In all that time, did you ever consider 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?
We now insert our hollow sphere (somehow, suddenly and magically, it doesn't matter, this is assumed) which fully encloses the heat source. It is 7mm away from the heat source, and it is 7mm away from the wall. And we let things come back up to radiative steady-state.
And now, to do this properly, we must make a bit of a mental leap, which may be difficult for some people: 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).
This is a place where "thermodynamic thinking" will mess you up. Some people will insist that the TOTAL heat transfer must take place between EACH object. But that is simply not true. This was CLUE #3: a quote from a heat transfer engineering textbook about how "thermodynamic thinking" will lead one astray. [Jane Q. Public, 2014-09-10]
As I said, in the unlikely event that you wrote down equations, they'd violate conservation of energy. Thermodynamic thinking like this leads one back to reality, not astray. Draw a boundary inside the inner surface of the enclosing shell at your steady-state values. Since nothing inside that boundary is changing, power in = power out. But that's completely impossible. Your solution violates conservation of energy, as predicted.
So I predict that Jane's answer won't include any equations that could be used to calculate the enclosed source temperature. Instead, he'll probably grace us with another lengthy, incoherent rant about "problems" in my analysis which are (as usual) too vague to be expressed in equations. In the extremely unlikely event that Jane musters up the courage and competence to actually write down an equation that could be used to calculate the enclosed source temperature, it will almost certainly violate conservation of energy.
... Slashdot has a time limit on these old threads. If you don't post the rest by tomorrow, they will likely close the thread and archive it. I don't know the exact time limit but I have given you plenty of time already, and overly indulged you, but that is ending now. You stated yourself, just above, that it is not difficult to do.... If this thread is archived before you post the last bit of your supposed refutation (you still have plenty of time), I am going to declare you a fraud and a failure.... [Jane Q. Public, 2014-09-09]
After this thread is closed, this conversation can continue here.
Just so we are absolutely clear on what your claim is: starting at the agreed-upon initial conditions, heat source at 150F, when a hollow sphere is suddenly inserted into the chamber, completely surrounding the heat source, of the specified dimensions, then when allowed to reach steady-state the actual temperature of the heat source is 234.1 degees F.
Did I summarize that accurately enough? I don't want to re-hash the initial conditions we agreed upon. I still agree with them.
We will most certainly have to disagree on that, because it's wrong. That equation is for finding Q, the net heat transfer, which is not "equal" to power at all. It is energy in Joules.[Jane Q. Public, 2014-09-09]
No, Jane. I linked to Wikipedia's equation for radiative heat transfer, which is in Watts, not Joules. You can verify this by noticing the "dot" over the heat transfer "Q" on the left hand side of that equation. In physics-speak, a "dot" means a "time derivative" so that equation is in units of power (Watts). Or you could've checked the units on the right hand side, and verified that they're also in units of Watts, just like I said.
... So where is your final answer for the temperature of the heat source at stead-state? THAT was what you said you were calculating, so where is it?... [Jane Q. Public, 2014-09-09]
The final answer for the enclosed source at steady-state is 385.4 K (234.1 F). Anyone with a calculator could have verified this based on my comment yesterday.
... How could I possibly be "wrong"? I'm not doing anything. This is YOUR claim, not mine.... [Jane Q. Public, 2014-09-09]
Your claim that the source doesn't warm after the passive plate is added is wrong.
... Why should I do that? YOU said you were going to refute Latour. It wasn't my claim. You got partway through, now you refuse to finish, and you're trying to blame ME somehow? How do you figure?... [Jane Q. Public, 2014-09-09]
The final answer for the enclosed source at steady-state is 385.4 K (234.1 F). Anyone with a calculator could have verified this based on my comment yesterday.
... Hahaha! I've been WAITING for you to show me how this is done. I've asked you about five times now to show me. What are you waiting for? I want you to show us how you did what you claimed you have already done -- refute Latour -- so I, and anyone else who reads this later, can check your work.... Here's your incentive: if you can actually, successfully complete a refutation of Latour, and show us, and it checks out, I will be happy to declare to everyone that I was wrong and you were right about that issue. You have my word. I will shout it out loud. I'll admit it here on Slashdot and even open a Twitter account and post it there.... I have said what I have to say, unless and until you decide to post the rest of YOUR refutation of Latour. if I have to finish your problem for you, using YOUR methods, I'm still going to declare you a failure, regardless of whether the answer turns out to be correct. Because YOU claimed you could do it. So show us. [Jane Q. Public, 2014-09-09]
The final answer for the enclosed source at steady-state is 385.4 K (234.1 F). Anyone with a calculator could have verified this based on
As before, that net radiative power is described by Wikipedia’s equation which accounts for areas and view factors. [Dumb Scientist]
... You say you're using the equation for radiative power, when you're linking to the equation for heat transfer. We already know what the equation for radiative power is: (epsilon)(sigma)T^4. [Jane Q. Public, 2014-09-09]
And then:
Once again, we'll obviously have to agree to disagree about the net heat transfer between two gray surfaces. [Dumb Scientist]
What the HELL are you talking about? I understand the equation from Wikipedia. I just happened to mention that you called it a power equation rather than a heat transfer equation. THAT IS ALL. [Jane Q. Public, 2014-09-09]
We'll obviously have to agree to disagree that I explicitly used the equation for net radiative power, and linked to an equation described as: "The radiative heat transfer from one surface to another is equal to the radiation entering the first surface from the other, minus the radiation leaving the first surface."
We've agreed that net radiative power is power out minus power in through a boundary, but we'll obviously have to agree to disagree that Wikipedia's radiative heat transfer is "equal" to net radiative power.
... THEN I gave you an equation for radiant emittance: (epsilon)(sigma)T^4, and you called it a "heat transfer" equation having something to do with 0K black bodies, which is simply false.... [Jane Q. Public, 2014-09-09]
Again, we'll obviously have to agree to disagree that I explicitly used the equation for net radiative power (or net heat transfer). If I hadn't, it might make sense for Jane to say "We already know what the equation for radiative power is: (epsilon)(sigma)T^4."
