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My doubt is with regards to radiation emitted by a body and how we define the rate of loss/gain of heat due to the same.

For my question, let us consider a body of: * surface area A

                                         * emissivity e
                                         
                                         * absorptivity  a
                                         
                                         * σ-stephan's constant

source:CENGAGE PHYSICS BY BM SHARMA

In the above image which clearly describes Stefan's law, I can understand that the amount of radiation emitted by any body depends on its temperature as well as the temperature of the surroundings.

i)By the same logic, would it be right to say that the radiation absorbed by the body depends primarily on the temperature of the surroundings in which it is kept?

ii)if that is the case, then this is the continuation of my next doubt

source:CENGAGE PHYSICS BY BM SHARMA

source:CENGAGE PHYSICS BY BM SHARMA

In the above image,which considers a body whose body temperature T is initially greater than the surrounding temperature Tnot begins to emit radiation and absorb some radiation. Hence there is a transfer of heat between the body and the surroundings.

ii)If we define emissive power E as

                              E(emit)= eσT^4
    

Shouldn't the absorptive power be defined as

                                  E(absorb)= aσT(not)^4

Hence ΔQ = E(emit)- E(absorb)

     =(eσT^4 - aσT(not)^4)A

as opposed to Aeσ(T^4 - T(not)*4) given in the image.

iii) Why is the absorptive power not dependent on $a$?

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1 Answer 1

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The absorptive power is dependant on $a$. However, from Kirchoff's Law we know that a good absorber is a good emitter i.e. $a=e$ which simplifies your equation into the one given.

Also see Why do dark objects radiate thermal electromagnetic energy faster than light objects?

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  • $\begingroup$ i understand that a good absorber would always be a good emitter..but..we defined these equations for a general body right..at least from the textbook's point of view $\endgroup$ Jul 17, 2022 at 11:33
  • $\begingroup$ or do we talk about these equations with reference to good emitters and absorbers? $\endgroup$ Jul 17, 2022 at 11:34
  • $\begingroup$ Not only is a good absorber a good emitter, but a bad absorber is a bad emitter as well. The point I'm trying to make is that a general body is only as good at absorbing radiation as it is at emitting radiation. $\endgroup$
    – Cathedral
    Jul 17, 2022 at 11:38
  • $\begingroup$ so the emissivity should always be equal to the absorptivity at the same temperature for all bodies. $\endgroup$ Jul 17, 2022 at 11:41
  • $\begingroup$ since that should be the only way to explain the equilibrium of different bodies kept in the same surrounding right? $\endgroup$ Jul 17, 2022 at 11:42

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