Adiabatic vs Polytropic

I might be wrong, but I would guess that compressed air is not so much involved with processing chemicals, or in thermodynamic applications where precise temperature are not important to the downstream process, such as powering drills and tools. Other gases include a wide range of uses, refrigeration being one. As well as some of those other gases may have pronounced heat transfer effects in either high or low direction that could be important to capture.

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

I suspect you are dealing with volumes of air but with small pressure rise. Essentially this is not a compressor but rather a blower (large volume air handling equipment) OR a fan (small volume air handling equipment). Because of the small pressure rise, the density difference across the equipment is almost negligible and so is the temperature rise. As such, their performance imitates that of a pump. As such, in such cases, there is no polytropic gas compression (ideal gas laws or modified version) but rather adiabetic version (no change in heat loss due to zero / negligible temperature rise.

If you've got oil flooded screw compressors, then neither will work.