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conquertheworld5
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Homework Statement
A sphere full of air at room temp and 1 atm is placed in a chamber filled with He gas at room temp and 1 atm. The sphere is permeable to He only. What will the equilibrium pressure in the sphere be?
Homework Equations
Variables:
Po=initial pressure
V=vol of sphere
V'=vol of chamber
Na=number of air particles
Nh=number of He particles
Ideal gas law: P=NRT/V
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I think that's all i need, but other eqs that might be relevant:
S=ln(Q) : entropy=ln(number of states)
dS/dE=1/T : derivative of entropy wrt Energy = 1/temp
The Attempt at a Solution
Here's what I think:
since He is a noble gas, we can assume it does not interact with the air particles. Therefore, at equilibrium, a single He molecule is equally likely to be found anywhere in the chamber (V'), which means that the mean number of He particles in the sphere (V) will be V/V'*Nh.
Then use the ideal gas law:
P=(V/V'*Nh+Na)RT/V
can also solve for Nh and Na initially in terms of Po, R, T and V or V':
Nh=PoV'/(RT), Na=PoV/(RT)
and then plug in, rearrange and reduce:
P=(Po/(RT))(V/V'*V'/V+V/V)*RT=Po(1+1)=2Po=2 atm
So, is there anything wrong with what I did? I don't know what the answer should be, but I'm not confident in my answer because my prof mentioned that we should start by maximizing entropy... which I could do, but this way seemed so much simpler. Suggestions? Any errors in my assumptions or approach? I don't find this material intuitive, so I could very well have made mistakes.
Thanks!