Three plates are in thermal equilibrium. The left and right plates are blackbodies and emit only toward the center. The center plate emits in both directions, and any radiation not absorbed from the blackbody plates is transmitted through the center plate (thus no reflection). Show that the emissivity and absorptivity of the center plate must be equal to one another and that the temperatures of all the plates are equal.

Three plates are in thermal equilibrium. The left and right plates are blackbodies and emit only toward the center. The center plate emits in both directions, and any radiation not absorbed from the blackbody plates is transmitted through the center plate (thus no reflection). Show that the emissivity and absorptivity of the center plate must be equal to one another and that the temperatures of all the plates are equal.

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