In the end, you signed a contract and are legally bound to continue to pay for almost any type of service inturruption.
Except that I didn't. When my cable was installed I signed a small receipt acknowledging that the tech had been there. I signed no contract.
That might have been an oversight on their part, but that doesn't matter.
Further, the KIND of contract that Comcast has customers sign is known in the legal industry as a "contract of adhesion". What that means is that it was a non-negotiable, take-it-or-leave-it "contract". The problem being that contract law assumes that every party is free to negotiate before signing.
So in many genuine, legal senses of the term, it's not a "real" contract anyway, and honest judges are required in principle to view them "with a jaundiced eye", and lean toward the customer when a dispute arises.
I'm not saying all judges are honest enough to do that, but they're supposed to.
And one more thing I would like to make very clear:
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.
In fact let's just face this directly, with no mincing of words:
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.
We are not AT thermal equilibrium, so that is a ridiculous straw-man argument.
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.
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.
YOU are disputing the Stefan-Boltzmann law. But it is a known physical law, and this is a textbook demonstration of it. You lose.
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.
You showed no such thing. Your calculations contradict themselves, and your methodology contradicts itself.
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.
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.
This is a simple requirement of the Stefan-Boltzmann law. The radiative power output of a given body does not depend on other nearby bodies. It's inherent in the law itself. And this is precisely where you are getting it wrong.
I find it highly amusing that you derive your own calculations from the Stefan-Boltzmann law, then deny that it is valid. Every time you try to squirm out of this you just contradict yourself again.
I am further amused that you find it "adorable" that you've been proven wrong. Be a man for a change and admit it. Or show us your own replacement for the Stefan-Boltmann law. You don't get to have it both ways.
Besides, 99.99% is not nearly reliable enough. (And besides, this number is misleading... probably outright false.)
According to calculations I did a year or two ago, in order for a "smart firearm" to be worthwhile and actually solved the problem for which is supposed to be designed, for modern arms, it needs to have AT LEAST three 9s behind the decimal point for true positives: 99.999%, and probably actually 4.
And that's assuming the stats are correct. What does that 99.99% represent? True positives? What is its rate at rejecting true negatives? After all, that's the entire purpose it was designed for.
Further yet: how long does the battery last? What is its success rate with a dead battery? Current battery tech is not capable of delivering 99.99% reliability because batteries go bad even on the shelf.
Well, I didn't interpret the article the same way you did. I thought the article was saying that you can be logical and still feel wonder. It wasn't saying that science-oriented people need to be religious, but rather that religious people should stop seeing them as somehow inhuman and unfeeling without a belief in their God.
Atheists will be in for a rude awakening when they die as they will realize that their belief was incomplete. Regardless, they can be just as good, (or as bad) as theists if they practice the golden rule.
Why would they be in for a "rude" awakening, when one would think that any awakening at all should be a pleasant surprise?
Further, as Sam Harris argues quite well, one need not be a theist to have moral values. Science + secular society are perfectly capable of agreeing upon ethical and moral rules, without resorting to theism.
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.
NO!!! I did not. I held the power constant, just as Spencer stipulated.
For a gray body, which you stipulated, radiant power out = (emissivity) * (S-B constant) * T^4. This is the Stefan-Boltzmann relation between radiant temperature of a gray body and its power output.
T is known: 150F or 338.71 K.
Solving for radiant power out we get 82.12 Watts/m^2. Times khayman80's stipulated area (510.065 m^2) = 41886.54 Watts.
It is this POWER that remains constant according to Spencer. Khayman80 himself asserted that "power in = power out". Therefore POWER IN = POWER OUT = 41886.54 Watts.
But because of the equation I showed above, which is a physical law, after the hollow sphere is inserted (which is COLDER than the heat source), nothing at the power source has changed. Emissivity is still the same. Power input is still 41886.54 Watts = radiant power output of 41886.54 Watts. Which (by the equation above) yields the same temperature.
I didn't assume the same temperature, I calculated it using known physical law.
ANYTHING ELSE is a direct violation of the Stefan-Boltzmann law.
