Power for a blackbody radiation

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Discussion Overview

The discussion revolves around the relationship between the power emitted by a blackbody in equilibrium with its surrounding electromagnetic field and the energy density of that field, specifically focusing on the equation P=\frac{cu}{4}. Participants explore derivations of this equation and the role of temperature in blackbody radiation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant states that the power emitted by a blackbody is related to the energy density of the electromagnetic field by P=\frac{cu}{4} and seeks a derivation for this equation.
  • Another participant suggests that the power emitted would also depend on the temperature of the blackbody.
  • A participant questions the standard derivation found in textbooks, specifically referencing Reif's work, and expresses confusion over its clarity.
  • One participant affirms the clarity of Reif's derivation after reviewing it.
  • Another participant notes that as the temperature of a blackbody radiator increases, the overall radiated energy also increases.

Areas of Agreement / Disagreement

There is no clear consensus on the derivation of the equation or the clarity of existing texts. Multiple viewpoints regarding the dependence on temperature and the adequacy of standard derivations remain present.

Contextual Notes

Participants express uncertainty regarding the derivation of the equation and the clarity of standard texts, indicating potential limitations in understanding or assumptions about the derivations.

dEdt
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If a blackbody is in equilibrium with the surrounding electromagnetic field, the power emitted by the surface of the blackbody will be related to the energy density of the electromagnetic field by P=\frac{cu}{4}. Try as I might, I haven't found a good derivation for this equation (the Hyperphysics one has several problems). I thought that it shouldn't be too hard to derive, but playing with Poynting's theorem led me nowhere, so now I humbly turn to physicsforums for help.
 
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Wouldn't it also depend upon the temperature?
 
dEdt said:
Try as I might, I haven't found a good derivation for this equation (the Hyperphysics one has several problems).

What's wrong with the standard derivation in texts? See e.g. pp. 385-388 of Reif.

UltrafastPED said:
Wouldn't it also depend upon the temperature?

The usual temperature dependence of the blackbody power spectrum is contained in the expression for the energy density of the photon gas in the cavity.
 
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WannabeNewton said:
What's wrong with the standard derivation in texts? See e.g. pp. 385-388 of Reif.

I just checked Reif's book and found his derivation to be very clear. Thanks.
 
dEdt said:
I just checked Reif's book and found his derivation to be very clear. Thanks.

No problem! It's a brilliant gem of a book.
 
When the temperature of a blackbody radiator increases, the overall radiated energy increases
 

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