Again, we'll obviously have to agree to disagree that I explicitly used the equation for net radiative power (in Watts). If I hadn't, it might make sense for Jane to say we already know that equation is the equation for radiant emittance (in W/m^2).
Onceagain, if I had explicitly used the equation for net radiative power, Jane's equation would only be valid for net radiative power (or net heat transfer) to a 0K blackbody. But I've obviouslyfailed to explain net radiative power (or net heat transfer) between two gray surfaces, so we'll have to agree to disagree once again.
... Now, when I simply pointed out these apparent MISTAKES in terminology to you, in order to try to keep things straight, you're throwing a fit. Well, don't try to blame this on me. I was just explaining why the things YOU have been saying lead to confusion. I will not apologize for simply trying to
Once again, we'll obviously have to agree to disagree about the net heat transfer between two gray surfaces.
Again, you seem to be asserting that Jane's equation should be used instead of Wikipedia's equation. Is that the case? If so, all you need to do to catch up is to list the values you'll plug into that equation, like I did. This would only take a few minutes. If you're confused and need help, just ask.
No, that's my entire point. I already described my physics. If you need to see my final numerical answer before you can judge my method, then you're not actually judging my method based on its physics.
Ironically, you actually are judging my method based on its physics, which is actually a step forward:
I just want to make it very clear why I object to the way you ask for agreement, all the while throwing in ambiguities. You say you're using the equation for radiative power, when you're linking to the equation for heat transfer. We already know what the equation for radiative power is: (epsilon)(sigma)T^4. [Jane Q. Public, 2014-09-09]
Onceagain, your equation is only for net radiative power (or net heat transfer) to a 0K blackbody. But I've obviouslyfailed to explain net radiative power (or net heat transfer) between two gray surfaces, so we'll have to agree to disagree.
But this is good. You're actually judging my method based on its physics! I'm proud of you, Jane!
You seem to be asserting that Jane's equation should be used instead of Wikipedia's equation. Is that the case? If so, all you need to do to catch up is to list the values you'll plug into that equation, like I did. This would only take a few minutes. If you're confused and need help, just ask.
... Where is your method in action? Is there an answer in there somewhere? You told me you were going to calculate the temperature of the heat source at steady-state. This is utter nonsense. I simply asked you for an explanation of how you calculated the figure you stated (long) before, after we agreed on the nature of the problem and the initial conditions.... [Jane Q. Public, 2014-09-08]
Once again, you've seen my method in action from start to finish. I've repeatedly asked if we can agree on that method before posting my final numerical answer. That's because I think you deserve a chance to show that you're capable of judging my method based on its physics, as opposed to reflexively objecting if my numerical answer contradicts the PSI Sky Dragon Slayers.
I haven't even tried to calculate an answer yet. I won't know if I agree with your method until I see it. In action, that is. [Jane Q. Public, 2014-09-08]
You've seen my method from start to finish. If you're capable of judging my method based on its physics, why won't you know if you agree with my method until you see my final numerical answer? For instance, suppose I told you that my final numerical answer agrees with the PSI Sky Dragon Slayers. Would that make you agree with my method's physics? In that case, would you really be agreeing with my method, or agreeing with the answer you want to hear?
If you won't know if you agree with my method until you see my final numerical answer, you're depriving yourself of this chance to demonstrate your intellectual integrity.
Alternatively, you could finally explain your own method of solving for the enclosed source temperature.
... I haven't calculated a solution yet. And THAT is largely due to what I clearly stated before: I have been busy, and don't have a lot of time to devote to this right now. I've been trying to squeeze in what I could, around work and other obligations.... [Jane Q. Public, 2014-09-08]
Since it's important to agree on the equations before plugging in values, all you have to do to describe your method is to state the equation you're using, and state the values you'll plug in. This would only take about five minutes. I know because that's what I did below.
... I have explained several times now that these Sage equations are not exactly straightforward and easy to read. I have been doing my own calculations in a clear and straightforward manner, making them as easy to read as possible. You really expect me to read this stuff?... [Jane Q. Public, 2014-09-08]
Once again, I'm sorry. I take full responsibility. I've changed the formatting so that each value being plugged in is on its own line. Does that make it more readable? I've also added some comments to the code which might help you understand it:
Now that we've agreed on the inner shell temperature of ~149.9F, let's take the last step. Calculate the enclosed source temperature.
Draw a boundary just inside the inner surface of the enclosing shell. Because nothing in the boundary is changing with time, power in = power out. The same constant electrical power flows in as before the shell was added. Net radiative power flows out from the source to the enclosing shell's inner surface.
I haven't even tried to calculate an answer yet. I won't know if I agree with your method until I see it. In action, that is. [Jane Q. Public, 2014-09-08]
Once again, you've already seen my method. I just described my entire method start to finish once again because that's what you demanded:
... 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]
See? Same shit different day. You won't sit down and do the calculations start-to-finish, instead you do one small part, then start indulging in your hallmark game of out-of-context he-said, she-said, toss in a straw-man, then claim it's all proved.... It's simply another illustration of the depths of hand-waving you will go to, rather than actually doing all the calculations on the actual experiment from start to finish. All you're doing is tossing in more straw-men and irrelevancies. You won't do the actual experiment. The only reasonable conclusion to be drawn here is that you won't do it because you know you're wrong. [Jane Q. Public, 2014-08-30]
I was worried that Jane was just trolling, and had no intention of ever acknowledging my method even if I described them from start-to-finish. Now that I've described my method from start-to-finish and Jane is pretending that he hasn't seen my method "in action" it seems like my worries came true.
Jane, if you won't do a single, solitary calculation of your own, could you at least please stop pretending that you haven't seen my method from start to finish? Here's my last step again:
Now that we've agreed on the inner shell temperature of ~149.9F, let's take the last step. Calculate the enclosed source temperature.