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.
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.
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"?
It doesn't seem odd at all, because established science shows that his assertion that the temperature changes is wrong.
Considering that he is wrong, why should I find it odd that he said a wrong thing.
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. Spencer's stipulation. Therefore by the S-B relation, once everything comes up to radiative steady-state the input power and output power of the heat source are constant. There is no inconsistency here.
Further, because ALL the other surfaces are cooler than the heat source, ALL the net heat transfer is outward, because T(a)^4 - T(b)^4 is a positive number.
This is established science, and it doesn't depend on the incorrect opinions of either Spencer or yourself.
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.
You're misapplying your physics principles again. You're trying to introduce outside influences that the SIMPLE, UNREFUTABLE Stefan-Boltzmann relation says is ALWAYS true:
For a given gray body, its thermodynamic temperature is related ONLY to emissivity, radiant power output, and the S-B relation (emissivity)* (S-B constant) * T^4.
PERIOD. That's physics. And I repeat: given your OWN "draw a border around it" thermodynamic reasoning, the power input (whether it is electrical, chemical, or something else) must equal that output. That's physics.
You're trying to bring in energy from elsewhere, but it isn't relevant to this calculation AT ALL; it is erroneous thinking.
Power input is specified to be constant. Calculating the total power in initial conditions is, as I stated before, "dirt simple". Specified emissivity is known: 0.11. Temperature is known: 338.71K. Solving for the above we get 82.12 W/m^2.
We already have ALL the information needed to calculate this, given the Stefan-Boltzmann relation (above), relating these numbers. Nothing else is required, and in fact trying to introduce other factors is ERROR. That is what the accepted science says.
Since we CAN easily calculate that in initial conditions, and we know the area (YOU specified it), we can calculate the total power output (which is the ONLY power output) by multiplying Watts per area by the area. Our result is 82.12 W / m^2 * 510.065 m^2 = 41886.54 Watts.
This is simple physical fact, according to standard principles of physics. I repeat that you can twist and squirm all you want, but unless you can come up with a "khayman80 law" to replace the Stefan-Boltzmann law, this IS the answer, it is known, and it is unequivocal.
Further, even if you use the "long" equation from Wikipedia to calculate heat transfer, rather than my somewhat simplified estimate method, the primary terms in the denominator are still T1^4 minus T2^4, indicating that net heat flow is all OUTWARD from the heat source.
Introduce all the complications, and prevarications and half-assed reasoning you want. I have already shown you the correct answer according to established physics.
Give it up lest you make yourself look more of a fool than you already are. Because as I promised you, all of this is being recorded and will be made public, with your name displayed prominently. I promised that I would do that regardless of how it turned out. You have no reason to complain just because you lost.
Further, I'm going to INVITE people who teach heat transfer to examine my write-up, and evaluate it. I already know what they will say about your half-assed thermodynamic reasoning.
To be honest, I still don't see why YOU don't see, where I showed that you were clearly wrong. But again, I suspect that your CO2-based greenhouse gas religion will not let you accept the clearly established facts.
I have said all I need to say here. Nothing you say will change it, and no, I do not agree with your fallacious "reasoning". I'll stick with the engineering textbooks, thanks very much.
I look forward to the day I can break away from daily "work" and just pursue my interests and hobbies.
And in fact, this is the economy of Start Trek: an economy of plenty, rather than our current economy based on scarcity. People do what they do because they want to, not because they get paid for it.
I don't think the Star Trek scenario is unreasonable, if we were to find better ways to generate energy. Nobody has to be idle (though they could be if they wanted). That isn't a species-killing idea, it's just another evolutionary step.
The U.S. Supreme Court declared the navigable airspace to be "a public highway" and within the public domain.
HOWEVER:
the authority to govern "navigable" airways comes with some caveats, which most people here aren't considering.
First, "navibable" in U.S. law implies that manned craft can use that route to travel interstate. That is pretty much the same definition as "navibable" waters.
The Federal government's AUTHORITY to govern "navigable airways", just like their authority to govern "navigable waters", stems from their authority, granted by the Constitution, to govern interstate commerce.
