Temperature vs Volume in an expanding gas

Fwahm
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Homework Statement



The energy of a gas is given by: E = 3/2*NkT-aN2/V, where E, N, k, and a are held constant (or are just constants). Volume V1 with temperature T1 expands adiabatically into V2. Determine T2.


Homework Equations



All in part 1.

The Attempt at a Solution



I'm not exactly sure how to start on this problem. I'm not asking for an answer, but some tips on how to proceed would be appreciated.
 
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The system is naturally undergoing Adiabatic Cooling (as the Volume increases, the aN2/V term decreases, which means the 3/2*NkT term (and thus T) must also decrease for E to remain constant.

However, I don't know how to translate this into an equation for delta T/delta V, based on the other constants.
 
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So if the only things that can vary are temperature and volume, it seems to me that if you just use

<br /> \Delta E=0=\frac{3}{2}Nk\Delta T-\frac{aN^2}{\Delta V}<br />

you can solve for \Delta T=T_2-T_1.
 
Thank you very much.

I really need some extra sleep tonight, I can't believe I missed such an easy solution.
 
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