Why Does A Fan Cool The Air?

[jwferk]

This one was put to me by a colleague who used to be a high energy particle physicist (he's now a biophyicist).  He doesn't have the answer and neither do I.

 

1 - I'm sitting in a room that is 80oF;

2 - the outside air temperature is 70oF;

3 - I want to cool the room;

4 - I put a fan in the window and turn it on;

5 - the airflow is directed into the room;

6 - the fan starts blowing 70oF air into the room.

 

Simple enough.  However, remember that temperature is actually a measure of molecule motion.  The air being blown into the room by the fan is moving much much faster than the air outside the room or the air inside the room.  If temperature is a measure of molecular motion, I should be blowing very hot air into the room because I accelerated the gas molecules by turning on the fan.

 

So - why does the room get cooler?

 

Cheers,

jwf

 

(and this has nothing to do with the evaporation of moisture from my skin to yield a reduction in body heat).

[sanctus]

In my understanding, temperature is the random motion of the the particles wrt each other. If you have a fan, you kind of keep this random motion constant just adding an overall vector.
You can see it this way, if the overall motion of molecules would correspond to temperature (or just affect it) then a hurricane would start fires :-).

[CraigD]

If, as you describe, the temperature inside the room is greater than outside it, the fan arrangement you describe cools the room simply because, in addition to the 70 F air being blown into the room, the 80 F air is blown out. Assuming the volume of air moved is great enough, the room air temperature will eventually approach 70 F.

 

The air being blown into the room by the fan is moving much much faster than the air outside the room or the air inside the room. If temperature is a measure of molecular motion, I should be blowing very hot air into the room because I accelerated the gas molecules by turning on the fan.

The fault in this reasoning is that it doesn’t consider the actual speeds involved.

 

The average speed v of the molecules in room-temperature (23 C) air is about 500 m/s. Temperature T is related to speed by the formula T = k v². A typical fan produces about a 10 m/s wind speed v_fan. Since the fan move the air in roughly a single direction, the increased temperature from it will be roughly T = k/2 ((v+v_fan)² (v-v_fan)²). By this calculation, you can see that the fan increases the temperature of the air by about 0.04%, about 0.1 C. (see this hyperphysics page for details)

 

Now we need to consider that what we're usually less interested in air temperature than we are in the cooling effect of the air on our bodies and other objects. Calculating this effect is complicated, but a rough way is to use a standard wind chill formula. From one of these, we can find that the wind chill indexed difference between still room temperature air and 10 m/s air is about -4 C.

 

In short, fans don’t cool air, they air-cool the things they blow air on.

[HydrogenBond]

The reason the room feels cooler is the movement of air, because of the fan, causes water or sweat to evaporate faster from the skin.The extra evaporation absorbs more energy; heat of vaporization, cooling the surface of the skin. This process has to do with the convection of the air, allowing more mass and heat transfer away from the skin. 

 

A cooling sack uses this principle. The cooling sack is a leather pouch that contains water. It is slightly permeable, so water passes through the leather skin, at a slow rate and evaporates at the surface. In hot dry desert environments, the rate of surface evaporation from the pouch absorbs heat and allows the inside water to be 70 F even with 100 F outside, for a cool drink of water in the desert heat.