Draw a boundary just inside the inner surface of the enclosing shell. Because nothing in the boundary is changing with time, power in = power out. The same constant electrical power flows in as before the shell was added. Net radiative power flows out from the source to the enclosing shell's inner surface.
#Completely surrounded by shell with finite conductivity.
var('sigma T_c T_h A_c A_h F_hc power epsilon_h epsilon_c')
eq1 = power == sigma*(T_h^4 - T_c^4)/((1-epsilon_h)/(epsilon_h*A_h) + 1/(A_h*F_hc) + (1-epsilon_c)/(epsilon_c*A_c))
soln4 = solve(eq1.subs(T_c=338.629929346551,power=15028.4258648090,sigma=5.670373e-8,epsilon_h=0.11,epsilon_c=0.11, F_hc=1, A_h=510.064471909788, A_c=511.185932522526),T_h)
soln4[0].rhs().n()
... Please explain what calculations you are using where, because I find it hard to tell the Sage-formatted calculations apart. [Jane Q. Public, 2014-09-08]
The first line "var('sigma..." declares my variables.
The line "eq1 = power == sigma..." is my "power in = power out" equation using Wikipedia's equation for net radiative power.
The next line plugs in
Now that we've agreed on the inner shell temperature of ~149.9F, let's take the last step. Calculate the enclosed source temperature.
Draw a boundary just inside the inner surface of the enclosing shell. Because nothing in the boundary is changing with time, power in = power out. The same constant electrical power flows in as before the shell was added. Net radiative power flows out from the source to the enclosing shell's inner surface.
#Completely surrounded by shell with finite conductivity.
var('sigma T_c T_h A_c A_h F_hc power epsilon_h epsilon_c')
eq1 = power == sigma*(T_h^4 - T_c^4)/((1-epsilon_h)/(epsilon_h*A_h) + 1/(A_h*F_hc) + (1-epsilon_c)/(epsilon_c*A_c))
soln4 = solve(eq1.subs(T_c=338.629929346551,power=15028.4258648090,sigma=5.670373e-8,epsilon_h=0.11,epsilon_c=0.11, F_hc=1, A_h=510.064471909788, A_c=511.185932522526),T_h)
soln4[0].rhs().n()
... Please explain what calculations you are using where, because I find it hard to tell the Sage-formatted calculations apart. [Jane Q. Public, 2014-09-08]
The first line "var('sigma..." declares my variables.
The line "eq1 = power == sigma..." is my "power in = power out" equation using Wikipedia's equation for net radiative power.
The next line plugs in all the relevant variables and solves it for the enclosed source temperature T_h.
The last line displays the answer.
Because you've seemed to disagree with my method. That's why I've described my method for calculating the enclosed source temperature from start to finish. Before I post that final answer, can we agree with my method? If not, could you please describe your method?
Now that we've agreed on the inner shell temperature of ~149.9F, let's take the last step. Calculate the enclosed source temperature.
Draw a boundary just inside the inner surface of the enclosing shell. Because nothing in the boundary is changing with time, power in = power out. The same constant electrical power flows in as before the shell was added. Net radiative power flows out from the source to the enclosing shell's inner surface.
#Completely surrounded by shell with finite conductivity.
var('sigma T_c T_h A_c A_h F_hc power epsilon_h epsilon_c')
eq1 = power == sigma*(T_h^4 - T_c^4)/((1-epsilon_h)/(epsilon_h*A_h) + 1/(A_h*F_hc) + (1-epsilon_c)/(epsilon_c*A_c))
soln4 = solve(eq1.subs(T_c=338.629929346551,power=15028.4258648090,sigma=5.670373e-8,epsilon_h=0.11,epsilon_c=0.11, F_hc=1, A_h=510.064471909788, A_c=511.185932522526),T_h)
soln4[0].rhs().n()
... Please explain what calculations you are using where, because I find it hard to tell the Sage-formatted calculations apart. [Jane Q. Public, 2014-09-08]
The first line "var('sigma..." declares my variables.
The line "eq1 = power == sigma..." is my "power in = power out" equation using Wikipedia's equation for net radiative power.
The next line plugs in all the relevant variables and solves it for the enclosed source temperature T_h.
The last line displays the answer.
So I've described my method for calculating the enclosed source temperature from start to finish. Before I post that final answer, can we agree with my method? If not, could you please describe your method?
On general principle, yes. When all factors are considered, this is true. I haven't disagreed with this general principle, and at this point I'm only really interested in seeing the rest of your calculations. Please explain what calculations you are using where, because I find it hard to tell the Sage-formatted calculations apart. [Jane Q. Public, 2014-09-08]
In order to explain what calculations I'm using, we have to first agree on the fundamental principle all my calculations are based on.
I'm glad we agree that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes.
Notice that this general principle applies to all systems, even if they're at different temperatures or out of (thermal/radiative) equilibrium.
Now suppose that nothing inside that boundary is changing with time. Since this includes the energy inside that boundary, the rate at which energy inside the boundary changes is zero. This means power in = power out through any boundary where nothing inside that boundary is changing with time.
If we can agree so far, just say "yes" and ignore the rest of this comment. Then we can move on to the final step, which is calculating the enclosed source temperature.
If we can't agree, here's why we first need to agree that power in = power out through any boundary where nothing inside that boundary is changing with time.
... a simple power-in = power-out view is not always the right answer.... it shows how power-in = power-out calculations can easily mislead. [Jane Q. Public, 2014-09-07]
How could it mislead? Why won't it work? As long as nothing inside the boundary is changing, a simple power in = power out view is always the right answer.
... 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.... power-in = power-out is not necessarily true, and in fact that is probably a very rare exception. Therefore, you aren't going to prove anything with this approach. I wanted to stop you before you wasted more of your time. [Jane Q. Public, 2014-09-07]
How is it doomed to fail? How could it give very misleading results? As long as nothing inside the boundary is changing, power in = power out is necessarily true.
