One of the ways to model a 'black body' radiator is using this technique. The point being that the energy of the photons emitted through the hole have a statistical energy distribution that matches (at least close enough for experiments) the radiation emission of a black body at a characteristic temperature. On Fri, 17 Aug 2001, Anonymous wrote:
The photon discussion a few weeks back got me reading about cavity radiation. I'm puzzled. Perhaps somebody can point me in the right direction.
For those who don't already know, cavity radiation is a surprising phenomenon which required quantum theory to model.
Actually statistical mechanics, not quite the same thing as quantum theory. But you can't talk about QT w/o SM.
Metals radiate energy in the form of light. Each metal has a characteristic "radiance" for each temperature, the amount of energy it radiates.
That should probably be the amount of energy it radiates at particular frequencies.
If a block of a metal is hollowed out and a small port is drilled to see in, the radiance of the cavity is substantially higher than that of the surface of the metal. As if that weren't shocking enough, it turns out that the radiance of cavities is the same no matter what kind of metal is used. (This is so counterintuitive that I almost don't believe it!)
My book suggests that this is intuitively sound because if cavity radiation had different values, a violation of the second law of thermodynamics would occur.
Set up two cavity radiators of a metal X and a different metal Y like so:
XXXXXXXXXXXXXXXXXXXX YYYYYYYYYYYYYYYYYYYY XXXXXXXXXXXXXXXXXXXX YYYYYYYYYYYYYYYYYYYY XXXXXXXXXXXXXX XXX YYY YYYYYYYYYYYYYY XXXXXXXXXXXX XX YY YYYYYYYYYYYY XXXXXXXXXXX YYYYYYYYYYY XXXXXXXXXXXX XX YY YYYYYYYYYYYY XXXXXXXXXXXXXX XXX YYY YYYYYYYYYYYYYY XXXXXXXXXXXXXXXXXXXX YYYYYYYYYYYYYYYYYYYY XXXXXXXXXXXXXXXXXXXX YYYYYYYYYYYYYYYYYYYY
If X and Y have the same temperature and Y has a higher level of cavity radiation, then X will get hotter and Y will get cooler. In other words, you would have a perpetual motion machine. So the radiance of each cavity must be the same.
Actually not, as Y cools its emissions drop (looking at your example in reverse). At some point X becomes hotter than Y and the net travel of photons goes the other way. It's worth remembering that what is actually happening is that both bodies are emitting radiation continouly, only the statistical 'average' of the results model this 'one way' flow. Eventually they'll reach a point where the average energy emitted by one, and absorbed by the other, equals. From that point both objects will emit radiation into their surroundings and both will cool until that exchange balances.
So far so good, but this argument should also apply to surface radiance, which we know to be different:
XXXXXXXXXXXXXXXXXXXX YYYYYYYYYYYYYYYYYYYY XXXXXXXXXXXXXXXXXXXX YYYYYYYYYYYYYYYYYYYY XXXXXXXXXXXXXXXXXXXX YYYYYYYYYYYYYYYYYYYY XXXXXXXXXXXXXXXXXXXX YYYYYYYYYYYYYYYYYYYY XXXXXXXXXXXXXXXXXXXX YYYYYYYYYYYYYYYYYYYY XXXXXXXXXXXXXXXXXXXX YYYYYYYYYYYYYYYYYYYY XXXXXXXXXXXXXXXXXXXX YYYYYYYYYYYYYYYYYYYY XXXXXXXXXXXXXXXXXXXX YYYYYYYYYYYYYYYYYYYY XXXXXXXXXXXXXXXXXXXX YYYYYYYYYYYYYYYYYYYY
If Y has a higher level of surface radiance than X, then one would expect X to grow hotter, also making possible a perpetual motion machine.
Clearly, something went wrong somewhere. Can anybody clue me in?
The flat radiation of the surface isn't the same as with the hollow spheres. For the hollow spheres the greatest part of the radiation is re-absorbed by the relevant body (and re-emitted, and re-absorbed, ...). This re-adsorption is what leads to the black body behaviour. It acts as an averaging mechanism. The plates just emit into space and the majority of radiation is lost, not reabsorbed. -- ____________________________________________________________________ natsugusa ya...tsuwamonodomo ga...yume no ato summer grass...those mighty warriors'...dream-tracks Matsuo Basho The Armadillo Group ,::////;::-. James Choate Austin, Tx /:'///// ``::>/|/ ravage@ssz.com www.ssz.com .', |||| `/( e\ 512-451-7087 -====~~mm-'`-```-mm --'- --------------------------------------------------------------------