In your reference to the Hyperphysics site, nowhere is it mentioned that the first form radiates into a vacuum as you always claim.
In the phrase you quoted, "
net radiation loss rate" there is a link. Click on it.
At that link they repeat the net form of the SB law and say this"
While the typical situation envisioned here is the radiation from a hot object to its cooler surroundings, the Stefan-Boltzmann law is not limited to that case. If the surroundings are at a higher temperature (TC > T) then you will obtain a negative answer, implying net radiative transfer to the object.
They specifically agree with the Dartmouth site where the second fourth power term can be greater or less than the first term.
As far as the spontaneity of energy flow the same hyperphysics site says this:
It is important to note that when it is stated that energy will not spontaneously flow from a cold object to a hot object, that statement is referring to net transfer of energy. Energy can transfer from the cold object to the hot object either by transfer of energetic particles or electromagnetic radiation, but the net transfer will be from the hot object to the cold object in any spontaneous process. Work is required to transfer net energy to the hot object.
What they are saying is that radiant energy can transfer either way as long as "
net transfer will be from the hot object to the cold object in any spontaneous process."
Again, they specifically agree with the Dartmouth site. You are saying both the Dartmouth and Hyperphysics sites are wrong. The hyperphysics site refers to
net four times. It is no mistake. Net is NOT an assumption. It comes from a derivation at the Dartmouth site.
And yes...I see the word net...but the equation has no expression from which to derive net...net is an assumption based on an unobservable, unbearable, untestable model.
Net radiation exchange is the only concept that does not violate other laws of physics. The second form of the SB equation is a model that is well founded, and you want to substitute it for a model that leads to all sorts of contradictions in several other areas of physics.
Yet you always denigrate models, but that's what basic physics is - models that are consistent with experiments.
Your idea of the SB equation is contrary to science going all the way back to Stefan's conclusions of his own experiment.
Your reference to support your idea of the SB law was poorly chosen for your purposes.
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