I have looked this over, and looked at my references again. And you're still wrong. You're mischaracterizing the thermodynamics of this experiment rather egregiously. I don't know whether you are doing it intentionally or otherwise, but you're doing it.
I mentioned this to you several times, but you haven't picked up on it: just for one thing, you're claiming to be using flux but flux has an areal component which you are not accounting for. You say power in = power out, which may be true, but that total power is being transferred via emissive power, which is in W/m^2. Nowhere are you accounting for this. As I stated before: you are conflating power and emissive power, and you can't do that. Where are your areas? It might conserve energy but without areas you do not have the information required to calculate actual radiative temperature.
There are number of other factors you are 're not accounting for. My statement stands: your attempted analysis of Spencer's thought experiment is nothing but a clusterfuck pretending to be physics.
I told you where you can find a complete treatment of the actual thermodymics of this situation. If you'd actually read it and understood it (and were honest), you'd know that with a reasonable degree of precision it is correct.
You state on your website:
Radiation is proportional to T**4, so the magnitude of actual transfer is only related to T(h)**4 - T(c)**4 because hot objects absorb radiation from cooler objects. Thatâ(TM)s consistent with the second law because hot objects radiate more power to cold objects than vice versa.
Yes, this is true (with the exception of the word "only"), but you are neglecting so many other factors that this statement is meaningless in context. Nobody is claiming this statement is essentially wrong... in fact I've made it myself several times. But the devil is in the details. As you show quite well by going on to misapply it:
Nonsense. Start with conservation of energy just inside the chamber walls at equilibrium: power in = power out.
The plate is heated by constant electrical power flowing in. The cold walls at 0ÂF (T(c) = 255K) also radiate power in. The heated plate at 150ÂF (T(h) = 339K) radiates power out. Using irradiance (power/m**2) simplifies the equation:
electricity + sigmaT(c)**4 = sigmaT(h)**4
This is a joke, right? Trying to see if I'd catch it?
Again, among other things you are substituting irradiance for power without factoring in any area. That's just simply bad math. And I repeat: you have also invalidly ignored other factors which may not be ignored.
Create a realistic scenario, draw yourself a diagram, and run some actual numbers on them rather than just tossing equations around without seeing how they fit together in the real world.
I repeat: get the experiment with the two separate plates (actively heated plate and passive plate) right first. Then you can move on to a fully-enclosing plate. You say it's simpler but in a way it's not; you're trying to ride a bicycle when you haven't even managed to ride your tricycle without falling off.
There are numerous sources, including physics and engineering textbooks, which contradict your analysis and conclusions. Why don't you try the engineering textbooks Latour cited, which have examples of real-world situations? After all: ultimately what we're talking about here is the real world, not a thought experiment.