... Since emissivity doesn't change the input required to heat source to achieve 150F is constant, regardless of where it comes from. But as long as the walls of the chamber are cooler than the source, NONE of the power comes from the chamber walls... [Jane Q. Public, 2014-09-15]

But if the chamber walls are also at 150F, they're not cooler than the source and the input required to heat the source to 150F is zero.

... do you still maintain that after the enclosing passive sphere is inserted, the central heat source raises in temperature to approximately 241 degrees F? You haven't said anything about that in a while, so I'm just checking. [Jane Q. Public, 2014-09-15]

Once again, if the electrical heating power is held constant, the heat source has to warm. Once agin, Jane's heat source keeps the source temperature constant by halving its electrical heating power. Jane/Lonny Eachus might ask himself why his required electrical heating power goes down by a factor of two after the enclosing shell is added.

... Of course it wouldn't need a separate heat source if its environment were maintained at 150 degrees. ... [Jane Q. Public, 2014-09-15]

In other words, the electrical heating power is determined by drawing a boundary around the heat source:
power in = electrical heating power + radiative power in from the chamber walls
power out = radiative power out from the heat source

Since power in = power out:

electrical heating power + radiative power in from the chamber walls = radiative power out from the heat source

Right?

You asked me if I believed the power usage of the heat source would be the same if the walls were also at 150F. The answer is YES, and here is why: You are proposing to bring the whole system up to a level of higher thermodynamic energy, rather than just the heat source. And you are somehow proposing that it doesn't take more energy to do that. But of course it does. The power required to bring the heat source up to 150F remains the same, because the Stefan-Boltzmann law says it has to be. But NOW, you are ALSO bringing the walls up to that higher temperature, and THAT would require even more power (because of the slightly larger surface area). [Jane Q. Public, 2014-09-15]

Again, that's completely ridiculous. I've explained why the power used to set the chamber wall temperature is irrelevant. Any power used is simply being moved from some point outside the boundary to another point which is also outside the boundary. Because that power never crosses the boundary, it's irrelevant.

For example, you could simply place the vacuum chamber somewhere with an ambient temperature of 150F. That would require zero power, but once again it doesn't matter even if the vacuum chamber were on Pluto. Because that power never crosses the boundary.

Either way, as long as the chamber walls are held at 150F, the heat source would need absolutely no electrical heating power to remain at 150F. Zero. Period.

You asked me if I believed the power usage of the heat source would be the same if the walls were also at 150F. The answer is YES... [Jane Q. Public, 2014-09-15]

Here's our disagreement. Conservation of energy demands that a heat source at 150F requires no electrical heating power inside 150F vacuum chamber walls.

You're either disputing conservation of energy, or you're not calculating the actual electrical heating power. If you're calculating the actual electrical heating power, your calculation has to account for radiation from the chamber walls because it passes in through that boundary. That's why the electrical heating power would be zero if the chamber walls were also at 150F!

Nonsense. This is textbook heat transfer physics. We have a fixed emissivity. Therefore, according to the Stefan-Botlzmann radiation law, the ONLY remaining variable which determines radiative power out is temperature. NOTHING else. That's what the law says: (emissivity) * (S-B constant) * T^4. That's all. Nothing more. This makes it stupidly easy to calculate the radiative power out, and therefore the necessary power in. [Jane Q. Public, 2014-09-15]

It's "stupidly easy" to calculate radiative power out and power in through what boundary? The boundary you're describing has to include the source's radiative power passing out through it, without including radiative power from the chamber walls passing in. I think that's impossible, but feel free to explain exactly where such a boundary would be drawn.

One question only: do you agree with the Stefan-Boltzmann relation: power out P = (emissivity) * (S-B constant) * T^4 ?? No more bullshit. "Yes" if you agree that equation is valid, or "No" if you deny that it is valid. Just that and no more. I'm not asking your permission. I'm just trying to find out whether you're actually crazy or just bullshitting. [Jane Q. Public, 2014-09-15]

Once again, I agree that "power out" through a boundary drawn around the heat source is given by the Stefan-Boltzmann law. But I've obviously failed to communicate that the power from the chamber walls has to pass in through that boundary, so you're only using half the equation to calculate the electrical heating power.