... it does not translate directly into power in = power out at a boundary just inside the cavity surface. It most certainly does not if the bodies are not in thermal equilibrium, which again I must point out this system is not in.... [Jane Q. Public, 2014-09-07]
No, energy is conserved even when the bodies aren't in thermal equilibrium. As long as nothing inside the boundary is changing, power in = power out.
... energy does not have to be conserved between two bodies at different temperatures. That was what Incorpora was saying in his book.... [Jane Q. Public, 2014-09-07]
Since we've had to agree to disagree about the definition of the term "equilibrium" (whether radiative or thermal), it's necessary to agree on the fundamental principle of energy conservation using a simple statement that doesn't use the term "equilibrium" (of any kind).
Wait. Are you claiming that the enclosing hollow sphere is NOT at radiative equilibrium with its surroundings? [Jane Q. Public, 2014-09-08]
No. I'm saying that since we've had to agree to disagree about the definition of the term "equilibrium" (whether radiative or thermal), it's necessary to agree on the fundamental principle of energy conservation using a simple statement that doesn't use the term "equilibrium" (of any kind).
Once again, can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
... there is definitely no thermal equilibrium, and without at least radiative equilibrium, there is no equilibrium at all and we might as well just stop again right here.... no thermal equilibrium... [Jane Q. Public, 2014-09-08]
That's why I'm trying to see if we can agree on a general principle that applies even to systems that aren't in thermal equilibrium.
... why the hell are you trying to blame me for being confused? The condition you described is impossible, so how do you expect me to know what "equilibrium" you mean?... [Jane Q. Public, 2014-09-04]
Since we've had to agree to disagree about the definition of the term "equilibrium" (whether radiative or thermal), it's necessary to agree on the fundamental principle of energy conservation using a simple statement that doesn't use the term "equilibrium" (of any kind).
... I very definitely did NOT mean net power at radiative steady-state represents zero energy flow.... [Jane Q. Public, 2014-09-08]
Then our statements aren't equivalent, which means there's an innocent misunderstanding here. To help resolve this miscommunication, could we please agree on a general principle that applies to all systems, even if they're not in thermal or radiative equilibrium?
Once again, can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
... there is definitely no thermal equilibrium, and without at least radiative equilibrium, there is no equilibrium at all and we might as well just stop again right here.... no thermal equilibrium... [Jane Q. Public, 2014-09-08]
That's why I'm trying to see if we can agree on a general principle that applies even to systems that aren't in thermal equilibrium.
... why the hell are you trying to blame me for being confused? The condition you described is impossible, so how do you expect me to know what "equilibrium" you mean?... [Jane Q. Public, 2014-09-04]
Since we've had to agree to disagree about the definition of the term "equilibrium" (whether radiative or thermal), it's necessary to agree on the fundamental principle of energy conservation using a simple statement that doesn't use the term "equilibrium" (of any kind).
... I very definitely did NOT mean net power at radiative steady-state represents zero energy flow.... [Jane Q. Public, 2014-09-08]
Then our statements aren't equivalent, which means there's an innocent misunderstanding here. To help resolve this miscommunication, could we please agree on a general principle that applies to all systems, even if they're not in thermal or radiative equilibrium?
Once again, can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
Since you keep place qualifiers on energy conservation, your wording isn't equivalent to mine because my statement applies even for systems that aren't in radiative equilibrium.
But that should not matter because we are discussing a system in radiative equilibrium.... [Jane Q. Public, 2014-09-08]
Really? Since when?
... There is no thermal equilibrium. Period. None. There MAY (and eventually would) arise a condition of radiative equilibrium for the (enclosing, passive, however you want to describe it) plate. But the other objects (heat source and chamber walls) do not meet this criteria because they are heated/cooled by means that may be other than radiative. "The system" is not in radiative equilibrium.... [Jane Q. Public, 2014-09-03]
... I don't necessarily have a problem with a broader definition, but I prefer to stick to things that are pertinent to this discussion. So can we move on? [Jane Q. Public, 2014-09-08]
Since Jane's insisted that the system is not in radiative equilibrium, it's necessary to agree on a general principle that applies even for systems that aren't in radiative equilibrium. Then we can move on.
Can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
I'm not sure I agree with your wording. It could easily be misinterpreted to mean something it does not. I agree that power in minus power out of your boundary equals power through that boundary, which at radiative steady-state represents a constant rate of energy flow through that boundary. [Jane Q. Public, 2014-09-08]
I prefer my wording, which I think most people would agree is an equivalent statement regarding your drawn boundary, but (in my opinion) is less open to misunderstanding. I agree that power into your boundary minus power out of your boundary equals the power through the boundary, which at radiative equilibrium is equivalent to a constant rate of energy flow through that boundary.... [Jane Q. Public, 2014-09-08]
Your wording could easily be misinterpreted to mean a constant other than zero. Didn't you mean that net power through that boundary at radiative steady-state represents zero energy flow through that boundary? If not, our misunderstanding is much more fundamental than I first thought.
This principle applies even for systems that are changing, and even for systems that aren't in radiative equilibrium. Again, can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
How could my wording be easily misinterpreted? Once again, this fundamental principle applies even for systems that are changing, and even for systems that aren't at radiative steady-state.
I prefer my wording, which I think most people would agree is an equivalent statement regarding your drawn boundary, but (in my opinion) is less open to misunderstanding. I agree that power into your boundary minus power out of your boundary equals the power through the boundary, which at radiative equilibrium is equivalent to a constant rate of energy flow through that boundary. Were you trying to say something else? If not, let's please move on. [Jane Q. Public, 2014-09-08]
Once again, this principle applies even for systems that are changing, and even for systems that aren't in radiative equilibrium. Again, that's why I disagree with your claim that:
... energy does not have to be conserved between two bodies at different temperatures. That was what Incorpora was saying in his book.... [Jane Q. Public, 2014-09-07]
Since you keep place qualifiers on energy conservation, your wording isn't equivalent to mine because my statement applies even for systems that aren't in radiative equilibrium.