"Navigable airways" are particular altitudes and routes. They are clearly defined in aviation charts.
Everything else is "fair game", and by the Constitution (and Common Law) is up to the landowners and the States.
To put it in a nutshell: by ancient common law (which still holds; U.S. is a Common Law country) everything EXCEPT the clearly-defined "navigable airways" is indeed legally controlled by the landowner below, and is not subject to Federal jurisdiction.
Further, in my state, it is not legal to use any means to "surveil" property which isn't normally visible from the street, by ANY means, including aircraft, without a warrant. And yes, that means using a stepladder to see over the fence IS a crime.
In the U.S. -- or at least in the states around here -- that's already illegal. So the problem isn't one of rules, it's more one of enforcement.
The other problem is that we have a Federal agency trying to throw its weight around when by our Constitution, this is very clearly a state matter.
The only reason the FAA has any authority, anywhere, is because it is charged with regulating interstate commercial flight, which the Constitution allows it to do. Some people, unfortunately, have picked up this weird idea that FAA has authority over anything in the air, which is simply false.
A month or two ago, a Federal judge ruled that FAA has no authority over drones that are not flown in the (clearly defined on aviation charts) navigable interstate airways. And it is pretty clearly the correct decision, on Constitutional grounds.
However, in the meantime the FAA has appealed the decision. And though they are almost certain to lose in any honest court, they have taken advantage of the hiatus and are trying to regulate everything in site, apparently under the assumption that once it's regulated, however illegally, it will be that much harder to remove that regulation later.
I think they're mistaken, and they're just going to get shot down again by the next court. And they should be. Not just because they're wrong, but also because they're being corrupt assholes.
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.
I "assumed" nothing. I calculated it. One stipulation of Spencer's challenge was that the power input to the heat source remains constant. He did NOT, however, make that stipulation for the refrigerated chamber walls. Not that it matters in this case. Because the power input to the heat source does remain constant (as a requirement of this problem), and therefore, by the Stefan-Botzmann relation between thermodynamic temperature and radiation, the temperature of the heat source does not change. This is not an assumption, it is called "physics".
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...."
YOU can disagree all you like, but the words are there in plain English: "constant flow of energy into the plate from the electric heater."
Now you're trying to say more energy is coming in from the other end? Pardon me, but that won't work either, by your own "boundary" principle: power in = power out. If you're putting energy in from both ends, then where is it coming out?
There is only one "heat source" in this problem, and it is at the center. And according to (epsilon)(sigma)(T1^4 - T2^4), ALL heat transfer is outward from the source to the walls! It's called physics!
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.
No, I explained [slashdot.org] 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.
And I've explained twice or maybe 3 times now how how your "thermodynamic" thinking led you astray. AFTER having given you a very clear warning out of a textbook, once I saw that you were headed in the wrong direction.
A body at thermodynamic temperature X outputs its total radiant power from ALL its surfaces. Not just one of them. By assuming total radiant power outward, across your boundary, you miscalculated the power out by 100% (give or take a couple of thousandths).
You are disputing the established, "consensus" science of heat transfer by making assumptions that don't apply. I used those words before, too. Misapplication of a true principle can still give you the wrong answer. Your calculated temperature for the enclosing sphere was off by approximately 33 degrees K.
You then back-calculated this erroneous figure in order to give another erroneous value to your heat source. And once again, the proof is dirt simple because your input power at steady-state is fixed, and a value that we already know: 41886.54 W.
Using the standard Stefan-Boltzmann relation between radiant temperature of a gray body, its emissivity, and radiant power out, we can very easily (even on paper, without a calculator) that using your own "energy boundary" concept, your answer "creates" approximately 3 kW more power out than you're putting in. This is an indisputable fact that follows directly from the Stefan-Boltzmann law.
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.
Your calculation was off by 100%. (Or close enough to 100% that it isn't worth talking about the difference.)
You own statements (again, I still have them) prove this.
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...."
You're only confirming what I already stated.
