Radiation by a transparent body We know that the rate of radiation is proportional to the surface area offthe emitting body. However, this is true for an opaque body.
When considering a transparent body, will the radiation still be proportional to the surface area? Or, will it be proportional to the volume of the body which seems more likely to me?
(I am assuming that the material is ideally transparent to all wavelengths)
Also, taking it a bit further say if a (transparent) sphere having sphereicaly symmetric temperature distribution maintained constantly by some hypothetical arrangement how should the amount of radiation emitted be calculated?
 A: A perfectly transparent sphere will not emit any electromagnetic radiation (this could happen if we consider a blob of cold dark matter, for example). 
However, there are cases like optically thin plasmas where radiation is released and each photon unlikely to be captured by another particle before it escapes. In particular, there is thermal Bremsstrahlung where free electrons and ions in a plasma will radiate energy like $P_{br} \propto n_e n_i \sqrt{T}$ where $n_e,n_i$ is the number density of electrons and ions. The total emissions will be proportional to the volume rather than the surface area as long as the density is low enough that there is not too much self-absorption; as density increases the spectrum becomes more blackbody-like. 
If the sphere is maintained at constant temperature the best way of estimating the radiation is to measure how much energy is being put into the sphere per unit of time to maintain the disequilibrium. In more realistic cases like astrophysicists looking at intergalactic plasmas they use the shape of the spectrum to estimate parameters like temperature and density and then estimate the total power from that. 
