IMO You should either contain the chilled air or vent out non-chilled. One method of keeping the room at 80 degrees or so is to just pump all the heat out. That is what police are looking for with infrared technology though. If you use AC just contain it. You can recirculate your air in a closed loop and scrub it for smells with various methods.
Air-Cooled Hoods with the lenses on them, with ducting going threw them and out the room. Thus lights are constantly getting the heat moved away, while the A/C also cools the room/plants.
Rescrubbing carbon filter in the room.
To answer your question directly: Could someone explain how an air conditioner can work when you are contstantly exhausting air from the grow room?
When you are constantly exhausting air out of a room, there is always air that is being pulled into that same area from somewhere or another, via something called negative pressure. So introducing an A/C helps with the flow or air in your growing space, which is what you want.
Yes, using an air-cooled hood and venting the exhaust does help to reduce the heat in a grow room. Of course when it's in the 90's F outside, I don't care how much venting is performed, it's still going to be hot in the grow room. It's on those days I break out the AC unit. It's one of those 10k BTU jobs that sits on the floor, with an exhaust hose that goes to a window vent (light sealed, of course). I know I'm pumping some of that expensive cool air through the lights and right outside, but I chalk it up as the cost of doing a grow. It keeps the room plenty cool enough to ensure good growth by the girls.
As for the room exhaust, I have it pumping into my attic. I always figured it was plenty hot up there just from the sun beating down on the roof all day. The exhaust air is actually cooler than the normal attic temperature. Yes, my attic reeks but no smell is noticed outside. Besides, I don't have neighbors very close so I just don't worry about the smell.
G-Dogn - Thanks for the link to the FLIR video. I hadn't seen that before and found it interesting.
If your room is closed off with an ac you still need to exchange the air with an outake fan every now and then cause an ac just recirc's your air in the room and you need to exchange the air to renew the co2 in the room.