Right, so I've got this Thermo assignment, and the question I'm having problems with looks like this:

I can easily work out all the conditions in both compartments before the heating, using PV=nRT. There are two things I'm having problems with, however.

Firstly, to find the conditions AFTER the heating, I get 3 unknowns and 2 equations, which is obviously a problem.

What I have so far is this:

P

_{A} = P

_{B}, since I'm assuming energy was added to the system slowly enough such that we can take the process to be reversible.

Using the ideal gas equation for both compartments, we get

n

_{A}T

_{A}/V

_{A} = n

_{B}T

_{B}/V

_{B}and we also know that V

_{A} + V

_{B} = V

_{tot}The unknowns are V

_{A}, V

_{B} and T

_{B}.

Anyone have any ideas on where I can find a third equation?

Also, once I have worked out the conditions, I'll have to work out the amount of energy added by the heater. Since dU = 0 for an ideal gas, the energy balance reduces to Q = -W where W=-?PdV. Am I right in saying I'll need to work out separate W terms for each of the two compartments? If so, how would I do this? My initial thought is simple enough, just use P=nRT/V in the integral, but the obvious problem is that the expansion of compartment A and the compression of B are not isothermal, so T cannot be taken as constant in the integration... How do I get around this?

Any help will be much appreciated! Thanks in advance!