# Free expansion of a Van der Waal's Gas

1. Feb 1, 2010

### mathman44

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

There are two vessels connected by a stopper. Both have the same volume. One has "N_a" moles of gas, the other "N_b". Find the expression for the change in temperature when the stopper is opened and the system is allowed to come to a new equilibrium state.

3. The attempt at a solution

I'm supposed to use this equation: $$u = C_vT - a/v + const$$

I tried doing this: $$dt/dv = (du/dv) / (du/dt)$$ were the denominator is just Cv, but that just gave me:

$$-a/v^2 * 1/C_v$$

The answer is supposed to look like:

$$(2n_an_b - n^2_a - n^2_b)*a/(c_v*2V[n_a + n_b])$$

How do I get the # of moles into this expression? Thanks.

2. Feb 1, 2010