Further, your own quotation there is proving you wrong. Power input to the heat source is constant. It is sufficient to heat the source to 150 deg. F (338.71K). Given the known temperature, and the emissivity, we compute the power out with (epsilon)(sigma)(338.71^4) = 82.12 W/m^2. Using that radiant emittance and the fixed, agreed upon area we get 41886.54 Watts total radiated power output.
By the DEFINITION of the problem (and even your own "boundary" principle) this is what it is. We have the equation for it we calculate it. Dirt simple.
That is what the Stefan-Boltzman relation stipulates. There is NO provision anywhere in that equation for whether another body nearby is a black body or a gray body or a white body or anything else. That's the way the damned thing works. I didn't invent it. Stefan came up with the concept, and Boltzmann quantified it some time later. This is the STANDARD equation for radiant power from temperature. There is nothing non-standard, equivocal, or even really debatable about it. It is a standard physics equation, and it does not require your agreement.
If you're saying the STANDARD Stefan-Boltzman relation between radiant power output, temperature, and emissivity doesn't apply here, then you're disputing the Stefan-Boltzmann law. If that is so, then please show is the "khayman80 law" you have invented to replace it.
You keep talking about "consensus" and "accepted science". Well, this is the long-accepted science of radiant heat transfer. If you want to refute THAT, go right ahead and try. I'll be here watching and laughing all the way.
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 [slashdot.org], but obviously we'll have to agree to disagree.
I have already explained how your "boundary" assumed that all the power was output from the outside of the enclosing sphere. However, that's not the case. If area is A, the Stefan-Boltzmann equation states that total radiant power output is (e * s) * A * T^4. BUT, you neglected to account for the fact that the hollow sphere has TWO surfaces it is radiating from. You left out half the m^2 in A, so your figure for W/m^2 was off by very nearly 100%. Q.E.D.
Jane agreed that the general principle is true [slashdot.org] 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.
I agreed that "given your assumptions", that was the correct answer. I stated that in plain English. But your assumptions (see above) were incorrect. I just didn't mention that at the time. I was waiting for you to finish so I could show how you were "hanging yourself", as the saying goes. Hoist by your own petard.
I'm not to bother replying to the rest of your nonsense. Here is a simple proof that you are wrong, and nothing else need be said:
The formula for radiant power is (e * s) * area * T^4. Period. This is according to the Stefan-Boltzmann law, and no other variables are required at steady-state. The initial temperature of the heat source was 150F, or 338.71K.
So we agreed that the input power to the heat source is sufficient for the equation (e * s) * (heat source area) * 338.71^4.
The power input doesn't change. Yet your final calculated temperature was 241F or something like that (about 389.26K).
All you need to do is draw your precious "boundary" around the heat source. The S-B equation now says power out is:
(e * s) * (heat source area) * 389.26^4.
e, s, and the area haven't changed. But you changed the temperature. It is easy to see that 389.26^4 is much greater than 338.71^4. Your power output is now greater than your power input, which is a violation of conservation of energy. It's right there, man.
If you need specific figures: the total power output (and therefore power input) at the heat source, in initial conditions, was (we agreed on this) 82.12 W/m^2 * 510.065 m^2 = 41886.54 Watts. Power in = power out.
But the Stefan-Boltzmann law says at your calculated final temperature, power out is: 73039.94 Watts.
According to your OWN "boundary rule", you have just created 31153.4 Watts greater output than input. Conservation of energy is violated. Q.E.D.
Slashdot Mirror
Actually NASA (or was it NOAA?) changed their tune again and are saying it was 1937.
Gotta keep up with this stuff, man.
The raw, unadjusted temperature records always have said 1937. It's the adjustments that are questionable, not the historical record.
In the end, you signed a contract and are legally bound to continue to pay for almost any type of service inturruption.
Except that I didn't. When my cable was installed I signed a small receipt acknowledging that the tech had been there. I signed no contract.
That might have been an oversight on their part, but that doesn't matter.