The REASON there would not be as great a power DIFFERENCE if the chamber walls were also at 150F, is that the walls would themselves be radiating more power out, so there would be less heat transfer (in that case 0). It is NOT, as you assert, because the heat source would be using less power. That's false, by the S-B equation. Its power output remains the same because (Spencer's stipulation) the power input remains the same. The reason my solution does not violate conservation of energy, is that the power consumption of the chamber wall is allowed to vary. THAT is where the change takes place, not at the heat source. Again, this is a stipulation of Spencer's challenge. Once again: power out of heat source remains constant, because P = (emissivity) * (S-B constant) * T^4. There is nothing in these conditions that changes this at all. Therefore, BECAUSE the power out and power in at the heat source remain constant, so does the temperature. It's all in that one little equation. [Jane Q. Public, 2014-09-15]

Once again, no. Draw a boundary around the heat source:
power in = electrical heating power + radiative power in from the chamber walls
power out = radiative power out from the heat source

Since power in = power out:

electrical heating power + radiative power in from the chamber walls = radiative power out from the heat source

"Power in" has to include the radiative power passing in through the boundary. Otherwise energy isn't conserved, because power in = power out through any boundary where nothing inside that boundary is changing with time.

... EVEN IF we accepted your idea that the "electrical" power required to be input to the heat source is dependent on the temperature difference between the heat source and chamber wall (a violation of the S-B law), you still contradict yourself because your answer of a hotter heat source would still then require MORE power, because the difference is greater. But that is not allowed by the stated conditions of the experiment, and you keep glossing over that simple check of your own work which proves it wrong. So no matter how you cut it, your answer is wrong, by your own rules. ... [Jane Q. Public, 2014-09-15]

Once again, no. I've already shown that the electrical power in my solution remains constant.

Once again, that's because I'm correctly applying the principle of conservation of energy to determine the electrical heating power.

It seems like we can't agree that "power in" includes the radiative power passing in through a boundary around the heat source. Is that because you disagree that power in = power out through any boundary where nothing inside that boundary is changing with time? Or is it because you disagree that the radiative power from the chamber walls passes in through a boundary around the heat source?

The REASON there would not be as great a power DIFFERENCE if the chamber walls were also at 150F, is that the walls would themselves be radiating more power out, so there would be less heat transfer (in that case 0). It is NOT, as you assert, because the heat source would be using less power. ... [Jane Q. Public, 2014-09-15]

That's absurd. A 150F plate surrounded by 150F chamber walls wouldn't need an electrical heater at all. Period. The electrical heating power would be exactly zero. Maybe you're mistaking "electrical heating power" with "radiative power out"? Or maybe you're missing half the equation necessary to calculate the required electrical heating power, and it's leading you to bizarre conclusions?

I am disputing nothing of the sort. As I have explained many times now, you are not drawing your lines properly. You keep making the same bullshit assertions, after I have proved them false. Why do you do this? You're just going to look that much more foolish later. [Jane Q. Public, 2014-09-13]

You're either disputing conservation of energy, or you're not calculating the actual electrical heating power. If you're calculating the actual electrical heating power, your calculation has to account for radiation from the chamber walls because it passes in through that boundary. That's why the electrical heating power would be zero if the chamber walls were also at 150F!

Can we agree that the required electrical heating power would be zero if the chamber walls were also at 150F?

... I held the power constant, just as Spencer stipulated. ... [Jane Q. Public, 2014-09-13]

It's so adorable that Jane keeps insisting that Jane kept the power constant, even after I showed that Jane's calculation was only able to hold the source temperature constant after the enclosing shell was added by halving the actual electrical heating power.

It's also adorable that Jane keeps ignoring the fact that his "electrical heating input" calculation wouldn't change even if the chamber walls were also at 150F. Even Jane should be able to comprehend that a 150F source inside 150F chamber walls wouldn't need electrical heating power.

