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nakamura25
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Homework Statement
A rigid ( ie. Constant volume), non-conducting ( ie. Perfectly insulated, no heat losses or gain) tank with a volume of 4.6 m^3. The tank is divided into two unequal parts by a thin membrane. One side of the membrane representing 1/3 of the tank is filled with nitrogen ( may be assumed to be an ideal gas) at 3.1 bar and 333.5 K. The other side of the membrane is evacuated. The membrane ruptures and the gas fills the entire tank. Heat capacity of nitrogen, Cp=3.5 R.
What is the final pressure of the gas in the tank?
The Attempt at a Solution
My thought was:
Non-conducting means adiabatic, hence Q = 0.
Free expansion, no external work, W = 0.
delta u = Q + W = Cp*(deltaT) = 0. So the temperature stays the same.
Since nitrogen can be assumed to be ideal gas, I used ideal gas law to calculated final pressure.
(P1)*(V1) = (P2)*(V2)
(3.1 bar)*(1/3)V = (P2)*(V)
P2 = 3.1/3 = 1.03 bar
Later on I saw this video lecture by UC Boulder:
http://www.learncheme.com/page/ideal-gas-expansion-closed
I think the question and result are the same for my case. So I summited my answer. But it turned out that the temperature does change, since the gas will do work to expand. Also, the final pressure should be 1.76 bar. I tried to use the adiabatic process equation p2/p1 = (V1/V2)^(Cp/Cv). Still could not get the right answer.
My questions are:
What's wrong with my reasoning? Does that mean the solution in the video is also wrong?
How to solve this problem for final pressure and temperature?
I'd really appreciate your effort. Any hint or solution would be helpful. Thank you.
Best Regards,
Naka
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