There is a lot of confusion concerning the physics behind Plank's radiation law and its integrated form of Stefan-Boltzmann's law in the following two algebraically equivalent but physically different forms:
- E = sigma Te^4 - sigma Ta^4, (photon particle model: difference of two-way gross flows)
- E = sigma (Te^4 - Ta^4) ~ 4 sigma Te^3 (Te - Ta), (wave model: net one-way flow)
where E is the intensity of the heat energy transferred from a blackbody (emitter) of temperature Te to a blackbody (absorber) of temperature Ta smaller than Te, and sigma is a constant.
Version 1 reflects two-way energy transfer by two way photon particles emitted by both emitter and absorber into a void (of zero Kelvin), and can be seen as an a hoc version cooked up from Planck's original law of one blackbody emitting into a void (of zero Kelvin).
In Slaying the Sky Dragon and Mathematical Physics of Blackbody Radiation I present a derivation of Version 2 based on a principle of finite precision computation in a wave model.
Version 1 reflects simple physics of particles with the two bodies like two very young children playing side by side without interaction both spitting out photons in two directions into a void (of zero Kelvin).
Version 2 reflects more complex physics with the two bodies playing together, talking to each other by a two-way wave equation, but with one-way net transfer of heat: The effect of the finite precision computation is a high frequency cut-off depending on temperature limiting the ability of the absorber to re-emit only frequencies below cut-off, with frequencies above cut-off being absorbed and turned into heat.
Version 2 is like two educated people talking and listening to each other, with the emitter being the smarter and the frequencies above the cut-off of the dumber being absorbed by the dumber and then transformed into heat (frustration).
Which version is better? The trivial 1 or the educated 2? Is there an intimate relation between emitter and absorber into a system relation, where emission from one body is directly connected to absorption of another? Is the play between adults more interesting that than between babies?
Are these questions above your cut-off frequency and will only lead to heated frustration?
Inlägg
I think I get your point Claes. But wouldn't it be useful to explain to the "babies" that version 1 doesn't lead to a greenhouse effect. Why shoot a fly with bazzoka?
SvaraRaderaYou are right, but what do you when there is no communication, when there is no wave equation, when there are only soul-less particles emptied into a void?
SvaraRaderaBut Claes, why do you have to invent such mystical communication theories when he reality is so simple. If the atmosphere is at the same temterature as the earth surface and is supposed to be a black body, like the earth surface, there is of course no net radiation in any direction. But you can be sure that there is a lot af electromagnetic waves, carrying energy, exchanged between the two black bodies, acc to the SB two body law.
SvaraRaderaI hope you don`t deny this, for if so, there is no meaning of having a discussion with you.
And if you gradually increases one of the temperatures, I hope you easily understand that the other body not suddenly stops emitting at the same level as before. The body with increased temperature of course increases the emitted energy compared to the earlier state. I really hope you agree with me in this very simple case.
But this doesn`t mean that there must be a green house effect. The "back radiation" from the atmosphere is of course reradiated back to the atmosphere, starting the same procedure over again, but some energy is every time passing through the atmosphere into space, and finally all the original energy is reaching space. Perhaps some part of it is absorbed in the atmosphere heating it. And this heated atmosphere makes the earth loose a little less energy acc to the SB two body law, and thus the earth is heated a little, but perhaps not very much. So I think you can stop the discussion about babies and so on. It doesn`t add anything to the greenhouse debate.
Who formulated and proved the two-body SB law you refer to?
SvaraRaderaSee also new blog post.
SvaraRaderaIf there is only one body, the radiated energy is given by the SB law. The empty space is at 0´K. If this temp instead was at T, the same as the body, the net energy radiated would be zero. So there has to be some mathematical expression describing this, and the SB two body law, your eq 1, is the best eq found to make this job. And I think it is in accordance with experiments.
SvaraRaderaThe equation can be interpreted in different ways, and this is what we are discussing. You did not answer my question about who proved 1.
SvaraRaderahe "back radiation" from the atmosphere is of course reradiated back to the atmosphere, starting the same procedure over again,
SvaraRadera