Physicspunks

[Anonymous]

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.  Metals radiate
energy in the form of light.  Each metal has a characteristic
"radiance" for each temperature, the amount of energy it radiates.

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.

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?