I'm going to correct/clarify myself again:

It's not that I don't agree. You might come up with the right answer for some sub-calculation. I don't know, I don't care, and I'm not even going to bother to check, much less agree. The issue is that I have already solved the problem, and arrived at the correct answer (within reasonable limits).

So I don't HAVE to agree or disagree with you. I've already done it, according to the correct textbook-approved physics. AND (unlike you) I checked my work and it checks out. And unlike your answer it doesn't violate conservation of energy.

Nothing you can say is going to change that.

You're misapplying your physics principles again. You're trying to introduce outside influences that the SIMPLE, UNREFUTABLE Stefan-Boltzmann relation says is ALWAYS true:

For a given gray body, its thermodynamic temperature is related ONLY to emissivity, radiant power output, and the S-B relation (emissivity)* (S-B constant) * T^4.

PERIOD. That's physics. And I repeat: given your OWN "draw a border around it" thermodynamic reasoning, the power input (whether it is electrical, chemical, or something else) must equal that output. That's physics.

You're trying to bring in energy from elsewhere, but it isn't relevant to this calculation AT ALL; it is erroneous thinking.

Power input is specified to be constant. Calculating the total power in initial conditions is, as I stated before, "dirt simple". Specified emissivity is known: 0.11. Temperature is known: 338.71K. Solving for the above we get 82.12 W/m^2.

We already have ALL the information needed to calculate this, given the Stefan-Boltzmann relation (above), relating these numbers. Nothing else is required, and in fact trying to introduce other factors is ERROR. That is what the accepted science says.

Since we CAN easily calculate that in initial conditions, and we know the area (YOU specified it), we can calculate the total power output (which is the ONLY power output) by multiplying Watts per area by the area. Our result is 82.12 W / m^2 * 510.065 m^2 = 41886.54 Watts.

This is simple physical fact, according to standard principles of physics. I repeat that you can twist and squirm all you want, but unless you can come up with a "khayman80 law" to replace the Stefan-Boltzmann law, this IS the answer, it is known, and it is unequivocal.

Further, even if you use the "long" equation from Wikipedia to calculate heat transfer, rather than my somewhat simplified estimate method, the primary terms in the denominator are still T1^4 minus T2^4, indicating that net heat flow is all OUTWARD from the heat source.

Introduce all the complications, and prevarications and half-assed reasoning you want. I have already shown you the correct answer according to established physics.

Give it up lest you make yourself look more of a fool than you already are. Because as I promised you, all of this is being recorded and will be made public, with your name displayed prominently. I promised that I would do that regardless of how it turned out. You have no reason to complain just because you lost.

Further, I'm going to INVITE people who teach heat transfer to examine my write-up, and evaluate it. I already know what they will say about your half-assed thermodynamic reasoning.

To be honest, I still don't see why YOU don't see, where I showed that you were clearly wrong. But again, I suspect that your CO2-based greenhouse gas religion will not let you accept the clearly established facts.

I have said all I need to say here. Nothing you say will change it, and no, I do not agree with your fallacious "reasoning". I'll stick with the engineering textbooks, thanks very much.

I disagree. It isn't worrisome at all.

I look forward to the day I can break away from daily "work" and just pursue my interests and hobbies.

And in fact, this is the economy of Start Trek: an economy of plenty, rather than our current economy based on scarcity. People do what they do because they want to, not because they get paid for it.

I don't think the Star Trek scenario is unreasonable, if we were to find better ways to generate energy. Nobody has to be idle (though they could be if they wanted). That isn't a species-killing idea, it's just another evolutionary step.

HOWEVER:

the authority to govern "navigable" airways comes with some caveats, which most people here aren't considering.

First, "navibable" in U.S. law implies that manned craft can use that route to travel interstate. That is pretty much the same definition as "navibable" waters.

The Federal government's AUTHORITY to govern "navigable airways", just like their authority to govern "navigable waters", stems from their authority, granted by the Constitution, to govern interstate commerce.

"Navigable airways" are particular altitudes and routes. They are clearly defined in aviation charts.

Everything else is "fair game", and by the Constitution (and Common Law) is up to the landowners and the States.

To put it in a nutshell: by ancient common law (which still holds; U.S. is a Common Law country) everything EXCEPT the clearly-defined "navigable airways" is indeed legally controlled by the landowner below, and is not subject to Federal jurisdiction.

Further, in my state, it is not legal to use any means to "surveil" property which isn't normally visible from the street, by ANY means, including aircraft, without a warrant. And yes, that means using a stepladder to see over the fence IS a crime.

In the U.S. -- or at least in the states around here -- that's already illegal. So the problem isn't one of rules, it's more one of enforcement.

The other problem is that we have a Federal agency trying to throw its weight around when by our Constitution, this is very clearly a state matter.

