# Find the final volume

1. ### KFC

396
1. The problem statement, all variables and given/known data
Two ideal gas (n mole A and m mole B) was separated by a piston (impermeable and diathermal) the whole setup is confine in a adiabatic walls so no heat exchange with outside. Let the piston move, at equilibrium, find the final volume. Assume the final temperature of both gas is T and the total volume is V.

2. The attempt at a solution
First of all, both gas satisfy ideal gas state equation

$$\frac{P_AV_A}{T_A} = nR, \qquad \qquad \frac{P_BV_B}{T_B} = mR$$

Since we know the final temperature, and at equilibrium, the pressure is the same on both compartment (otherwise, the piston will move), so assuming the final volume of A is $$V_A$$, then the final volume of B will be $$V-V_B$$, we conclude that

$$\frac{P}{T} = nRV_A = \frac{P}{T} = mR(V-V_A)$$

We can solve for $$V_A$$ and $$V_B$$, right?

2. ### CompuChip

4,299
Your setup looks correct, except for a mathematical error...
If $\frac{P V}{T} = n R$, then $\frac{P}{T} = \cdots$ ?

By the way, once you have found the answer, it'll be nice trying to explain its physical meaning and saying something about whether you could have foreseen the outcome.

3. ### KFC

396
Oh, careless. Thanks