# Temperature vs Volume in an expanding gas

1. Feb 11, 2010

### Fwahm

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

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.

2. Relevant equations

All in part 1.

3. 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.

2. Feb 11, 2010

### jdwood983

3. Feb 11, 2010

### Fwahm

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.

Last edited: Feb 11, 2010
4. Feb 11, 2010

### jdwood983

So if the only things that can vary are temperature and volume, it seems to me that if you just use

$$\Delta E=0=\frac{3}{2}Nk\Delta T-\frac{aN^2}{\Delta V}$$

you can solve for $\Delta T=T_2-T_1$.

5. Feb 11, 2010

### Fwahm

Thank you very much.

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