## Monday, May 17, 2010

### Ask a Physicist: Volume I

We have received our first Ask a Physicist e-query! An entity known only to us as "Hungry" writes:

"We had a dispute at a dinner party about whether blowing on hot food actually makes it cool down faster, or only gives you something to do while you wait for your food to cool."

While it is questionable whether or not I am indeed a physicist (but people do pay me to do physics) and whether I will answer definitively (there'll be some hand-waving), I'll give it my darndest.

Let's imagine a hot baked potato you just sliced open. The mass of potato is capable of transferring energy as heat to the surrounding air (and therefore cooling down) via a number of mechanisms. The most common we hear about are conduction, radiation, and convection. Conduction is the process by which two objects in intimate contact exchange heat. Radiation is a bit more mysterious, but in the same way that a poker in the fire can glow white hot, all things at non-zero temperature emit electromagnetic radiation, which carries away energy from your potato.

Convection is even more complicated, but is one of the most important processes by which solids exchange heat with gases. Convection in our case occurs when the potato heats up the gas at its surface. The random motion of air molecules (now a little hotter) will "randomly" dissipate heat. However, the hotter gas is less dense than the room temperature gas, and buoyant forces (think Helium balloon) will create a current of hot gas upwards from the potato surface. Both of these processes constitute convection.

Convection is REALLY hard to describe with physical models. You can do some computer simulations of the motion of the gas in convection. I found this cool picture on Wikipedia of someone who did just that:

Pretty cool. Now! To actually answer your question. To get a qualitative answer, we don't even need to consider models of convection, etc. Isaac Newton was kind enough to find an empirical relation for the process of cooling, aptly named "Newton's law of cooling". If we call the amount of heat transferred from the potato Q, the found that the rate of heat being lost by the potato is proportional to the temperature difference between the surrounding gas and the potato itself:

$\text{Rate of Heat Loss}=\frac{\text{Amount of Heat Loss}}{\text{Amount of time}}=\frac{\Delta Q}{\Delta t} \propto T_{\text{Potato}}-T_{\text{Air }}$

So the quantity which is of primary importance is the temperature difference between your potato and the surrounding air.  Now we can answer the question.  If you let your potato cool down naturally, then the potato heats the air which then starts to convect.  This means that the air immediately above the potato is quite hot.  If you blow on the potato, however, you get the air circulating faster than it would by convection alone, effectively replacing the hot air with slightly cooler air.  And since the cooling rate is proportional to to temperature difference; this will result in a faster cooling rate.  To first order, blowing on your food should help.

So, Hungry,  feel free to blow on your food, Miss Manners be damned.

1. But what if the temperature of your breath is a lot higher than the average temperature of the room? I would guess that one's breath is warmer than the temp in most rooms but not enough to tip the balance but in a very, very cold room ...

2. Actually, the temperature of your breath shouldn't make much of a difference. For the sake of argument, take your breath to be the same temperature as the inside of your mouth. Now, if we start out with hot food, we probably want it to feel warm when we put it in our mouths. this means that the food is warmer than our mouths.

Suppose that the air right around our hot object is at the same temperature as the object. Then, as we want the object to remain warmer than our breath, blowing on it will always result in replacing that hot layer with a cooler layer, speeding cooling as discussed above. Now, since our breath is probably warmer than the room, a fan might do a better job than a you blowing on it, but I for one don't want to carry a fan everywhere with me just in case my food is too hot!

Finally, try blowing on your hand. If you puckered up to do so, your breath probably felt cool. I think this is an example of an adiabatic expansion cooling, as I discussed recently. Your breath may be cooler than you think!

3. Cooling rate is proportional not only to the temperature of the flow, but also to the velocity of the flow doing the convection, it scales linearly. So the harder you blow on the potato the faster it will cool.

Additionally keep in mind that flow mixing occurs when your breath leaves your body, that is air from the room gets carried along by the momentum of the air so the air gets much cooler the farther away it gets from your mouth.