In the proof that I have studied, there is a Isothermal cavity that behaves as a black body. there is another small opaque body inside the cavity at the same temperature with emissivity e, absorptivity a and area s. now the irradiation on the small body is Eb = σ times T raised to 4. now the small body absorbs "a" times Eb. And emissive power is e times Eb. Then by conservation of energy we have a*Eb= e* Eb. therefore a = e. What i havent understood is that since the cavity emits Eb watts per unit area, shouldnt we multiply it by the internal area of the cavity to get energy flow in watts and then equate it with the emissive power of the small body also multiplied by its own area. This way we will be equating the rates of energy streaming rather than the radiation fluxes as has been done in the proof. But since the areas of the small body and the internal area of the cavity are obviously not equal, will a not be equal to e then?