poor application of the gas law. There is no reason to treat the situation as adiabatic. Theoretical assumptions are important!

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.