Heat Management vs. Color

Question: You are in a room, windows open but no sunlight coming in the 
windows.  The air temperature out and inside is say 103F, you are concerned 
about feeling too warm.  Using some physics, you decide that the color of you 
t-shirt will help you "cool" off which is the correct answer?  A) White 
because it will reflect IR from your warm surroundingskeeping you cooler or B) 
Black because you would then be a black body radiator able to lose heat at the 
fastest rate I opt for B, but another physics teacher in my county says A?  
Which is right?
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Why do Arabs were black robes in the desert?  A white-colored 
object reaches a higher equilibrium temperature than a black one.  On the 
other hand, why are all astronomical observatory domes painted flat white?  I 
assume because flat white is almost as good as flat black for being a good 
black-body radiator AND it absorbs heat much more slowly.  So, if you are 
going to be in the Sahara all day, do you wear black robes or white ones?

John Hawley
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With no sun coming in the windows, your ability to reflect 
radiant heat is immaterial.  Black body radiation does not have anything to do 
with the color of the object.  The answer is that the color of your shirt will 
not have any affect on your temperature.  Take the shirt off and fan yourself 
with it, because evaporation of your sweat is the only way your 98 degree body 
is going to cool down in a 103 degree room.
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First of all, heat is generally transferred by 3 mechanisms:  
convection, conduction, and radiation.  Convection is the actual motion of hot 
things (air etc.) into cooler places, conduction is a microscopic transfer of 
heat from particle to particle so it gradually diffuses to cold areas (not so 
gradually for solid materials) and finally radiation, which seems to be the 
main topic of this question, is the generation of electromagnetic waves by a 
hot body, to be absorbed by cooler bodies.  Now, there is an additional 
complication when you talk about a living person - the person is actually 
generating heat (otherwise the person is dead).  To put the question in its 
simplest form then, imagine a corpse in a vacuum-filled container (to prevent 
conduction and convection effects) with a window to the outside world.  The 
container and world are at 103 degrees, the corpse at something cooler, 
initially (the vacuum does not have any meaningful temperature in this 
example).  We know, thermodynamically, that eventually the corpse will reach 
the surrounding 103 degrees (two objects in equilibrium are at the same 
temperature).  The only meaningful question to pose is, what color T-shirt 
should the corpse be wearing, to stay cool for as long as possible?  Now, the 
spectrum of radiation from a body is always peaked at an energy that is 
roughly the same as the temperature multiplied by Boltzmann's constant.  The 
sun, at 5000 degrees, has a peak around 0.5 eV, or slightly below the visible 
region.  That is why the color of a shirt makes a difference when you are 
absorbing light from the sun - a black shirt does absorb in this region, a 
white shirt presumably does not absorb as much.  But when we talk about 
radiation from bodies at 103 degrees Fahrenheit, or about 300 absolute degrees 
(Kelvin), the peak in the spectrum of radiation is down by a factor of 10-20. 

You cannot tell by looking at an object just how well it will absorb radiation 
in that region - it is way outside the visible.  Shiny metallic things 
generally do not absorb anything very much at long wavelengths though, so you 
can at least count on those being good reflectors.  So the answer to the 
question as rephrased in the preceding response is that neither the black T-
shirt nor the white T-shirt can be counted on to keep the corpse cool for 
long, but a shiny metal T- shirt would probably do the job as well as it could 
be done.

A. Smith
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