- 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)
fredag 22 juli 2011
The Emitter-Absorber Relation of Radiation
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:
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?