# Homework Help: Entropy change with identical and different gases

1. Oct 29, 2008

### Antti

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

There's a thermally insulated container with a removable wall. So there are two compartments inside, one with volume V (i call it left box) and the other with volume V + B (right box) so the total volume is 2V + B. Both boxes have N molecules of an ideal gas and are in thermal equilibrium with eachother. The compartment with volume V has initial pressure p.

Find

a) the final pressure of the mixed gas when the wall is removed
b) the total change in entropy if the gases in the left and right box are different
c) the total change in entropy if the gases are identical

I've done a). I just imagine that the gas in the left box expands into vacuum and then i do the same for the right box and add the final pressures of both boxes to get the final total pressure.

Using the idel gas law:

p_left = NkT/(2V+B) = p/(2+B/V)
p_right = p/(2+B/V)

The pressures turn out the same because the same number of molecules occupy the same volume at the same temperature.

p_tot = 2p/(2+B/V)

But what to do with the two other questions? How and why does the entropy change when the boxes contain different gases?