)^.5)/kTA equal to tau. See that dP=-1/tau dt

then get P(t)=P_o e^(-t/tau).

So I think this is all right, but how to tackle the second part is a bit beyond my current understanding. Any tips? Insights? Recommendations? Have I blown something already?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution