# Stefan Boltzmann law and absorptivity

I have this really big confusion , and it is about the Stefan Boltzmann law

Does this law works for absorption? Or is it only radiation

I have seen my textbook replacing emissivity with absorptivity to find the rate at which energy is absorbed. However I don’t see any correlation This equation caused the trouble(equation to din the net radiation rate ). [Also Assumption a=e, a is the absorptivity ] $$dq/dt=eA\sigma(T1^4-T2^4)$$

(Also a proof will be really helpful)

## 1 Answer

Yes, the Stefan Boltzmann law will tell you how much heat a blackbody will absorb from another blackbody.

Your equation is giving the net heat flowing from body 1 to body 2.

To break it apart a little and relate this to absorption.

Body 1 is emitting $$e A \sigma T_1^4$$ to body 2 and absorbing $$e A \sigma T_2^4$$ from body 2. Hence the net heat flow body 1 emits is the difference between these fluxes $$e A \sigma T_1^4 - e A \sigma T_2^4 = e A \sigma \left( T_1^4 - T_2^4 \right)$$ which is the equation you stated.

Regarding the absorption aspect of you question.

The main axiom regarding a blackbody is that it is a perfect absorber. So any radiation falling on it is absorbed and contributes to raising the temperature of the blackbody.

In your example, you are considering a blackbody with an emissivity/absorptivity. This is the factor of incident radiation which is absorbed, via Kirchoff’s law, it also reduces the emission rate of the body. Sometimes a non-ideal blackbody is called a grey body.

• How did u find the rate of absorption
– user287374
Commented Mar 30, 2021 at 1:37
• My question is how do we calculate rate of absorption from Stefan Boltzmannl aw
– user287374
Commented Mar 30, 2021 at 1:48
• @boyfarell cuz all my books tend to use this equation to find the radiation absorbed but I don’t see any reason why it is supposed to work
– user287374
Commented Mar 30, 2021 at 1:49
• I understand that the net heat flow is emission - absorption but how did u find the absorption
– user287374
Commented Mar 30, 2021 at 1:58
• That’s the main axiom regarding a blackbody; any radiation hitting it is absorbed. In this case, the body is not perfect but absorbs a fraction proportional to its emissivity/absorptivity. Commented Mar 30, 2021 at 5:59