Further, the KIND of contract that Comcast has customers sign is known in the legal industry as a "contract of adhesion". What that means is that it was a non-negotiable, take-it-or-leave-it "contract". The problem being that contract law assumes that every party is free to negotiate before signing.
So in many genuine, legal senses of the term, it's not a "real" contract anyway, and honest judges are required in principle to view them "with a jaundiced eye", and lean toward the customer when a dispute arises.
I'm not saying all judges are honest enough to do that, but they're supposed to.
And one more thing I would like to make very clear:
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.
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.
We are not AT thermal equilibrium, so that is a ridiculous straw-man argument.
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.
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.
YOU are disputing the Stefan-Boltzmann law. But it is a known physical law, and this is a textbook demonstration of it. You lose.
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.
You showed no such thing. Your calculations contradict themselves, and your methodology contradicts itself.
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.
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.
This is a simple requirement of the Stefan-Boltzmann law. The radiative power output of a given body does not depend on other nearby bodies. It's inherent in the law itself. And this is precisely where you are getting it wrong.
I find it highly amusing that you derive your own calculations from the Stefan-Boltzmann law, then deny that it is valid. Every time you try to squirm out of this you just contradict yourself again.
I am further amused that you find it "adorable" that you've been proven wrong. Be a man for a change and admit it. Or show us your own replacement for the Stefan-Boltmann law. You don't get to have it both ways.
Besides, 99.99% is not nearly reliable enough. (And besides, this number is misleading... probably outright false.)
According to calculations I did a year or two ago, in order for a "smart firearm" to be worthwhile and actually solved the problem for which is supposed to be designed, for modern arms, it needs to have AT LEAST three 9s behind the decimal point for true positives: 99.999%, and probably actually 4.
And that's assuming the stats are correct. What does that 99.99% represent? True positives? What is its rate at rejecting true negatives? After all, that's the entire purpose it was designed for.
Further yet: how long does the battery last? What is its success rate with a dead battery? Current battery tech is not capable of delivering 99.99% reliability because batteries go bad even on the shelf.
Well, I didn't interpret the article the same way you did. I thought the article was saying that you can be logical and still feel wonder. It wasn't saying that science-oriented people need to be religious, but rather that religious people should stop seeing them as somehow inhuman and unfeeling without a belief in their God.
Atheists will be in for a rude awakening when they die as they will realize that their belief was incomplete. Regardless, they can be just as good, (or as bad) as theists if they practice the golden rule.
Why would they be in for a "rude" awakening, when one would think that any awakening at all should be a pleasant surprise?
Further, as Sam Harris argues quite well, one need not be a theist to have moral values. Science + secular society are perfectly capable of agreeing upon ethical and moral rules, without resorting to theism.
No, you don't. You just have to give enough people cheap energy that they're no way to put the genie back in the bottle.
Once you do that, the Gateses and Kochs of the world can be safely ignored. They won't have any power anymore.
"Any dick and his Cessna" is not involved in commercial interstate transportation.
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.
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.
NO!!! I did not. I held the power constant, just as Spencer stipulated.
For a gray body, which you stipulated, radiant power out = (emissivity) * (S-B constant) * T^4. This is the Stefan-Boltzmann relation between radiant temperature of a gray body and its power output.
T is known: 150F or 338.71 K.
Solving for radiant power out we get 82.12 Watts/m^2. Times khayman80's stipulated area (510.065 m^2) = 41886.54 Watts.
It is this POWER that remains constant according to Spencer. Khayman80 himself asserted that "power in = power out". Therefore POWER IN = POWER OUT = 41886.54 Watts.
But because of the equation I showed above, which is a physical law, after the hollow sphere is inserted (which is COLDER than the heat source), nothing at the power source has changed. Emissivity is still the same. Power input is still 41886.54 Watts = radiant power output of 41886.54 Watts. Which (by the equation above) yields the same temperature.
I didn't assume the same temperature, I calculated it using known physical law.
ANYTHING ELSE is a direct violation of the Stefan-Boltzmann law.
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.
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.
I do think it's cute, however, how you tried to use Spencer's statement as proof of itself.
