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Scintillation
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Homework Statement
We start with an ideal gas confined to half a container. Then, without heat flow, the gas flows into the other half as the partition is punctured. Find the new temperature after the expansion.
Homework Equations
Since there is no heat flow, I assume the process is adiabatic.
Relevant equations are:
(T1)(V1)^(y-1)=(T2)(V2)^Y-1
(P1)(V1)^y=(P2)(V2)^y
The Attempt at a Solution
Using my first equation, with T1= To, and V2=2V1, my final Temperature should be To/(2^y-1).
Except, my solution key states that there is NO change in temperature. Using the equation 1/2m(vrms)^2=3/2kt, since the velocity of each individual particle has not changed, then the temperature has not changed either.
But then what does my value of To/(2^y-1) mean? I always have trouble with these equations for adiabatic expansion/pressure. Another question I had (I can discuss this in more information if needed) is I was given the original volume, original and final pressure, as well as the original and final temperatures, and asked to find the final volume. I understand I could have used PV=nRT, but I tried using (P1)(V1)^y=(P2)(V2)^y to see if it would be the same. It was not the same, unfortunately, but I don't understand why. Can anyone help clarify either of these problems?