Once again, can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes? Even for systems that are changing? Even for systems that aren't in radiative equilibrium?
Given your assumptions so far, I will not dispute your calculation of the temperature of the inner surface of the enclosing plate. Please continue your calculations, as a reply to my other comment, so we can continue this exchange in a linear fashion. [Jane Q. Public, 2014-09-08]
I'm glad you don't dispute the enclosing shell's inner temperature of ~149.9F, but we should agree on my assumption that energy is conserved before proceeding.
Can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
I'm not sure I agree with your wording. It could easily be misinterpreted to mean something it does not. I agree that power in minus power out of your boundary equals power through that boundary, which at radiative steady-state represents a constant rate of energy flow through that boundary. [Jane Q. Public, 2014-09-08]
How could my wording be easily misinterpreted? Once again, this fundamental principle applies even for systems that are changing, and even for systems that aren't at radiative steady-state.
Again, can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
Maybe an analogy would help. The rate at which water flows into a bathtub minus the water flowing out equals the rate at which water in the bathtub changes. No qualifications needed.
If we can't agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes, could you please explain exactly why we can't agree on this?
Obviously at radiative equilibrium energy between objects in the system is being transferred at a constant rate. [Jane Q. Public, 2014-09-07]
This principle applies even for systems that are changing, and even for systems that aren't in radiative equilibrium.
Again, can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
... Energy of an entire system is conserved. It need not be conserved between individual elements of that system. That's what I've been saying.... Heat transfer between two bodies that are not at thermal equilibrium does not conserve energy between those two bodies.... [Jane Q. Public, 2014-09-07]
Can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
The reason my "dirt simple" calculation was wrong, as any reader of this exchange should be able to tell (and so should you have), that I misunderstood what your power figure represented. [Jane Q. Public, 2014-09-07]
I'm very sorry for not being more clear. I take full responsibility.
It absolutely does translate directly into power in = power out at a boundary just inside the cavity surface when everything inside that boundary isn't changing. In that case, the rate at which energy changes inside the boundary equals zero, which means power in = power out.
Are you also then presuming that power transferred from the outer surface of the enclosing plate to the chamber walls is the same as the power transferred from the heat source to that plate? [Jane Q. Public, 2014-09-07]
Anything else would violate conservation of energy. But we still have one more step before the net power transferred from the heat source to that enclosing plate becomes relevant.
No, of course I got the same answer, given your assumption that power-in = power-out: 149.59F. [Jane Q. Public, 2014-09-07]
Excellent. And can we also agree about the enclosing aluminum shell's final inner steady-state temperature?
Now to calculate the enclosing shell's inner temperature. At steady-state, power in = power out through some boundary. This time, draw the boundary within the enclosing shell. Again, constant electrical power flows in. But all the other boundaries we drew were in vacuum, so heat transfer was by radiation. This time the boundary is inside aluminum, so heat transfer out is by thermal conduction.
electricity = k*(T_h - T_c)/x (Eq. 4)
The shell's thickness "x" is 1mm, and the thermal conductivity "k" of aluminum is 215 W/(m*K). We just found that:
Outer shell temperature: 338.629792627809 K (149.864 F).
So:
Inner shell temperature: 338.629929668632 K (149.864 F).
Of course, that's a flat plate approximation of heat conduction through a spherical shell, which is derived here. That more accurate equation yields:
#Calculate enclosing shell's inner temperature.
var('T_c T_h power k r_c1 r_c2')
eq2 = power == 4*pi*k*r_c1*r_c2*(T_h - T_c)/(r_c2 - r_c1)
soln3 = solve(eq2.subs(T_c=338.629792627809,power=15028.4258648090,k=215,r_c1=6.378,r_c2=6.379),T_h)
soln3[0].rhs().n()
Inner shell temperature: 338.629929346551 K (149.864 F).
Now for the final step. Calculate the steady-state temperature of the enclosed heated plate (Jane's "source").
... My point was that it does not translate directly into power in = power out at a boundary just inside the cavity surface. It most certainly does not if the bodies are not in thermal equilibrium, which again I must point out this system is not in.... [Jane Q. Public, 2014-09-07]
It absolutely does translate directly into power in = power out at a boundary just inside the cavity surface when everything inside that boundary isn't changing. In that case, the rate at which energy changes inside the boundary equals zero, which means power in = power out.
... energy does not have to be conserved between two bodies at different temperatures. That was what Incorpora was saying in his book.... [Jane Q. Public, 2014-09-07]
No. Energy is always conserved. Always.
Once again, the next step is calculating the enclosing shell's final outer steady-state temperature once it's added. This should have only taken you a few minutes to calculate. Did you get a different answer than me?
Once again, energy is conserved, which means that if you draw a boundary around some system (like the heated plate), power going in minus power going out equals the rate at which energy inside that boundary changes. At steady-state, that rate is zero because the system doesn't change. So at steady-state, power in = power out.
Perhaps it would be more informative if you calculate ENERGY in and ENERGY out, since that is what is actually conserved. You seem to keep forgetting that (A) power is a RATE, not a unit of energy, and (B) we are not at thermal equilibrium.... [Jane Q. Public, 2014-09-07]
No. Once again, I said that power going in minus power going out equals the rate at which energy inside that boundary changes. Once again, that rate is zero if the system doesn't change.
... are you suggesting that if I hollowed out enough of a mountain to make a hollow rock sphere (assume the rock is diffuse gray body) 1000 m diameter, suspended a 1m dia. sphere of the same rock in the center, and evacuated the cavity: the inner sphere is going to get much hotter than the surrounding rock? Power in = power out would seem to demand that very thing. [Jane Q. Public, 2014-09-07]
Using what equation? A month ago I said we could use Wikipedia’s equation which includes areas, and later mentioned view factors. I've been using this equation to calculate the net heat transfer between the heated plate (Jane's "source") and the chamber walls.