Have I reminded you lately that your grasp of logic seems a bit off?
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"?
It doesn't seem odd at all, because established science shows that his assertion that the temperature changes is wrong.
Considering that he is wrong, why should I find it odd that he said a wrong thing.
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. Spencer's stipulation. Therefore by the S-B relation, once everything comes up to radiative steady-state the input power and output power of the heat source are constant. There is no inconsistency here.
Further, because ALL the other surfaces are cooler than the heat source, ALL the net heat transfer is outward, because T(a)^4 - T(b)^4 is a positive number.
This is established science, and it doesn't depend on the incorrect opinions of either Spencer or yourself.
I'm going to correct/clarify myself again:
It's not that I don't agree. You might come up with the right answer for some sub-calculation. I don't know, I don't care, and I'm not even going to bother to check, much less agree. The issue is that I have already solved the problem, and arrived at the correct answer (within reasonable limits).
So I don't HAVE to agree or disagree with you. I've already done it, according to the correct textbook-approved physics. AND (unlike you) I checked my work and it checks out. And unlike your answer it doesn't violate conservation of energy.
Nothing you can say is going to change that.
You're misapplying your physics principles again. You're trying to introduce outside influences that the SIMPLE, UNREFUTABLE Stefan-Boltzmann relation says is ALWAYS true:
For a given gray body, its thermodynamic temperature is related ONLY to emissivity, radiant power output, and the S-B relation (emissivity)* (S-B constant) * T^4.
PERIOD. That's physics. And I repeat: given your OWN "draw a border around it" thermodynamic reasoning, the power input (whether it is electrical, chemical, or something else) must equal that output. That's physics.
You're trying to bring in energy from elsewhere, but it isn't relevant to this calculation AT ALL; it is erroneous thinking.
Power input is specified to be constant. Calculating the total power in initial conditions is, as I stated before, "dirt simple". Specified emissivity is known: 0.11. Temperature is known: 338.71K. Solving for the above we get 82.12 W/m^2.
We already have ALL the information needed to calculate this, given the Stefan-Boltzmann relation (above), relating these numbers. Nothing else is required, and in fact trying to introduce other factors is ERROR. That is what the accepted science says.
Since we CAN easily calculate that in initial conditions, and we know the area (YOU specified it), we can calculate the total power output (which is the ONLY power output) by multiplying Watts per area by the area. Our result is 82.12 W / m^2 * 510.065 m^2 = 41886.54 Watts.
This is simple physical fact, according to standard principles of physics. I repeat that you can twist and squirm all you want, but unless you can come up with a "khayman80 law" to replace the Stefan-Boltzmann law, this IS the answer, it is known, and it is unequivocal.
Further, even if you use the "long" equation from Wikipedia to calculate heat transfer, rather than my somewhat simplified estimate method, the primary terms in the denominator are still T1^4 minus T2^4, indicating that net heat flow is all OUTWARD from the heat source.
Introduce all the complications, and prevarications and half-assed reasoning you want. I have already shown you the correct answer according to established physics.
Give it up lest you make yourself look more of a fool than you already are. Because as I promised you, all of this is being recorded and will be made public, with your name displayed prominently. I promised that I would do that regardless of how it turned out. You have no reason to complain just because you lost.
Further, I'm going to INVITE people who teach heat transfer to examine my write-up, and evaluate it. I already know what they will say about your half-assed thermodynamic reasoning.
To be honest, I still don't see why YOU don't see, where I showed that you were clearly wrong. But again, I suspect that your CO2-based greenhouse gas religion will not let you accept the clearly established facts.
I have said all I need to say here. Nothing you say will change it, and no, I do not agree with your fallacious "reasoning". I'll stick with the engineering textbooks, thanks very much.
I disagree. It isn't worrisome at all.
I look forward to the day I can break away from daily "work" and just pursue my interests and hobbies.
And in fact, this is the economy of Start Trek: an economy of plenty, rather than our current economy based on scarcity. People do what they do because they want to, not because they get paid for it.
