# Why aren't there any air conditioning systems that compress, cool, then expand air directly?

I realize there would not be any phase change in this system, but as long as the compressed air get hot enough above the outside ambient temp it seems like you could extract heat (and even some humidity) from it. In some cases couldn't this end up being more practical than using a refrigerant and then needing a heat exchanger to indirectly cool the air?

Why does it seem to never be used?

If you look at Freon, which is a common refrigerant, then the specific heat of the vapour is around $0.6$ kJ/kg/K while the latent heat of vaporisation is around 160 kJ/kg.