The only reason the FAA has any authority, anywhere, is because it is charged with regulating interstate commercial flight, which the Constitution allows it to do. Some people, unfortunately, have picked up this weird idea that FAA has authority over anything in the air, which is simply false.

A month or two ago, a Federal judge ruled that FAA has no authority over drones that are not flown in the (clearly defined on aviation charts) navigable interstate airways. And it is pretty clearly the correct decision, on Constitutional grounds.

However, in the meantime the FAA has appealed the decision. And though they are almost certain to lose in any honest court, they have taken advantage of the hiatus and are trying to regulate everything in site, apparently under the assumption that once it's regulated, however illegally, it will be that much harder to remove that regulation later.

I think they're mistaken, and they're just going to get shot down again by the next court. And they should be. Not just because they're wrong, but also because they're being corrupt assholes.

From your other (now archived) comment:

I "assumed" nothing. I calculated it. One stipulation of Spencer's challenge was that the power input to the heat source remains constant. He did NOT, however, make that stipulation for the refrigerated chamber walls. Not that it matters in this case. Because the power input to the heat source does remain constant (as a requirement of this problem), and therefore, by the Stefan-Botzmann relation between thermodynamic temperature and radiation, the temperature of the heat source does not change. This is not an assumption, it is called "physics".

YOU can disagree all you like, but the words are there in plain English: "constant flow of energy into the plate from the electric heater."

Now you're trying to say more energy is coming in from the other end? Pardon me, but that won't work either, by your own "boundary" principle: power in = power out. If you're putting energy in from both ends, then where is it coming out?

There is only one "heat source" in this problem, and it is at the center. And according to (epsilon)(sigma)(T1^4 - T2^4), ALL heat transfer is outward from the source to the walls! It's called physics!

If the power input to the heated sphere is fixed, then the power output in the form of radiant temperature is fixed: (epsilon)(sigma)T^4. It's physics!

It doesn't matter how you try to squirm and twist this. You have been owned. End of story.

And I've explained twice or maybe 3 times now how how your "thermodynamic" thinking led you astray. AFTER having given you a very clear warning out of a textbook, once I saw that you were headed in the wrong direction.

A body at thermodynamic temperature X outputs its total radiant power from ALL its surfaces. Not just one of them. By assuming total radiant power outward, across your boundary, you miscalculated the power out by 100% (give or take a couple of thousandths).

You are disputing the established, "consensus" science of heat transfer by making assumptions that don't apply. I used those words before, too. Misapplication of a true principle can still give you the wrong answer. Your calculated temperature for the enclosing sphere was off by approximately 33 degrees K.

You then back-calculated this erroneous figure in order to give another erroneous value to your heat source. And once again, the proof is dirt simple because your input power at steady-state is fixed, and a value that we already know: 41886.54 W.

Using the standard Stefan-Boltzmann relation between radiant temperature of a gray body, its emissivity, and radiant power out, we can very easily (even on paper, without a calculator) that using your own "energy boundary" concept, your answer "creates" approximately 3 kW more power out than you're putting in. This is an indisputable fact that follows directly from the Stefan-Boltzmann law.

PRECISELY! Here you are confirming, once again, my explanation of how you got it wrong.

You assumed the total radiant power output of the heat source was also being put out by the outside of the hollow sphere, through the "boundary" you drew around it. BUT... as I very clearly explained, that is not so. The hollow sphere has TWO surfaces, of nearly equal area. So the power output at the outside surface is actually only approximately HALF of what you thought it was. Because your calculations (I still have them) assume 511.346 m^2 when the actual radiating surface area is 511.346 m^2 + 511.186 m^2 = 1022.53 m^2.

Your calculation was off by 100%. (Or close enough to 100% that it isn't worth talking about the difference.)

You own statements (again, I still have them) prove this.

You're only confirming what I already stated.

Further, your own quotation there is proving you wrong. Power input to the heat source is constant. It is sufficient to heat the source to 150 deg. F (338.71K). Given the known temperature, and the emissivity, we compute the power out with (epsilon)(sigma)(338.71^4) = 82.12 W/m^2. Using that radiant emittance and the fixed, agreed upon area we get 41886.54 Watts total radiated power output.

By the DEFINITION of the problem (and even your own "boundary" principle) this is what it is. We have the equation for it we calculate it. Dirt simple.

That is what the Stefan-Boltzman relation stipulates. There is NO provision anywhere in that equation for whether another body nearby is a black body or a gray body or a white body or anything else. That's the way the damned thing works. I didn't invent it. Stefan came up with the concept, and Boltzmann quantified it some time later. This is the STANDARD equation for radiant power from temperature. There is nothing non-standard, equivocal, or even really debatable about it. It is a standard physics equation, and it does not require your agreement.