I don't think the Star Trek scenario is unreasonable, if we were to find better ways to generate energy. Nobody has to be idle (though they could be if they wanted). That isn't a species-killing idea, it's just another evolutionary step.
The U.S. Supreme Court declared the navigable airspace to be "a public highway" and within the public domain.
HOWEVER:
the authority to govern "navigable" airways comes with some caveats, which most people here aren't considering.
First, "navibable" in U.S. law implies that manned craft can use that route to travel interstate. That is pretty much the same definition as "navibable" waters.
The Federal government's AUTHORITY to govern "navigable airways", just like their authority to govern "navigable waters", stems from their authority, granted by the Constitution, to govern interstate commerce.
"Navigable airways" are particular altitudes and routes. They are clearly defined in aviation charts.
Everything else is "fair game", and by the Constitution (and Common Law) is up to the landowners and the States.
To put it in a nutshell: by ancient common law (which still holds; U.S. is a Common Law country) everything EXCEPT the clearly-defined "navigable airways" is indeed legally controlled by the landowner below, and is not subject to Federal jurisdiction.
Further, in my state, it is not legal to use any means to "surveil" property which isn't normally visible from the street, by ANY means, including aircraft, without a warrant. And yes, that means using a stepladder to see over the fence IS a crime.
In the U.S. -- or at least in the states around here -- that's already illegal. So the problem isn't one of rules, it's more one of enforcement.
The other problem is that we have a Federal agency trying to throw its weight around when by our Constitution, this is very clearly a state matter.
The only reason the FAA has any authority, anywhere, is because it is charged with regulating interstate commercial flight, which the Constitution allows it to do. Some people, unfortunately, have picked up this weird idea that FAA has authority over anything in the air, which is simply false.
A month or two ago, a Federal judge ruled that FAA has no authority over drones that are not flown in the (clearly defined on aviation charts) navigable interstate airways. And it is pretty clearly the correct decision, on Constitutional grounds.
However, in the meantime the FAA has appealed the decision. And though they are almost certain to lose in any honest court, they have taken advantage of the hiatus and are trying to regulate everything in site, apparently under the assumption that once it's regulated, however illegally, it will be that much harder to remove that regulation later.
I think they're mistaken, and they're just going to get shot down again by the next court. And they should be. Not just because they're wrong, but also because they're being corrupt assholes.
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.
I "assumed" nothing. I calculated it. One stipulation of Spencer's challenge was that the power input to the heat source remains constant. He did NOT, however, make that stipulation for the refrigerated chamber walls. Not that it matters in this case. Because the power input to the heat source does remain constant (as a requirement of this problem), and therefore, by the Stefan-Botzmann relation between thermodynamic temperature and radiation, the temperature of the heat source does not change. This is not an assumption, it is called "physics".
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.
YOU can disagree all you like, but the words are there in plain English: "constant flow of energy into the plate from the electric heater."
Now you're trying to say more energy is coming in from the other end? Pardon me, but that won't work either, by your own "boundary" principle: power in = power out. If you're putting energy in from both ends, then where is it coming out?
There is only one "heat source" in this problem, and it is at the center. And according to (epsilon)(sigma)(T1^4 - T2^4), ALL heat transfer is outward from the source to the walls! It's called physics!
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.
No, I explained [slashdot.org] 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.
And I've explained twice or maybe 3 times now how how your "thermodynamic" thinking led you astray. AFTER having given you a very clear warning out of a textbook, once I saw that you were headed in the wrong direction.
A body at thermodynamic temperature X outputs its total radiant power from ALL its surfaces. Not just one of them. By assuming total radiant power outward, across your boundary, you miscalculated the power out by 100% (give or take a couple of thousandths).
You are disputing the established, "consensus" science of heat transfer by making assumptions that don't apply. I used those words before, too. Misapplication of a true principle can still give you the wrong answer. Your calculated temperature for the enclosing sphere was off by approximately 33 degrees K.
You then back-calculated this erroneous figure in order to give another erroneous value to your heat source. And once again, the proof is dirt simple because your input power at steady-state is fixed, and a value that we already know: 41886.54 W.
