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In Concepts of Physics part-2 by H.C.-Verma, it is written on page 87 right under section 28.10 :

"The energy of thermal radiation emitted per unit time by a black body of surface Area is given by: $$ U =\sigma AT^4.$$

...now the accepted answer in this stack post by Daniel Sank says that the above equation describes thermal power emitted by the body rather than thermal radiation and so does Wikipedia for that matter. I think that thermal radiation and thermal power are different, so, is HC-Verma wrong here?

My understanding: Thermal power means heat after considering all the heat emitting mechanisms whilst thermal radiation is just the heat emittance due to radiation.

tryst with freedom
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    An energy emitted per unit time is a power – Hadrien Oct 06 '20 at 07:09
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    General tip: Since 'accept' status may in principle change, it is not recommended to refer to 'the accepted answer'. – Qmechanic Oct 06 '20 at 08:07
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    Check this out: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html Note that this site refers to the radiant power as "net radiated power" when the equation includes a cold body temperature. – Bob D Oct 06 '20 at 13:15
  • Where does wikipedia describe it as "thermal power" without being clear it's talking particularly about radiation? – JMac Oct 07 '20 at 19:03
  • I had misunderstood that point and I had explicitly mentioned it when I wrote my answer. – tryst with freedom Oct 07 '20 at 19:05

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Thermal radiation is a way of energy transfer. The power of that radiation -- the energy carried by the radiation per unit time -- is given by the expression you quoted in your question.

Yejus
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Generally speaking, thermal power includes all three forms of heat transfer. However, In the reference stack which I had posted in the question, it is used to mean about radiation transfers. Hence thermal power and thermal radiation is equivalent in this context. It can be found in this paper that Stefan's law is regarding radiation and holds even for non equilibrium states.

tryst with freedom
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This is all a matter of language confusion. Thermal radiation is a phenomenon. The energy or power of thermal radiation are quantities used to describe the phenomenon quantitatively. You can see that your book is careful to say "energy of the thermal radiation" and not just thermal radiation when refers to that formula. So thermal radiation has no formula. The quantities associated with it do. You don't have formulas for wind but you may have for pressure or velocity associated with wind.

nasu
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