To elaborate on the other comment, the ideal gas law isn't applicable when you can add or remove energy/mass to the system. There's no reason you can't pack a refrigerator sized chamber with enough air to be high pressure at a low temperature. Based on the equation, you get to choose what n is so you if you set T to a normal refrigerator temp of ~4C then you can vary n to get whatever P you want. I hope that made sense.
poor application of the gas law.
There is no reason to treat the situation as adiabatic.
Theoretical assumptions are important!