| MadSci Network: Physics |
So, if I understand the question correctly, you are stuck in a giant meat freezer. The lights are broken, so it's completely dark inside, but the refrigerating equipment is functioning, so it's very cold. Will you last longer if you are dressed in dark clothes, or in light clothes?
The real difference between clothes of different colors will be subtle -- a matter of seconds, and overwhelmed by other factors (such as "are you sitting or walking?" or "do you keep your mouth opened or closed?" or "are you wearing a hat?"). Still, let's pretend that this is the one critical factor, and see which way it goes.
Let's start with a limiting case: no clothes. You are naked, trapped in a dark freezer. What happens? Obviously, you freeze. But what does that mean? It means that your body starts out much warmer (about 37 degrees Celsius) than the surroundings (about -5 Celsius). Your body radiates energy -- heat -- away into space. The walls of the freezer are also radiating energy towards you. But because your body is warmer, it radiates away more energy than it receives from the walls. You can look up the relationship between temperature of an object and the amount of radiation it emits per unit area in a textbook. So, you radiate away more energy than you receive; therefore, the total heat energy in your body decreases. In other words, you grow cold.
Now, your body could try to replace that heat in several ways: it could metabolize fatty molecules stored in under your skin; it could shiver, contracting mucles rapidly and repeatedly to generate heat. You could also jump around, swing your arms, and move your muscles voluntarily, again turning some of the energy stored in your cells into heat. But eventually, your body temperature would drop so low -- around 5 or 10 degree Celsius below the normal value -- that you would die. Sob.
Now, let's start over, and this time, give you some clothes. Once again, you are trapped in a dark freezer. Your body radiates energy, again, but this time, it does not travel unimpeded into the air and reach the cold, cold walls. Instead, it bumps into your clothes. Three things can happen to the infrared radiation: first, it can pass through the clothes. Let's ignore this possibility by saying that you have a thick enough layer of material to prevent it. Second, the energy can be absorbed by the clothing. Third, the energy can be reflected off the material so that it bounces back at your skin.
If the energy is absorbed by the cloth, then the inside surface of the cloth becomes a bit warmer. It will never reach the temperature of your skin, but it can come close to it. The outer surface of the clothing, on the other hand, does radiate away its heat energy to the cold, cold air and walls. Because there's a temperature difference between the inner and outer surfaces of the clothing, heat is transferred outwards. The thicker the clothing, the more slowly heat travels through the material; and, therefore, the more slowly heat leaves your own body. Clothes can give you more time inside the freezer before you freeze. In fact, if you wear enough clothing, you can reduce the rate of heat loss to a level which is smaller than the rate at which heat is generated inside your body by your metabolism. So, with thick enough clothes, and with big supply of food, you could live inside the freezer for quite a long time -- long enough for someone to rescue you.
"But the color," you say, "what does the color have to do with it?" Okay, go back to the third possibility for the radiation when it strikes your clothes: it may be reflected back onto your skin. This is exactly what you want to happen. If the energy leaving your body is reflected back towards your body, then the chances are good that it will be re-absorbed by your skin. If every single photon of radiation which left your skin bounced off the inner layer of your clothing and came back to be absorbed, then the rate at which heat radiated away from your skin would equal the rate at which heat was absorbed by your skin .... and the net flow of heat would be zero. You wouldn't lose any heat at all, and you would feel warm and toasty.
So, in a simplified world in which clothing surrounded your skin without ever touching it, so that the only means by which energy could leave your skin was radiation, then you'd want your clothes to have as reflective an inner layer as possible. That would provide the maximum reflecting of radiation, and so the minimum flow of energy outwards.
Moreover, consider the energy which was absorbed by your the inner layer of your clothes. It would reach the outer layer of the material eventually, and then would radiate away towards the cold, cold walls. That's bad news for you, since the faster the outer layer radiates away energy, the faster you'll freeze. You would like the outer layer to radiate away as little energy as possible. It turns out that the color of the material does affect its ability to radiate away heat. It turns out that one particular color is the most efficient at radiating energy (bad), and a different color is the least efficient at radiating energy (good).
You should now be able to answer your question.
[note added by MadSci Admin: The visible color of the cloth does not necessarily
relate in any way to the "color" that would be "seen" by somebody who could "see" the radiation at
"thermal" temperatures (temperatures at or near "room" temperature), which is near 10 microns
(micrometers) (thermal infrared) and is much
different than visible radiation (which is between 0.4 and 0.7 microns, more or less). At the
wavelengths associated with thermal radiation it is the texture and/or surface properties
of the material that are
most important. However, as the answerer (Michael) has said, there will be differences
in the way materials radiate even the thermal infrared wavelengths, and one could assign "color" to
those differences even though our eyes can not see the thermal infrared differences.]
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