If that's the equation Jane is thinking about using to take account of the view factor, Jane should ponder what happens in that equation when the two temperatures in that equation are equal. As I've repeatedly said, the net heat transfer goes to zero when the two temperatures are equal. Regardless of their areas.
... a simple power-in = power-out view is not always the right answer.... it shows how power-in = power-out calculations can easily mislead. [Jane Q. Public, 2014-09-07]
... The black body example I gave shows why your "energy conservation just inside the surface" won't work. Aside from just "view factor" and a few other things, a certain amount of the power in (often a very significant amount) just ends up going right back out, but you often don't see that in the formulas....
Slashdot Mirror
In all that time, did you ever consider 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?
As I said, in the unlikely event that you wrote down equations, they'd violate conservation of energy. Thermodynamic thinking like this leads one back to reality, not astray. Draw a boundary inside the inner surface of the enclosing shell at your steady-state values. Since nothing inside that boundary is changing, power in = power out. But that's completely impossible. Your solution violates conservation of energy, as predicted.
Jane's obligations include continuing to spread misinformation about ocean acidification even after I've repeatedly debunked him.
So I predict that Jane's answer won't include any equations that could be used to calculate the enclosed source temperature. Instead, he'll probably grace us with another lengthy, incoherent rant about "problems" in my analysis which are (as usual) too vague to be expressed in equations. In the extremely unlikely event that Jane musters up the courage and competence to actually write down an equation that could be used to calculate the enclosed source temperature, it will almost certainly violate conservation of energy.
After this thread is closed, this conversation can continue here.
Yes, that summary is accurate enough.
No, Jane. I linked to Wikipedia's equation for radiative heat transfer, which is in Watts, not Joules. You can verify this by noticing the "dot" over the heat transfer "Q" on the left hand side of that equation. In physics-speak, a "dot" means a "time derivative" so that equation is in units of power (Watts). Or you could've checked the units on the right hand side, and verified that they're also in units of Watts, just like I said.
The final answer for the enclosed source at steady-state is 385.4 K (234.1 F). Anyone with a calculator could have verified this based on my comment yesterday.
Your claim that the source doesn't warm after the passive plate is added is wrong.
The final answer for the enclosed source at steady-state is 385.4 K (234.1 F). Anyone with a calculator could have verified this based on my comment yesterday.
The final answer for the enclosed source at steady-state is 385.4 K (234.1 F). Anyone with a calculator could have verified this based on
And then:
We'll obviously have to agree to disagree that I explicitly used the equation for net radiative power, and linked to an equation described as: "The radiative heat transfer from one surface to another is equal to the radiation entering the first surface from the other, minus the radiation leaving the first surface."
We've agreed that net radiative power is power out minus power in through a boundary, but we'll obviously have to agree to disagree that Wikipedia's radiative heat transfer is "equal" to net radiative power.
Again, we'll obviously have to agree to disagree that I explicitly used the equation for net radiative power (or net heat transfer). If I hadn't, it might make sense for Jane to say "We already know what the equation for radiative power is: (epsilon)(sigma)T^4."
Again, we'll obviously have to agree to disagree that I explicitly used the equation for net radiative power (in Watts). If I hadn't, it might make sense for Jane to say we already know that equation is the equation for radiant emittance (in W/m^2).
Once again, if I had explicitly used the equation for net radiative power, Jane's equation would only be valid for net radiative power (or net heat transfer) to a 0K blackbody. But I've obviously failed to explain net radiative power (or net heat transfer) between two gray surfaces, so we'll have to agree to disagree once again.
Once again, we'll obviously have to agree to disagree about the net heat transfer between two gray surfaces.
Again, you seem to be asserting that Jane's equation should be used instead of Wikipedia's equation. Is that the case? If so, all you need to do to catch up is to list the values you'll plug into that equation, like I did. This would only take a few minutes. If you're confused and need help, just ask.
No, that's my entire point. I already described my physics. If you need to see my final numerical answer before you can judge my method, then you're not actually judging my method based on its physics.
Ironically, you actually are judging my method based on its physics, which is actually a step forward:
Once again, your equation is only for net radiative power (or net heat transfer) to a 0K blackbody. But I've obviously failed to explain net radiative power (or net heat transfer) between two gray surfaces, so we'll have to agree to disagree.
But this is good. You're actually judging my method based on its physics! I'm proud of you, Jane!
You seem to be asserting that Jane's equation should be used instead of Wikipedia's equation. Is that the case? If so, all you need to do to catch up is to list the values you'll plug into that equation, like I did. This would only take a few minutes. If you're confused and need help, just ask.
Once again, you've seen my method in action from start to finish. I've repeatedly asked if we can agree on that method before posting my final numerical answer. That's because I think you deserve a chance to show that you're capable of judging my method based on its physics, as opposed to reflexively objecting if my numerical answer contradicts the PSI Sky Dragon Slayers.
You've seen my method from start to finish. If you're capable of judging my method based on its physics, why won't you know if you agree with my method until you see my final numerical answer? For instance, suppose I told you that my final numerical answer agrees with the PSI Sky Dragon Slayers. Would that make you agree with my method's physics? In that case, would you really be agreeing with my method, or agreeing with the answer you want to hear?
If you won't know if you agree with my method until you see my final numerical answer, you're depriving yourself of this chance to demonstrate your intellectual integrity.
Alternatively, you could finally explain your own method of solving for the enclosed source temperature.
Since it's important to agree on the equations before plugging in values, all you have to do to describe your method is to state the equation you're using, and state the values you'll plug in. This would only take about five minutes. I know because that's what I did below.
