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 [tex] \frac{P_AV_A}{T_A} = nR, \qquad \qquad \frac{P_BV_B}{T_B} = mR [/tex] 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 [tex]V_A[/tex], then the final volume of B will be [tex]V-V_B[/tex], we conclude that [tex] \frac{P}{T} = nRV_A = \frac{P}{T} = mR(V-V_A) [/tex] We can solve for [tex]V_A[/tex] and [tex]V_B[/tex], right?
Your setup looks correct, except for a mathematical error... If [itex]\frac{P V}{T} = n R[/itex], then [itex]\frac{P}{T} = \cdots [/itex] ? 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.