Is this correct from a thermodynamics point of view?

Question

(Taken from Cengel's book)
Would it be feasible to try to cool a house by compressing air, letting its temperature go down, using the compressed air to power a turbine and then discharging the cold air into the house?

The compressor's power source is NOT the turbine.

Actually, the answer in the answers guide is a plain "no", but I do not understand why not.

Answer 1

Yes, the concept is used all the time, but not for cooling homes.
Even prior to 1950, early jet fighters, due to the huge compressors on the jet engines, used the waste air for cooling their cockpits.
The problem is energy efficiency.
A superficial glance would lead you to believe it would be a very environmentally friendly way of providing cooling, but the problem is the cost of compressed air.
The most efficient air compressors are expensive energy consumers.
The power stored by compressing air is best used to accomplish mechanical work. Expanding it to provide cooling by using a turbine works, but is much less energy efficient than using a mechanical refrigeration system. (Typical air conditioning system)
There are other methods being researched and under development at this time, but I have yet to see any type demonstrated that equals the efficiency of what is already in production.
I'm not saying it will NEVER be done, and I encourage research into the subject, but so far the technology is far from where it must be to replace the air conditioning systems we already produce.

Answer 2

It's possible if that's what you mean. That's how they make liquid nitrogen and liquid oxygen. Compression adds heat to most gases and expansion removes heat so if you compress a gas isoenthalpically (no change in heat) and then expand it, it will cool off. As far as feasible I wouldn't recommend it.

Answer 3

it's more efficient to open a window