... I will do you a favor here, and say: don't bother to go calculating the energy, either. The problem is that an analysis of this kind, based on the assumption that power-in = power-out, is doomed to fail except in coincidental cases. Even conservation of energy can give very misleading results. The black body example I gave shows why your "energy conservation just inside the surface" won't work. ... power-in = power-out is not necessarily true, and in fact that is probably a very rare exception. ... [Jane Q. Public, 2014-09-07]
Energy is always conserved, so power in = power out through any boundary where nothing inside is changing.
For the hundredth time: nobody is disputing this. ... [Jane Q. Public, 2015-03-19]
"Nobody" is disputing this, apparently in the same way that "nobody" is disputing my simple substitution of the standard physics definition of the term "net" into Jane's equation.
... The equation for radiative power output of a body at steady-state does not change in the presence of cooler bodies. It remains exactly the same. It is dependent ONLY on emissivity, thermodynamic temperature, and the Stefan-Boltzmann constant. [Jane Q. Public, 2015-03-17]
... The statement that "no net energy is transferred to the warmer body from the colder" is exactly WHY the equation for radiant heat output does NOT change in the presence of colder bodies. BUT... you neglect the fact that it would have to, if it were absorbing and re-radiating radiation from those colder bodies. ... [Jane Q. Public, 2015-03-19]
No, Jane. The equation for radiant heat output is still the Stefan-Boltzmann equation. As I've repeatedly told you, we agree that it is dependent ONLY on emissivity, thermodynamic temperature, and the Stefan-Boltzmann constant.
However, temperature is determined by internal energy. That's determined by a fundamental law called "conservation of energy" which is necessarily true and certainly isn't a "very rare exception" or "doomed to fail".
The fact that conservation of energy determines temperature doesn't change the equation for radiant heat output, even in the presence of colder bodies. The Stefan-Boltzmann equation remains exactly the same, as I've repeatedly explained.
... even if you tried to maintain that it wasn't a feedback loop but just a new equilibrium, with the hotter temperature you would still have to increase the power to maintain the exterior walls at a constant temperature. Which means you would be extracting more thermal energy from the system... but not adding any more. Contradiction. ... [Jane Q. Public, 2015-03-19]
Jane, I've repeatedly failed to explain how "conservation of energy" works. Once again: any power used by the exterior wall cooler (or heater) 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.
The word you're looking for isn't "contradiction". It's "irrelevant." As in, "Jane's objection is irrelevant because that power never crosses the boundary."
I've repeatedly explained that in every single equation I've derived, more power is radiated from hot to cold than vice versa. So my solution doesn't violate the second law of thermodynamics (or the first).
And this is where YOU are mis-stating what is meant by "net". You say "more" goes from hot to cold, but you have also been claiming that SOME goes from cold to hot. ... [Jane Q. Public, 2015-03-19]
Exactly! Because that doesn't violate the second law of thermodynamics. But ignoring the power passing through a boundary around the source violates the first law of thermodynamics.
... But what you're not getting is: given the nature of the experiment, that would be creating energy from nothing. You are increasing the thermodynamic energy of a hotter body by transferring heat to it from a colder body or bodies. And I'm not sorry to tell you: nature doesn't work that way. ... [Jane Q. Public, 2015-03-19]
Jane, do you agree that the way to tell if an equation is "creating energy from nothing" is to see if it satisfies the first law of thermodynamics, which is "conservation of energy"?
If your answer is no... how do you tell if an equation is creating energy from nothing?
If your answer is yes... that's why I've repeatedly asked you to write down an energy conservation equation for a boundary around the source without wrongly "cancelling" terms. Jane/Lonny Eachus adamantly refuses to take the very first step in applying the first law of thermodynamics to this problem, but as usual he's willing to endlessly insist that he's right.
Jane, if you'd just take a few seconds to apply conservation of energy to this problem, you'd see that your solution violates conservation of energy. That's the law which tells us energy isn't created from nothing, so it's extremely ironic that you keep refusing to take that very first step and yet continue to accuse me of creating energy from nothing, after I've repeatedly asked you to please write down an energy conservation equation for a boundary around the source without wrongly "cancelling" terms.
... Your statement is a contradiction. Whether you claim it is a "raising" of energy of the warmer body, or "less loss" from the warmer body, the only other input power is the same. So you end up with a "hotter" hot body. But if your hot body is hotter, then its radiative output CHANGES, and so then does the temperature of the colder body, and you have created a feedback loop, not a new equilibrium. As I have already mentioned, you don't get to do that. You're adding energy from nowhere. ... [Jane Q. Public, 2015-03-19]
See above. If you want to prove that someone is "adding energy from nowhere" then you need to write down an energy conservation equation for a boundary around the source without wrongly "cancelling" terms.
If you ever find it in your heart to take those few seconds, you'll find that a new equilibrium (i.e. steady-state constant temperatures) is reached, exactly as I've repeatedly told you. Once again, the enclosed source temperature doesn't warm above 235F. Once it reaches that point, power in = power out, so the energy inside the boundary doesn't change. Thus the source reaches a new steady-state condition, where temperatures are constant.
Again, the universe is safe.
... A given input energy is only going to raise a body of given properties to a certain maximum temperature. ... [Jane Q. Public, 2015-03-19]
No, because "conservation of energy" says that power in = power out through any boundary where nothing inside is changing. Thus, both power flowing in the boundary over some time period (which Jane calls "input energy") and power flowing out of that boundary are required to determine the steady-state temperature of a body of given properties.
Again, warming the chamber walls is like partially closing the drain on a bathtub where water is flowing in at a constant rate. This raises the bathtub water level simply by reducing the water flow out. In exactly the same way, a source heated with constant electrical power warms when the chamber walls are warmed because that reduces the net power out.
Pretending that we only need to know the power flowing in and not the power flowing out is like pretending we only need to know a bathtub's faucet flow rate to determine the steady-state water level in the bathtub, and it doesn't matter if the drain is open or closed.
... It doesn't matter whether that energy is electricity or cow farts. Any other assertion is... well... hot air. ... [Jane Q. Public, 2015-03-19]
Jane, I just finished explaining that it doesn't matter if the energy is electricity or kerosene. I didn't see the point of addressing your "friction from a horse's ass" observation because that didn't seem productive, but I hoped it would be clear from my response that "horse ass friction" heating power would be treated exactly the same as electrical or kerosene heating power.
Sadly, once again I seem to have overestimated you. So I'll be more explicit.
I'm not saying the power source matters. Whether you're using an electrical source or a kerosene heater or "horse ass friction" or cow farts, the important point is that required heating power (electrical or kerosene) is zero if the chamber walls are at the same temperature as the heat source.
That's not true for "radiative power out", as I've explained ad nauseum. That's because "radiative power out" doesn't depend on the chamber wall temperature. But that's different than "heating power" (electrical or kerosene or "horse ass friction" or cow farts) which does depend on the chamber wall temperature. "Heating power" tells you how much electricity or kerosene you'd need to keep the source at a certain temperature, given the temperature of the chamber walls.
One way to check your solution is to make sure that your equation for heating power (electrical or kerosene or "horse ass friction" or cow farts) agrees that no heating power is necessary if the chamber walls are at the same temperature as the heat source. My equations have all passed that check. Jane's mistaken equation doesn't.