I read this what-if XKCD article recently: (Fire from Moonlight) http://what-if.xkcd.com/145/ ..so here's a nice little brain-teaser about radiating bodies in thermal equilibrium! Let's say you have a large, perfectly reflecting elliptical cavity (a prolate ellipsoid). At one focus, you place a golf-ball sized blackbody (ball A) that's at 2000 Kelvin, and at the other focus, you place another golf ball blackbody (ball B) at the same temperature (2000 Kelvin). You seal up the cavity, and let it come to equilibrium. At equilibrium, it makes sense that both balls will have equal temperature (i.e., the same temperatures they started with). The power absorbed and emitted by each ball will be identical, However, the challenge comes from the case where ball B is made smaller, say, a marble-sized blackbody. With the elliptical geometry of the cavity, and the spherical geometry of balls A and B, it seems that all light emitted by A, would be absorbed by B, being a blackbody and all. However, the power emitted by a blackbody per unit surface area is proportional to the fourth power of its temperature (the Stefan-Boltzmann law). What this would mean, is that at thermal equilibrium, the marble blackbody would have to have a higher temperature than the golf-ball blackbody, on account of its smaller surface area absorbing the same amount of radiation. The second law of Thermodynamics forbids heat from flowing from cold to hot without extra work. The question is, how are we to understand Balls A and B, remaining at the same temperature given their geometries, and the shape of the elliptical cavity?