Once again, I'm sorry. I take full responsibility. I've changed the formatting so that each value being plugged in is on its own line. Does that make it more readable? I've also added some comments to the code which might help you understand it:
Now that we've agreed on the inner shell temperature of ~149.9F, let's take the last step. Calculate the enclosed source temperature.
Draw a boundary just inside the inner surface of the enclosing shell. Because nothing in the boundary is changing with time, power in = power out. The same constant electrical power flows in as before the shell was added. Net radiative power flows out from the source to the enclosing shell's inner surface.
Once again, you've already seen my method. I just described my entire method start to finish once again because that's what you demanded:
I was worried that Jane was just trolling, and had no intention of ever acknowledging my method even if I described them from start-to-finish. Now that I've described my method from start-to-finish and Jane is pretending that he hasn't seen my method "in action" it seems like my worries came true.
Jane, if you won't do a single, solitary calculation of your own, could you at least please stop pretending that you haven't seen my method from start to finish? Here's my last step again:
Now that we've agreed on the inner shell temperature of ~149.9F, let's take the last step. Calculate the enclosed source temperature.
Draw a boundary just inside the inner surface of the enclosing shell. Because nothing in the boundary is changing with time, power in = power out. The same constant electrical power flows in as before the shell was added. Net radiative power flows out from the source to the enclosing shell's inner surface.
As before, that net radiative power is described by Wikipedia’s equation which accounts for areas and view factors.
#Completely surrounded by shell with finite conductivity.
var('sigma T_c T_h A_c A_h F_hc power epsilon_h epsilon_c')
eq1 = power == sigma*(T_h^4 - T_c^4)/((1-epsilon_h)/(epsilon_h*A_h) + 1/(A_h*F_hc) + (1-epsilon_c)/(epsilon_c*A_c))
soln4 = solve(eq1.subs(T_c=338.629929346551,power=15028.4258648090,sigma=5.670373e-8,epsilon_h=0.11,epsilon_c=0.11, F_hc=1, A_h=510.064471909788, A_c=511.185932522526),T_h)
soln4[0].rhs().n()
The first line "var('sigma..." declares my variables.
The line "eq1 = power == sigma..." is my "power in = power out" equation using Wikipedia's equation for net radiative power.
The next line plugs in
Now that we've agreed on the inner shell temperature of ~149.9F, let's take the last step. Calculate the enclosed source temperature.
Draw a boundary just inside the inner surface of the enclosing shell. Because nothing in the boundary is changing with time, power in = power out. The same constant electrical power flows in as before the shell was added. Net radiative power flows out from the source to the enclosing shell's inner surface.
As before, that net radiative power is described by Wikipedia’s equation which accounts for areas and view factors.
#Completely surrounded by shell with finite conductivity.
var('sigma T_c T_h A_c A_h F_hc power epsilon_h epsilon_c')
eq1 = power == sigma*(T_h^4 - T_c^4)/((1-epsilon_h)/(epsilon_h*A_h) + 1/(A_h*F_hc) + (1-epsilon_c)/(epsilon_c*A_c))
soln4 = solve(eq1.subs(T_c=338.629929346551,power=15028.4258648090,sigma=5.670373e-8,epsilon_h=0.11,epsilon_c=0.11, F_hc=1, A_h=510.064471909788, A_c=511.185932522526),T_h)
soln4[0].rhs().n()
The first line "var('sigma..." declares my variables.
The line "eq1 = power == sigma..." is my "power in = power out" equation using Wikipedia's equation for net radiative power.
The next line plugs in all the relevant variables and solves it for the enclosed source temperature T_h.
The last line displays the answer.
Because you've seemed to disagree with my method. That's why I've described my method for calculating the enclosed source temperature from start to finish. Before I post that final answer, can we agree with my method? If not, could you please describe your method?
Now that we've agreed on the inner shell temperature of ~149.9F, let's take the last step. Calculate the enclosed source temperature.
Draw a boundary just inside the inner surface of the enclosing shell. Because nothing in the boundary is changing with time, power in = power out. The same constant electrical power flows in as before the shell was added. Net radiative power flows out from the source to the enclosing shell's inner surface.
As before, that net radiative power is described by Wikipedia’s equation which accounts for areas and view factors.
#Completely surrounded by shell with finite conductivity.
var('sigma T_c T_h A_c A_h F_hc power epsilon_h epsilon_c')
eq1 = power == sigma*(T_h^4 - T_c^4)/((1-epsilon_h)/(epsilon_h*A_h) + 1/(A_h*F_hc) + (1-epsilon_c)/(epsilon_c*A_c))
soln4 = solve(eq1.subs(T_c=338.629929346551,power=15028.4258648090,sigma=5.670373e-8,epsilon_h=0.11,epsilon_c=0.11, F_hc=1, A_h=510.064471909788, A_c=511.185932522526),T_h)
soln4[0].rhs().n()
The first line "var('sigma..." declares my variables.
The line "eq1 = power == sigma..." is my "power in = power out" equation using Wikipedia's equation for net radiative power.
The next line plugs in all the relevant variables and solves it for the enclosed source temperature T_h.
The last line displays the answer.
So I've described my method for calculating the enclosed source temperature from start to finish. Before I post that final answer, can we agree with my method? If not, could you please describe your method?
In order to explain what calculations I'm using, we have to first agree on the fundamental principle all my calculations are based on.
I'm glad we agree that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes.
Notice that this general principle applies to all systems, even if they're at different temperatures or out of (thermal/radiative) equilibrium.
Now suppose that nothing inside that boundary is changing with time. Since this includes the energy inside that boundary, the rate at which energy inside the boundary changes is zero. This means power in = power out through any boundary where nothing inside that boundary is changing with time.
If we can agree so far, just say "yes" and ignore the rest of this comment. Then we can move on to the final step, which is calculating the enclosed source temperature.
If we can't agree, here's why we first need to agree that power in = power out through any boundary where nothing inside that boundary is changing with time.
