This is a continuation of the previous post Two Proofs of Planck’s Law vs Backradiation with a clarification that the spectrum is like a boxing weigh-in giving information about potential before match rather than actual exchange during match.
It is a common belief that the spectrum of blackbody directly translates to transfer of heat energy according to Planck’s radiation law
- , (Planck’s Law)
where is the heat energy radiated from a blackbody as a function of temperature and frequency , is a universal constant, and is a high frequency cut-off factor (with suitable normalization) defined by
- , ,
so that for and for .
The corresponding formula for the heat transfer between two blackbodies B1 and B2 of temperatures and , is commonly written
- (Gross Transfer)
suggesting that B1 emits to B2 and absorbs emitted from B2 as backradiation. If , then backradiation would correspond to heat transfer from a cold body to a warmer body seemingly in contradiction to the 2nd Law.
The contradiction is resolved by rewriting (Gross Transfer) as
- , (Net Transfer)
expressing the net transfer from B1 to B2, from warm to cold.
We can thus view (Net Transfer) as the actual transfer, while (Plank’s Law) and the form (Gross Transfer) can be viewed as potential of transfer.
We thus make a distinction between potential and actual transfer, and we understand that the confusion concerning backradiation comes from mixing up potential and actual heat transfer. What counts in the end is the actual transfer, not the potential of transfer.
Backradiation can thus be seen as a potentiality, not as an actuality and thus is not physical reality but only fiction. Potentiality without actuality is not science, only science fiction.