... power in = 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. ... [Jane Q. Public, 2014-08-29]
Again, start with power in = power out through a boundary with surface area "A". Using irradiance (power/m^2) simplifies the equation because we can divide both sides by "A" to obtain irradiance in = irradiance out.
... 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. ... [Jane Q. Public, 2014-08-29]
Again, as long as the enclosing shell is nearly the same size as the heated plate, those areas are nearly irrelevant. And because it's a simpler problem (like a tricycle) one should master it before trying to ride a bicycle with complicated view factors. I already specified my areas. Again, neglecting area ratios predicts that the heated plate warms from 150F to 235F after it's enclosed. Accounting for area ratios similar to Earth's predicts that the heated plate warms from 150F to 233.8F.
So the tricycle isn't too inaccurate compared to the bicycle, it's much easier to learn, and it provides a sanity check on the more complicated calculation. As the area ratio approaches "1.0" the bicycle should give the same answer as the simpler tricycle. And it does.
Incidentally, that tricycle is much more accurate than Jane's prediction that the heated plate remains at 150F even after it's enclosed.
... 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. ... [Jane Q. Public, 2014-08-29]
No. A spherical heated plate with a fully-enclosing shell has spherical symmetry, so the heated and enclosing plate temperatures are constant across their surfaces. That's why the equilibrium temperature solutions are just simple numbers.
However, if the passive plate doesn't fully enclose the heated plate then the heated and enclosing plate temperatures would be complicated functions of spherical coordinates theta and phi. That's a unicycle, not a tricycle.
... 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. [Jane Q. Public, 2014-08-29]
I already showed you that MIT's equation reduces to my Eq. 1 for blackbodies, and is consistent with these equations and Eq. 1 in Goodman 1957. I've stressed that this thought experiment has been tested for decades in the real world. Radiation shields allow for more accurate measurements of gas temperatures using thermocouples:
"The greatest problem with measuring gas temperatures is combatting radiation loss. ... surround the probe with a radiation shield ... The thermocouple bead radiates to the shield which is much hotter than the surrounding walls. Thus the radiative loss and hence temperature error is significantly reduced. The shield itself radiates to the walls."
These radiation shields have been used since at least Daniels 1968 (PDF), and they work like Dr. Spencer's insulating plate. They slow radiative heat loss from the hotter thermocouple without violating the first law, the second law, or the Stefan-Boltzmann law. Just like the greenhouse effect.
... 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. ... [Jane Q. Public, 2014-08-29]
How ironic. I've explained how to derive equations for increasingly realistic scenarios, ran "actual numbers" and repeatedly told you that you'd only be able to understand this thought experiment if you did the same. But you still haven't. Haven't you noticed that I'm the only one here deriving equations and doing calculations, while you're too busy saying things like this?
"... non-person... disingenuous and intended to mislead ... he is either lying ... dishonest ... intellectually dishonest ... intellectually dishonest ... Khayman80's intellectual dishonesty ... Pathetic. ... you've come out the loser in every case... you can't win a fucking argument. You don't know how. You don't understand logic. You've proved this many times. Get stuffed, and go away. The ONLY thing you are to me is an annoyance. I have NO respect for you either as a scientist or a person. ... cowardice ... odious person ... you look like a fool ... utterly and disgustingly transparent ... Now get lost. Your totally unjustified arrogance is irritating as hell. ... You are simply proving you don't know what you're talking about. ... Jesus, get a clue. This is just more bullshit. ... spewing bullshit ... You're making yourself look like a fool. ... Hahahahahaha!!! Jesus, you're a fool. ... a free lesson in humility... you either misunderstand, or you're lying. After 2 years of this shit, I strongly suspect it is the latter. ... Now I KNOW you're just spouting bullshit. ... if we assume you're being honest (which I do not in fact assume) ... I wouldn't mind a bit if the whole world saw your foolishness as clearly as I do. ... stream of BS... idiot ... Your assumptions are pure shit. ... I'm done babysitting you..." [Jane Q. Public]
"Jesus, you're a dumbshit. ... your adolescent, antisocial behavior ... keep making a fool of yourself. ... you're being such a dumbass ... your analysis of it is a total clusterfuck. ... you're so damned arrogant you think I'm the one being stupid. ... you were too goddamned stupid ..." [Jane Q. Public]
"... what a despicable human being you are ... an incorrigibly rude, insufferable human being ... Now I have given you your bone, doggie. GO AWAY. ... a clusterfuck pretending to be physics ... " [Jane Q. Public]