How could it mislead? Why won't it work? As long as nothing inside the boundary is changing, a simple power in = power out view is always the right answer.
How is it doomed to fail? How could it give very misleading results? As long as nothing inside the boundary is changing, power in = power out is necessarily true.
No, energy is conserved even when the bodies aren't in thermal equilibrium. As long as nothing inside the boundary is changing, power in = power out.
N
No. I'm saying that since we've had to agree to disagree about the definition of the term "equilibrium" (whether radiative or thermal), it's necessary to agree on the fundamental principle of energy conservation using a simple statement that doesn't use the term "equilibrium" (of any kind).
Once again, can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
That's why I'm trying to see if we can agree on a general principle that applies even to systems that aren't in thermal equilibrium.
Since we've had to agree to disagree about the definition of the term "equilibrium" (whether radiative or thermal), it's necessary to agree on the fundamental principle of energy conservation using a simple statement that doesn't use the term "equilibrium" (of any kind).
Then our statements aren't equivalent, which means there's an innocent misunderstanding here. To help resolve this miscommunication, could we please agree on a general principle that applies to all systems, even if they're not in thermal or radiative equilibrium?
Once again, can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
That's why I'm trying to see if we can agree on a general principle that applies even to systems that aren't in thermal equilibrium.
Since we've had to agree to disagree about the definition of the term "equilibrium" (whether radiative or thermal), it's necessary to agree on the fundamental principle of energy conservation using a simple statement that doesn't use the term "equilibrium" (of any kind).
Then our statements aren't equivalent, which means there's an innocent misunderstanding here. To help resolve this miscommunication, could we please agree on a general principle that applies to all systems, even if they're not in thermal or radiative equilibrium?
Once again, can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
Really? Since when?
Since Jane's insisted that the system is not in radiative equilibrium, it's necessary to agree on a general principle that applies even for systems that aren't in radiative equilibrium. Then we can move on.
Your wording could easily be misinterpreted to mean a constant other than zero. Didn't you mean that net power through that boundary at radiative steady-state represents zero energy flow through that boundary? If not, our misunderstanding is much more fundamental than I first thought.
Once again, this principle applies even for systems that are changing, and even for systems that aren't in radiative equilibrium. Again, that's why I disagree with your claim that:
Since you keep place qualifiers on energy conservation, your wording isn't equivalent to mine because my statement applies even for systems that aren't in radiative equilibrium.
Once again, can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes? Even for systems that are changing? Even for systems that aren't in radiative equilibrium?
I'm glad you don't dispute the enclosing shell's inner temperature of ~149.9F, but we should agree on my assumption that energy is conserved before proceeding.
How could my wording be easily misinterpreted? Once again, this fundamental principle applies even for systems that are changing, and even for systems that aren't at radiative steady-state.
Again, can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
Maybe an analogy would help. The rate at which water flows into a bathtub minus the water flowing out equals the rate at which water in the bathtub changes. No qualifications needed.
If we can't agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes, could you please explain exactly why we can't agree on this?
This principle applies even for systems that are changing, and even for systems that aren't in radiative equilibrium.
Again, can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
Can we agree that energy conservation means that power going in minus power going out through some boundary equals the rate at which energy inside that boundary changes?
I'm very sorry for not being more clear. I take full responsibility.
Anything else would violate conservation of energy. But we still have one more step before the net power transferred from the heat source to that enclosing plate becomes relevant.
Excellent. And can we also agree about the enclosing aluminum shell's final inner steady-state temperature?
Now to calculate the enclosing shell's inner temperature. At steady-state, power in = power out through some boundary. This time, draw the boundary within the enclosing shell. Again, constant electrical power flows in. But all the other boundaries we drew were in vacuum, so heat transfer was by radiation. This time the boundary is inside aluminum, so heat transfer out is by thermal conduction.
electricity = k*(T_h - T_c)/x (Eq. 4)
The shell's thickness "x" is 1mm, and the thermal conductivity "k" of aluminum is 215 W/(m*K). We just found that:
Outer shell temperature: 338.629792627809 K (149.864 F).
So:
Inner shell temperature: 338.629929668632 K (149.864 F).
Of course, that's a flat plate approximation of heat conduction through a spherical shell, which is derived here. That more accurate equation yields:
#Calculate enclosing shell's inner temperature.
var('T_c T_h power k r_c1 r_c2')
eq2 = power == 4*pi*k*r_c1*r_c2*(T_h - T_c)/(r_c2 - r_c1)
soln3 = solve(eq2.subs(T_c=338.629792627809,power=15028.4258648090,k=215,r_c1=6.378,r_c2=6.379),T_h)
soln3[0].rhs().n()
Inner shell temperature: 338.629929346551 K (149.864 F).
Now for the final step. Calculate the steady-state temperature of the enclosed heated plate (Jane's "source").
It absolutely does translate directly into power in = power out at a boundary just inside the cavity surface when everything inside that boundary isn't changing. In that case, the rate at which energy changes inside the boundary equals zero, which means power in = power out.
No. Energy is always conserved. Always.
Once again, the next step is calculating the enclosing shell's final outer steady-state temperature once it's added. This should have only taken you a few minutes to calculate. Did you get a different answer than me?
No. Once again, I said that power going in minus power going out equals the rate at which energy inside that boundary changes. Once again, that rate is zero if the system doesn't change.
No. I've repeatedly told you that power in = power out demands that an unheated inner sphere will be at exactly the same temperature as the chamber walls.
Using what equation? A month ago I said we could use Wikipedia’s equation which includes areas, and later mentioned view factors. I've been using this equation to calculate the net heat transfer between the heated plate (Jane's "source") and the chamber walls.
If that's the equation Jane is thinking about using to take account of the view factor, Jane should ponder what happens in that equation when the two temperatures in that equation are equal. As I've repeatedly said, the net heat transfer goes to zero when the two temperatures are equal. Regardless of their areas.