Quick question about pressure in gases.

[Beer-monster]

Two gases are in a vessel and separated by a partition. They start at different pressures P1 and P2. When the partition is removed and equilibrium restored am I right in thinking the new pressure is the average of the starting pressure i.e.

$$P_{f} = \frac{P1+P2}{2}$$

Thanks.

 

[gneill]

Nope. Volume and temperature count, too.

What would happen if one side of the vessel contained a thimble full of gas at 100 Pa, and the other side contained a tanker car full at 50 Pa? Would an average make sense?

 

[Beer-monster]

Okay using Boyle's Law I get:

$$P_{f}=\frac{P1V1+P2V2}{(V1+V2)}$$

If this is correct, I have the slight problem that my work for the full question (calculate the entropy change when the gases mix) end with:

$$\Delta S = nR \ln\left(\frac{P1P2}{P_{f}^{2}}\right)$$

Substituting the first expression in gives a mess, which I can't seem to simplify to give an expression in terms of P1 and P2. Anyone poke me in the right direction?