The question that started the discussion is will the compressor turn on---my answer was yes. Next question was will it the compressor come on while spraying---my answer was about every 4 minutes.
Boyle's Law you posted proves this out. You are missing one key thing about this entire topic and the equipment. This will occur in some way across some variable of time depending on the tank volume of the compressor on every compressor I have seen, serviced and know of. Someday you'll have that epiphany, followed by a forehead slap.
As you can see, I made sure the air hose was connected while the compressor was filling. By connecting the hose from the start it added a slight additional volume to the compressor and did not take away from the volume if I connected it after the compressor had shut off. I made sure the fluid hose valve was closed to not affect/increase the volume of the tank.
You will see the fluid line being purged, and the volume of fluid (in this case water, about 1 US gallon) that was displaced from the tank before the compressor turned back on. The gun is a T-70 with an 0.8mm nozzle/needle set and air cap, this is the smallest set available for the gun. I had finished spraying a piece earlier so the gun is set where it was when I sprayed the piece.
Again, I don't edit my videos you see this in real time as it happened.
My Jc10 is set 125 psi off (factory is 115 I believe)--95 psi on.
If the pot was full of fluid the compressor would not have turned on initially, but soon after beginning spraying.
Tom