Using the standard Stefan-Boltzmann relation between radiant temperature of a gray body, its emissivity, and radiant power out, we can very easily (even on paper, without a calculator) that using your own "energy boundary" concept, your answer "creates" approximately 3 kW more power out than you're putting in. This is an indisputable fact that follows directly from the Stefan-Boltzmann law.
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.
Your calculation was off by 100%. (Or close enough to 100% that it isn't worth talking about the difference.)
You own statements (again, I still have them) prove this.
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.
You're only confirming what I already stated.
Further, your own quotation there is proving you wrong. Power input to the heat source is constant. It is sufficient to heat the source to 150 deg. F (338.71K). Given the known temperature, and the emissivity, we compute the power out with (epsilon)(sigma)(338.71^4) = 82.12 W/m^2. Using that radiant emittance and the fixed, agreed upon area we get 41886.54 Watts total radiated power output.
By the DEFINITION of the problem (and even your own "boundary" principle) this is what it is. We have the equation for it we calculate it. Dirt simple.
That is what the Stefan-Boltzman relation stipulates. There is NO provision anywhere in that equation for whether another body nearby is a black body or a gray body or a white body or anything else. That's the way the damned thing works. I didn't invent it. Stefan came up with the concept, and Boltzmann quantified it some time later. This is the STANDARD equation for radiant power from temperature. There is nothing non-standard, equivocal, or even really debatable about it. It is a standard physics equation, and it does not require your agreement.
If you're saying the STANDARD Stefan-Boltzman relation between radiant power output, temperature, and emissivity doesn't apply here, then you're disputing the Stefan-Boltzmann law. If that is so, then please show is the "khayman80 law" you have invented to replace it.
You keep talking about "consensus" and "accepted science". Well, this is the long-accepted science of radiant heat transfer. If you want to refute THAT, go right ahead and try. I'll be here watching and laughing all the way.
In reply to this comment
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 [slashdot.org], but obviously we'll have to agree to disagree.
I have already explained how your "boundary" assumed that all the power was output from the outside of the enclosing sphere. However, that's not the case. If area is A, the Stefan-Boltzmann equation states that total radiant power output is (e * s) * A * T^4. BUT, you neglected to account for the fact that the hollow sphere has TWO surfaces it is radiating from. You left out half the m^2 in A, so your figure for W/m^2 was off by very nearly 100%. Q.E.D.
Jane agreed that the general principle is true [slashdot.org] 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.
I agreed that "given your assumptions", that was the correct answer. I stated that in plain English. But your assumptions (see above) were incorrect. I just didn't mention that at the time. I was waiting for you to finish so I could show how you were "hanging yourself", as the saying goes. Hoist by your own petard.
I'm not to bother replying to the rest of your nonsense. Here is a simple proof that you are wrong, and nothing else need be said:
The formula for radiant power is (e * s) * area * T^4. Period. This is according to the Stefan-Boltzmann law, and no other variables are required at steady-state. The initial temperature of the heat source was 150F, or 338.71K.
So we agreed that the input power to the heat source is sufficient for the equation (e * s) * (heat source area) * 338.71^4.
The power input doesn't change. Yet your final calculated temperature was 241F or something like that (about 389.26K).
All you need to do is draw your precious "boundary" around the heat source. The S-B equation now says power out is:
(e * s) * (heat source area) * 389.26^4.
e, s, and the area haven't changed. But you changed the temperature. It is easy to see that 389.26^4 is much greater than 338.71^4. Your power output is now greater than your power input, which is a violation of conservation of energy. It's right there, man.
If you need specific figures: the total power output (and therefore power input) at the heat source, in initial conditions, was (we agreed on this) 82.12 W/m^2 * 510.065 m^2 = 41886.54 Watts. Power in = power out.
But the Stefan-Boltzmann law says at your calculated final temperature, power out is: 73039.94 Watts.
According to your OWN "boundary rule", you have just created 31153.4 Watts greater output than input. Conservation of energy is violated. Q.E.D.
You are busted.