NO!!! I have told you 5 or 6 or maybe more times now, this is a VIOLATION of the very straightforward Stefan-Boltzmann law. How it applies in this situation is quite straightforward, and not at all as complex as you are making it out to be. Radiant power output of a gray body is calculated using ONLY the variables: emissivity and temperature. THAT IS ALL. There is no other variable dealing with incident radiation, or anything else. When the system is at radiant steady-state, power out (and therefore power in) are easily calculated, and I have calculated them. Further, Spencer's "electrical" input power was to the heat source, not to the whole system. YOUR OWN PRINCIPLE: power in = power out. Now you're trying to contradict yourself and say it meant something else. It's just bullshit. You're squirming like a fish on a hook. You just don't seem to realize you have already been flayed, filleted, and fried in batter. You're owned, man. [Jane Q. Public, 2014-09-13]

No. Draw a boundary between the source (T1=150F) and the chamber walls (T4=0F) before the hollow sphere is added. Power in = power out. Variable "electricity_initial" flows in at whatever rate is needed to keep T1=150F. Net heat transfer flows out from source to chamber walls. Power in = power out:

electricity_initial = p(14) = (e)(s) * ( T1^4 - T4^4 )

So are you disputing that power in = power out through a boundary where nothing inside that boundary is changing with time? Or are you disputing that the radiation from the chamber walls passes through a boundary drawn just inside them?

And again, if you keep ignoring that "power in" half of the equation that all Sky Dragon Slayers miss, you'll have to keep wondering why your "electrical heating input" calculation wouldn't change even if the chamber walls were also at 150F. Even Jane should be able to comprehend that a 150F source inside 150F chamber walls wouldn't need electrical heating power.

... 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. ... [Jane Q. Public, 2014-09-13]

I just showed that Jane/Lonny Eachus solved the "correct answer" to a different question. Instead of holding the electrical heating power constant like Dr. Spencer did, Jane/Lonny held the source temperature constant. In that case, the electrical heating power required to keep the source at 150F drops by a factor of two after the enclosing shell is added. This shows that holding the electrical heating power constant like Dr. Spencer did is different than holding the source temperature constant like Jane/Lonny did.

... SIMPLE CALCULATION, which I have already shown several times: power "sufficient" to heat the heat source under initial conditions to 150F: 41886.54 Watts. Power input at the source remains constant. ... [Jane Q. Public, 2014-09-13]

No, in your example the electrical heating power drops by a factor of two after the enclosing shell is added. And once again, your calculation of the power sufficient to heat the heat source would be exactly the same if the chamber walls were also at 150F. But the right answer there is zero, because an electric heater wouldn't be necessary. Is this really so hard to understand, or are you deliberately spreading misinformation?

... 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. ... [Jane Q. Public, 2014-09-13]

And that's why what you're calculating isn't Dr. Spencer's electrical heating power, because it should be "zero" if the chamber walls are also at 150F.

... 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. ... [Jane Q. Public, 2014-09-13]

If you draw a boundary around the heated source, you have to account for the 0F chamber walls because they're radiating power in through the boundary. Otherwise you're not actually calculating Dr. Spencer's electrical heating power, or you misunderstand conservation of energy.

So it seems like in your interpretation, Dr. Spencer's challenge is basically: "Assuming the source temperature is held fixed, does the source temperature change after a passive plate is added?"

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. [Jane Q. Public, 2014-09-13]

Jane, didn't it seem odd that you interpreted Dr. Spencer's challenge to mean "Assuming the source temperature is held fixed, does the source temperature change after a passive plate is added?"

How is that different than asking "Assume x = 150 forever. Will x change?"

Isn't that a silly question? Shouldn't you at least consider the possibility that you've misinterpreted "power input to the heat source"?

