Alexander P. Kirk
A hybrid ellipsoidal-spherical cavity — with a perfectly reflecting wall — that contains two identical temperature black bodies located at the foci of the ellipsoid has been claimed to represent a potential paradox in thermodynamics. The assumption has historically been that absorption in the black body that is located at the focal point of the ellipsoid that has been partially modified into a sphere exceeds absorption in the black body located at the other focal point of the unmodified portion of the ellipsoid. If the absorption was actually unbalanced, then it would appear that the black body partially surrounded by the sphere would become hotter than the other black body, an apparent violation of the second law of thermodynamics for a system that should be in thermal equilibrium. It is shown that the ellipsoid paradox in thermodynamics may be resolved through application of Kirchhoffs law of thermal radiation.