Bleed Air Heater Therodynamics
It goes like this....
Compressor draws in outside air.
Compressed (high pressure) air warms up.
Bleed valve allows hot/high pressure air into cabin.
Hot/high pressure air is released, returning to atmospheric pressure in cabin, thus cooling down....
So, why is the air hotter than when it started its journey if it has returned to its original pressure? Mechanical friction?
Hovering