Surface area dependence of radiative heat transfer

[Karthiksrao]

Hi all

I was just wondering about the dependence of radiative transfer from a body, on its surface area and not the volume. As per stefan's law, the variation is (StefanConstant * SurfaceArea* Temp^4)

The primary source of these electromagnetic radiation is from the charges in the body that are vibrating at a particular temperature. And the amount of charge would obviously depend on the volume of the body. Higher the volume, you would expect more charges to be vibrating, and hence higher would be the emitted radiation.

If that be the case, why is the net radiative transfer dependent on the surface area of the body and not the volume ?

Any thoughts ?
Thanks a lot!

 

[xts]

Stefan's law is an approximation of 'ideal black body' - the body having so large amount of various vibrating charges, that very thin (infinitesimaly thin) layer of that body emits all that radiation, but, at the same time, it absorbs radiation emitted from deeper layers.

If you take not so perfectly black body - then you'll have some emission coming from deeper parts of the body, as the surface layer is not able to absorb all the light from deeper layers. But, on the other hand, every layer also emits less. Effectively, those effect cancel, so black body idealisation may be used as an approximation.