Air Flow and Heating

I work in the HVAC industry.We make a piece of equipment which is basically a fan that draws in cold outside air and forces it into a duct.The duct is open on the other end.Inside the duct, just downstream of the fan is a heater.Sometimes the heater is on (winter time), and sometimes off (summer time).The question is, when the heater is on, is the airflow (CFM) after the heater, greater than the airflow before the heater?My first thought is, it should be greater, due to the ideal gas law - air expands when heated.But then, maybe due to the pressure drop across the heater, the ideal gas law doesn't apply.If you could point me to the laws of physics that apply, it would be appreciated.Thank you.
- Bruce Standerwick (age 64)
Cedar Hill, TX. USA

All your thoughts are very reasonable.  You know that since air isn't building up in the duct, the total flow of molecules is the same before and after the fan. If that flow is epressed in terms of volume, e.g. as CFM, however, it depends inversely on the density of the air. So using pV=NkT, we get that V=kN(T/p). N per minute is fixed. The question is how big the relative changes in T and p are. So you need  p_outsideT_inside/p_insideT_outside , where you express T as an absolute temperature, e.g. Kelvin. For example, you usually have T_inside = 295 K or so. On a typical cold Texas day you might have T_outside=275 K. That's about a 7% increase going in. If I had to guess, the pressure difference across the fan (again, absolute pressure, not difference from room pressure) wouldn't be as big as 7%, but you could check with a pressure gauge. If my guess is right, the density would be lower on the inside so the volume flow on the inside would be a little bigger.

Mike W.

(published on 01/31/2015)