Why do I get cold when I get out of the pool?

Sonny boy is taking swimming lessons again. His lips turn purple when he gets out of the pool, and he is sometimes unable to stop shivering. So, yesterday, he asked me "why do I get cold when I get out of the pool?"

Good question.

First of all, as you all know that water on your skin is evaporated away into the dry air. For water to change phase from liquid to gas requires input of energy (this is called the latent heat of vaporization). If your body is covered in water and the vapor pressure of water in the atmosphere is low enough, the water will want to evaporate. The evaporation requires heat input. The film of water on your body draws that heat from...your body, primarily. The air is, of course, another source, but most of the heat required to change the water to gas comes from your body.

Water has a latent of vaporization of 2441 kJ/kg at 25 degrees Celsius (by the way, centigrade is a meaningless term. There are no degrees centigrade.).

Let's say that a 6-year-old with a height of about 137 cm (4.5 feet for you weirdos) and a weight of about 25 kg (55 pounds...) has a volume of about 25 liters (average human density is about 1010 kg/m^3). Now, as all good physicists do, let's approximate this 6-year-old as a sphere with a volume of 25 liters. That gives us a surface area of .4 m^2 and a radius of 18 cm. Let's assume that there is a 1 mm layer of water on this spherical child. That's a volume of 409 milliliters or .409 kg.

It takes approximately 1000 joules to cause the phase change of this water. A completely unmeasured guess at how quickly Sonny lost heat is that he was shivering within a few seconds of exiting the pool. He had more than 1 mm of water on him, most of which was dried off with a towel. So, let's say he lost about 1000 joules in about 30 seconds. That's about 120kJ joules per hour.

This article talks about heat loss in sedentary people at various temperatures. The average heat loss due to evaporation was about 62 kJ/m^2/hour. Corrected for Son's surface area of 0.4 m^2, we get 300 kJ/m^2/hour, or about five times the sedentary rate of cooling.

You are more likely to lose body temperature (due to evaporation) in a warm, dry place such as AZ than in a cool, wet place like WA. The relative humidity in Flagstaff, AZ in June in the morning is 54% and 21% in the afternoon, but is 83% and 53%, respectively in Seattle. This is why it's easier to get heat exhaustion from 80 degree temperatures in Atlanta (84% and 56% in June) than from 110 degrees in Tucson, AZ (32% and 13% in June); your sweat isn't as effective at removing heat from your body because it's more difficult for it to evaporate.

Wind will cause what's called "forced convection" in which heat is whisked away by the movement of the air around your body (it's more complicated, but that's for another day, perhaps).

So, is there any way to stop kiddo from having purple lips and looking like a goth at 6? Not really. If the pool area had higher humidity, that would slow the evaporation, but people would probably complain about it. Similarly for keeping the pool area warmer (this would allow more heat to come from the air rather than the body). The best way is to dry the kid off as quickly as possible.