No. Holding constant the electrical power heating the source is very different than holding constant the source temperature. Like Jane, let's assume the source temperature is constant (rather than the electrical heating power) and use Jane's equation and notation:

... we have 4 surfaces, which I will call 1, 2, 3, 4 moving outward, so 1 is the surface of the heat source, 2 the inside of the hollow sphere, 3 the outside of the hollow sphere, and 4 the chamber wall. T3 for example would be radiative Temperature of surface 3. ... [Jane Q. Public, 2014-09-10]

Draw a boundary between the source (T1=150F) and the chamber walls (T4=0F) before the hollow sphere is added. Power in = power out. Variable "electricity_initial" flows in at whatever rate is needed to keep T1=150F. Net heat transfer flows out from source to chamber walls. Power in = power out:

electricity_initial = p(14) = (e)(s) * ( T1^4 - T4^4 ) = (e)(s) * (8908858139.78) = 55.5913 W/m^2

Now add the hollow sphere and draw a boundary between the source (T1=150F) and the inside of the hollow sphere (T2). A different "electricity_final" flows in, and heat transfer p(12) flows out.

electricity_final = p(12) = (e)(s) * ( T1^4 - T2^4 )

Now draw a boundary between the outside of the hollow sphere (T3=T2) and the chamber walls (T4=0F): "electricity_final" flows in, and heat transfer p(34) flows out. Since power in = power out:

electricity_final = p(34) = (e)(s) * ( T2^4 - T4^4 )

Combine these two equations:

T1^4 - T2^4 = T2^4 - T4^4

Solve for:

T2 = T3 = 305.47K = 90.176 deg. F.

electricity_final = 27.8 W/m^2.

So if the source temperature is held constant at 150F, adding the hollow sphere reduces the necessary electrical heating power to keep the source at 150F by a factor of two, from 55.6 to 27.8 W/m^2.

Can we agree on that?

... input power at steady-state is fixed, and a value that we already know: 41886.54 W. ... [Jane Q. Public, 2014-09-12]

Again, we disagree about what's held fixed. That value you keep calculating isn't the constant electrical power heating the source.

In this experiment there is a "... constant flow of energy into the plate from the electric heater... flowing in at a constant rate... the electric heater pumps in energy at a constant rate. ..."

In my interpretation, Dr. Spencer's challenge is basically: "Assuming an electric heater pumps energy at a constant rate to the source, does the source temperature change after a passive plate is added?"

You've repeatedly noted that there are no other factors involved in calculating your 82 W/m^2 (41886.54 W) value. So if it's held fixed, the source temperature is also held fixed.

So it seems like in your interpretation, Dr. Spencer's challenge is basically: "Assuming the source temperature is held fixed, does the source temperature change after a passive plate is added?"

Is that right?

... 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. ... [Jane Q. Public, 2014-09-11]

Once again, the constant electric power is sufficient to heat the source to 150F when it's surrounded by chamber walls at 0F. That's the initial condition in the experiment that we agreed on. Your "82 W/m^2" value isn't the constant electrical power sufficient to heat a 150F source inside 0F chamber walls.

Again, if you want to see why your calculation doesn't yield the power input to the heat source, just ask what power input would be necessary if the chamber walls were also at 150F. In that case Dr. Spencer's electric heater wouldn't be necessary, so that power input would be zero.

Since your "82 W/m^2" calculation can't do that, it's not the electric heater power that's held constant. On the other hand, your 55.6 W/m^2 calculation would be zero if the chamber walls were at 150F. So it represents the constant electrical power in your analysis. Hold it constant as Dr. Spencer said, and you'll obtain the correct solution if you correctly apply the principle of conservation of energy.

Any heat transfer which doesn't cross the boundary can't be included because it can't change the total amount of energy inside the boundary.

PRECISELY! Here you are confirming, once again, my explanation of how you got it wrong. ... [Jane Q. Public, 2014-09-11]

No, I explained why you can't add heat transfer from heat source to the inside of the enclosing plate to the heat transfer from the outside of the enclosing plate to the wall to get 55.6 W/m^2 from the shell to the chamber walls. Again, that's because any heat transfer which doesn't cross the boundary can't be included because it can't change the total amount of energy inside the boundary.