If you're saying the STANDARD Stefan-Boltzman relation between radiant power output, temperature, and emissivity doesn't apply here, then you're disputing the Stefan-Boltzmann law. If that is so, then please show is the "khayman80 law" you have invented to replace it.

You keep talking about "consensus" and "accepted science". Well, this is the long-accepted science of radiant heat transfer. If you want to refute THAT, go right ahead and try. I'll be here watching and laughing all the way.

khayman80 said our long conversation can continue here. So I am continuing. But I only have a few minutes to spend today, so I'm dashing this off briefly.

In reply to this comment

I have already explained how your "boundary" assumed that all the power was output from the outside of the enclosing sphere. However, that's not the case. If area is A, the Stefan-Boltzmann equation states that total radiant power output is (e * s) * A * T^4. BUT, you neglected to account for the fact that the hollow sphere has TWO surfaces it is radiating from. You left out half the m^2 in A, so your figure for W/m^2 was off by very nearly 100%. Q.E.D.

I agreed that "given your assumptions", that was the correct answer. I stated that in plain English. But your assumptions (see above) were incorrect. I just didn't mention that at the time. I was waiting for you to finish so I could show how you were "hanging yourself", as the saying goes. Hoist by your own petard.

I'm not to bother replying to the rest of your nonsense. Here is a simple proof that you are wrong, and nothing else need be said:

The formula for radiant power is (e * s) * area * T^4. Period. This is according to the Stefan-Boltzmann law, and no other variables are required at steady-state. The initial temperature of the heat source was 150F, or 338.71K.

So we agreed that the input power to the heat source is sufficient for the equation (e * s) * (heat source area) * 338.71^4.

The power input doesn't change. Yet your final calculated temperature was 241F or something like that (about 389.26K).

All you need to do is draw your precious "boundary" around the heat source. The S-B equation now says power out is:

(e * s) * (heat source area) * 389.26^4.

e, s, and the area haven't changed. But you changed the temperature. It is easy to see that 389.26^4 is much greater than 338.71^4. Your power output is now greater than your power input, which is a violation of conservation of energy. It's right there, man.

If you need specific figures: the total power output (and therefore power input) at the heat source, in initial conditions, was (we agreed on this) 82.12 W/m^2 * 510.065 m^2 = 41886.54 Watts. Power in = power out.

But the Stefan-Boltzmann law says at your calculated final temperature, power out is: 73039.94 Watts.

According to your OWN "boundary rule", you have just created 31153.4 Watts greater output than input. Conservation of energy is violated. Q.E.D.

You are busted.

But again: if you need to "draw a boundary", it needs to be drawn around the passive plate itself. We have already firmly established that your "boundary" around the heat source and the "enclosing shell" is even thermodynamically incorrect. It leads to an erroneous result of very close to (within a few thousandths) DOUBLE the radiative power from that surface that actually exists.

I have explained this to you 3 times now. If you can't get it through your head, that's your problem and nobody else's.

As I said, I am going to write this up more thoroughly, elsewhere. But I have presented enough here for anybody who is really interested to figure it out without too much difficulty. Present company apparently excepted.

s/should have drawn your shell/should have drawn your boundary

We have already shown that your particular application of "drawing boundaries" here was a MISAPPLICATION of the principle you are trying to use.

The "enclosing shell" (if by that you mean the passive plate that was inserted) is acted upon only by radiation. You should have drawn your shell around THAT, and that alone. And you should at least have tried drawing your boundary around your own goddamned heat source, both for initial conditions and your final result, to check your work. But you didn't. What you got was a universe-busting violation of conservation of energy.

But of course you are still trying to defend something which YOU claimed earlier is not valid to do. There is a word for that.

Face it. You've been spouting the wrong answer for 2 years, and using it to justify calling OTHER PEOPLE names, and bullying them online, and other nasty antisocial behavior.

But even if I made a small mistake somewhere (I did NOT make a large one), you're still busted.

One more correction and again it's minor, but again I plea that I have been very busy and had to dash this off in a hurry:

In my list of "clues" toward the bottom, Clue #1:

The bit about "Barring any issues like 'view factor'" was an irrelevant comment because that relates to interactions between bodies and my whole point was that the S-B equation for radiative power from a body does not include other bodies. The part about "view factor" can be left out of that passage without affecting its correctness.

Further, if you have a problem with my equations (including my minor corrections) you are welcome to do your own and prove me wrong.

But you aren't going to, because I'm not wrong, in any basic way. I might have gotten a hundredth or a thousandth off here or there, but unlike you I did double-check your work. All while (according to you) I was spouting something off on Facebook or something.

I spent about an hour and a half on this, give or take, between my regular work, and working on the car. That includes identifying your errors, and determining what the right way to do it was.