>air must be compressed quickly enough so it doesn't heat up The heating is inherent to the compression. Adiabatic means something else. To make air based ref

>air must be compressed quickly enough so it doesn't heat up The heating is inherent to the compression. Adiabatic means something else. To make air based refrigeration work, you would have to compress the air and transfer the extra heat somewhere else. Then you would get cooling when you let the air expand again. ... which is all still moot as the air would not be compressed enough to matter in this case.