Any heat transfer which doesn't cross the boundary can't be included because it can't change the total amount of energy inside the boundary.

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. [Jane Q. Public, 2014-09-11]

No. I've assumed that the electrical power heating the source to 150F inside 0F chamber walls is constant. (Note that this constant rate would be zero if the walls were at 150F.) That's the assumption we disagree on. I never assumed the total radiant power output of the heat source was also being put out by the outside of the hollow sphere. Maybe the fact that we disagree about what's held constant (the electrical heating power to keep the source at 150F inside 0F chamber walls) is leading to yet another miscommunication?

... 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. ... 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. ... [Jane Q. Public, 2014-09-11]

No. We've never agreed that the unchanging power input (my "constant electrical heating power") is "82 W/m^2". I've repeatedly failed to explain that the constant electrical heating power would only be "82 W/m^2" if the chamber walls were 0K blackbodies.

In this experiment there is a "... constant flow of energy into the plate from the electric heater... flowing in at a constant rate... the electric heater pumps in energy at a constant rate. ..."

Note that the constant rate of Dr. Spencer's electric heater would equal zero if the chamber walls were also at 150F. So any calculation of this crucial constant rate would also need to be zero in the case of chamber walls at 150F.

Since Jane's "82 W/m^2" value isn't the constant electrical heating power needed to keep the source at 150F inside 0F chamber walls, it isn't held constant. Here's where Jane actually calculated the constant electrical power heating the source inside 0F chamber walls:

... Calculate initial (denoted by "i") heat transfer from heat source to chamber wall. We are doing this only to check our work later. ... = 55.5913 [W/m^2]... [Jane Q. Public, 2014-09-10]

So Jane's source needs 55.6 W/m^2 of constant electrical heating power to stay at 150F inside 0F chamber walls. This value is held constant. After the enclosing shell is added and temperatures stabilize, conservation of energy demands that net heat transfer out equals Jane's 55.6 W/m^2. Does it?

... 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. ... [Jane Q. Public, 2014-09-11]

No, I drew that boundary for both initial and final conditions to guarantee conservation of energy. In fact, I repeatedly suggested that you check your work by drawing a boundary between the source and the enclosing shell at your proposed steady-state temperatures, then calculating power in = power out using the original constant electrical power you calculated before the source was enclosed.

Let's do that:

Jane's constant electrical power of 55.6 W/m^2 flows into that boundary. At steady-state, power in = power out. But power out through that boundary is the net heat transfer from the source to the shell, and Jane calculates that as 27.8 W/m^2.

Since power in > power out, energy isn't conserved between the source and the enclosing shell at Jane's proposed "steady-state" temperatures.

... the total heat transfer now from heat source to the chamber wall is equal to: (heat transfer from heat source to the inside of the enclosing plate) PLUS (heat transfer from the outside of the enclosing plate to the wall). ... [Jane Q. Public, 2014-09-10]

Once again, conservation of energy means that power in = power out through any boundary where nothing inside that boundary is changing with time. Any heat transfer which doesn't cross the boundary can't be included because it can't change the total amount of energy inside the boundary.

... 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. ... [Jane Q. Public, 2014-09-11]

Let's draw a boundary around the enclosing shell to check Jane's work:

Jane's constant electrical power of 55.6 W/m^2 flows into that boundary. At steady-state, power in = power out. But power out through that boundary is the net heat transfer from the shell to the chamber walls, and Jane calculates that as 27.8 W/m^2.

Since power in > power out, energy isn't conserved between the source and the enclosing shell at Jane's proposed "steady-state" temperatures.

