An adiabatic isolated system is formed of three identical balloons (of unknown volume). The balloons are joined by tubes of negligible volume. Each tube has a faucet/tap that is initially closed. The balloons have different quantities of the same ideal gas.
After opening only faucet R1, the system including balloons B and A reaches a state of equilibrium that has pressure p1 and temperature T1.
After opening only faucet R2, the system including balloons A and C reaches a state of equilibrium that has pressure p2 and temperature T2.
After opening only faucet R3, the system including balloons C and B reaches a state of equilibrium that has pressure p3 and temperature T3.
Find the initial pressure of the gas in each balloon (pA, pB and pC).
Also, the book that I'm using has the following results at the end:
PVγ = constant (adiabatic process)
The Attempt at a Solution
I tried to apply PV=nRT, but nothing that I did so far worked. I will edit the post if I have any ideas.