Air conditioner cools the air in a room with a power of 8.4*10^6J/h. Volume of the room is 62.5m^3. At first the air is at the temperature of 30C and air pressure is 1atm, which stays a constant. How long does it take to cool the room to 25C? Note that the air shrinks while cooling down and since the pressure stays constant, more air (at 30C) flows in from the outside. Treat the air as a diatomic gas. I am overwhelmed by this exercise. Normally I could make the equation (S is the integral sign) S Pdt = S nRdT (n=pV/RT), but now more air is flowing in, all the time warming the room and making the n change. How the hell does this work?