... the total heat transfer now from heat source to the chamber wall is equal to: (heat transfer from heat source to the inside of the enclosing plate) PLUS (heat transfer from the outside of the enclosing plate to the wall). ... Add them together for the total heat transfer: 27.7832 + 27.7813 = 55.5645 total heat transfer. ... [Jane Q. Public, 2014-09-10]

No. Since heat transfer from heat source to the inside of the enclosing plate never crosses a boundary drawn outside the enclosing plate, it can't affect energy conservation for that boundary. At Jane's temperatures, total heat transfer out through that boundary is actually just 27.8 W/m^2, while Jane's constant 55.6 W/m^2 electrical heating power still flows in.

Because power in = power out through any boundary where nothing inside that boundary is changing with time, Jane's "steady state" solution violates conservation of energy.

... 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. ... [Jane Q. Public, 2014-09-11]

Good grief. How predictably ridiculous. All boundaries where nothing inside changes have power in = power out. Seriously. All of them. That's why I tried to convince you that this general principle is true, but obviously we'll have to agree to disagree.

We have already shown that your particular application of "drawing boundaries" here was a MISAPPLICATION of the principle you are trying to use. ... [Jane Q. Public, 2014-09-11]

Jane agreed that the general principle is true that power in = power out through a boundary where nothing inside the boundary is changing. But now that this general principle contradicts Slayer dogma, Jane considers it a misapplication.

Jane might wonder why cooler power wasn't included in "power in = power out": because it just moves energy from one point outside the boundary to another point that's also outside the boundary. In the same way, energy moved from one point inside the boundary to another point that's also inside the boundary isn't included in the equation describing conservation of energy.

... 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. ... [Jane Q. Public, 2014-09-11]

Ironically, power in = power out through all the boundaries I've constructed. That includes the boundary around my own "goddamned heat source". But that's not true for Jane's solution, because it violates conservation of energy.

... The rate of energy transfer from surface 1 to 2 is (p12) = (e*s) * ( T1^4 - T2^4 ). And T1 is known! ... (e*s) * ( 338.71^4 - T2^4 ) ... [Jane Q. Public, 2014-09-10]

The enclosed source temperature at steady state is known to be 338.71 K (150F)? No, absolutely not. The chamber wall temperature is constant at 0F, and the electrical power heating the source is constant. But the enclosed source temperature is only constant in Jane's PSI Sky Dragon Slayer bizarro world.

Jane assumed the source's final enclosed steady state temperature was exactly the same as before it was enclosed. Surprise, Jane found that the source didn't warm! As a result, he got nonsensical answers and had to invent a new energy conservation law where power adds to the energy inside a boundary even if it never crosses that boundary.

We have already shown that your particular application of "drawing boundaries" here was a MISAPPLICATION of the principle you are trying to use. ... [Jane Q. Public, 2014-09-10]

Jane agreed that the general principle is true that power in = power out through a boundary where nothing inside the boundary is changing. But now that this general principle contradicts Slayer dogma, Jane considers it a misapplication.

Jane might wonder why cooler power wasn't included in "power in = power out": because it just moves energy from one point outside the boundary to another point that's also outside the boundary. In the same way, energy moved from one point inside the boundary to another point that's also inside the boundary isn't included in the equation describing conservation of energy.

... 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. ... [Jane Q. Public, 2014-09-10]

Ironically, power in = power out through all the boundaries I've constructed. That includes the boundary around my own "goddamned heat source". But that's not true for Jane's solution, because it violates conservation of energy.

... The rate of energy transfer from surface 1 to 2 is (p12) = (e*s) * ( T1^4 - T2^4 ). And T1 is known! ... (e*s) * ( 338.71^4 - T2^4 ) ... [Jane Q. Public, 2014-09-10]

The enclosed source temperature at steady state is known to be 338.71 K (150F)? No, absolutely not. The chamber wall temperature is constant at 0F, and the electrical power heating the source is constant. But the enclosed source temperature is only constant in Jane's PSI Sky Dragon Slayer bizarro world.

Jane assumed the source's final enclosed steady state temperature was exactly the same as before it was enclosed. Surprise, Jane found that the source didn't warm! As a result, he got nonsensical answers and had to invent a new energy conservation law where power adds to the energy inside a boundary even if it never crosses that boundary.