Hahahaha, 12 years on and still flogging the same dead horse, eh, Tom?Can anyone tell me where this formula originated and how it was verified? (With citations, please).
Thanks in advance
Tom
A bit more on this. As the concept of an absolute temperature scale was due to an 1848 paper by W Thomson (Lord Kelvin), the efficiency formula cast in terms of absolute temperature must be later than that. So not Carnot, who died in 1832. Clausius, perhaps?Hahahaha, 12 years on and still flogging the same dead horse, eh, Tom?![]()
I don't know historically who was the first to write down the efficiency formula in that form. It may have been Carnot, since it follows from Carnot's Theorem, or it may have been Thomson, Kelvin or Rankine, or someone else who first put it in that particular form. But you have an English translation of Carnot's "Réflexions sur la Puissance Motrice du Feu" - you posted a link to it on the thread in that other form. Have you checked whether it appears there?
As for verification, we went over this ad nauseam on the scienceforms.net site, before you were banned for posting in bad faith. You are unlikely to get a very different answer here, I suspect, though I'll be interested to see who else bites.![]()
Bingo!Gonna guess he's madly in pursuit of a Perpetulant Motion Machine.
Yeah, a fun idea to play with. I can see some upsides and some downsides.Bingo!
But to be fair, he did come up with a good one: an ice engine! Quite fun to analyse. Turned out to be conceptually similar to Newcomen’s atmospheric steam engine, in that the power stroke was due to a phase change, and the engine takes in heat on the return stroke rather than the power stroke.
In his proposal, the work was done by the expansion of ice on freezing, which is ~8% volume increase. Alternate freezing and thawing caused a piston to reciprocate. So it was very much like the process that causes frost shattering at the top of a mountain, in which water in cracks in the rock progressively jacks the cracks open.Yeah, a fun idea to play with. I can see some upsides and some downsides.
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Ice is safer to store than combustibles.
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Its efficiency/effectiveness is limited by the fact that heat capacity / temp is asymmetrical (zero in one direction, unlimited in the other. It's a lot easier to double room temp from 300K to 600K, than it is to halve 300K to 150K.
And this happened at what rate? One cylinder cycle per season? I suppose with a high enough gear ratio he's got something there...In his proposal, the work was done by the expansion of ice on freezing, which is ~8% volume increase. Alternate freezing and thawing caused a piston to reciprocate. So it was very much like the process that causes frost shattering at the top of a mountain, in which water in cracks in the rock progressively jacks the cracks open.
Oh it wasn't supposed to be a practical machine. His objective (in which he failed, naturally) was to show you could in principle devise a heat engine to run off ambient heat, implying, so he thought, no heat sink. (Perpetual motion of the 2nd kind is his bag, following our good friend of cranks everywhere Nikola TeslaAnd this happened at what rate? One cylinder cycle per season? I suppose with a high enough gear ratio he's got something there...
Surely the historical context isn't too hard to find, if you want it.Can anyone tell me where this formula originated and how it was verified? (With citations, please).
You would think, but actually no.Surely the historical context isn't too hard to find, if you want it.
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It comes I think from Clausius inequality: https://en.wikipedia.org/wiki/Clausius_theoremYou would think, but actually no.
I researched the origins of this for months, until I exhausted all available resources at my disposal. Assuming I may have missed or overlooked something, I began asking on science and physics forums such as this with similar non-responsive answers.
So far it seems we can rule out Carnot himself as the originator. That does little to narrow things down.
Also, though I have been reporting off-topic responses the thread continues to grow without any assistance in the way of an actual answer or specific reference or citation.
Can such off-topic material be removed so that anyone caring to actually respond to these questions may do so without having to wade through alot of irrelevant material.
Thanks.
Thank you very much.It comes I think from Clausius inequality: https://en.wikipedia.org/wiki/Clausius_theorem
So therefore η = (Qh - Qc)/Qh.
The tricky bit is justifying replacing Qh and Qc by Th and Tc and this is done by reference to the Clausius inequality, as described in the Wiki entry.
Tom, I've just amended my post to include the derivation and one more reference that makes it clearer what Clausius's Theorem says about the Carnot cycle. Suggest you read my amended post before doing anything else. But you are right: Clausius's inequality (or theorem) is the key.Thank you very much.
I agree: "The tricky bit is justifying replacing Qh and Qc by Th and Tc"
I have difficulty seeing the justification for that since Q represents a measurable quantity of energy in joules whereas temperature is the average kinetic energy of an indeterminate quantity of a given substance. There are additional problems in simply substituting temperature for heat.
Heat is energy transfered whereas temperature is a state. There is a conceptual problem in simply substituting one for the other.
But pinning down the origin should help give this some context and maybe help me to put this into some kind of proper perspective.
So I will study up on Clausius and his "inequality". Perhaps that is the missing piece of the puzzle that will make all this make sense.
Thanks!
Tom
I took a second look at that link I provided in post 12 and noted the following passage:Cutting to the chase;
Do you ("you"=anyone caring to offer their opinion here) agree with the statement that the Clausius inequality relies upon or is derived from the kelvin-plank statement?
See for example, timestamp around 3:00 in this lecture:
IMO (tentatively) I had suspected that to be the case while going over the math it appeared that certain values or equations (mathematical constraints) were introduced without explanation but which do not seem to follow from conservation of energy alone.
In other words, if I wish to constrain my math so as to avoid producing some unwanted result, I can draw a "line in the sand", so to speak, by introducing an inequality (greater than or equal to, or vice versa; less than or equal to).
This puts a constraint on my calculations insuring that the mathematics will not cross that boundary.
As such the "inequality" is essentially the mathematical embodiment of preceding conclusions.
Is that a fair statement?
On the contrary, guidance is always forthcoming. You just don't like the form it takes, which is: "Do not waste your time". Nobody is under any obligation to encourage you in delusional pursuits.Anyway, in my mind this is not in persuit of anything other than improved engine design.
My issue with the Carnot efficiency limit is that on the off chance it happened to be in error, it could hamper engine development as a kind of self-fulfilling prophesy.
Looking at this equation, and designing my engine I would conclude for example that I need to make provision for the "fact" that 85% of the heat going into the engine will end up as "waste heat".
Consequently, I'll incorporate a highly conductive copper lined heat exchanger into the system to siphon off the excess heat as quickly as possible so as to prevent overheating. After all, the greater the temperature difference the higher the efficiency, so the more cooling the better.
Now if such intentional cooling for such a high rate of heat rejection were not actually necessary, what would be the consequence nevertheless?
My intention to improve engine performance and efficiency to the maximum extent possible, (according to the best available math and science), results in my tossing out 85% of the energy supplied to power my engine without ever making any attempt at greater utilization, or designing for a higher rate of conversion.
The general proliferation of this "scientific knowledge" would also tend to inhibit manufacture and marketing of any engine that happened, by chance to slip through the cracks through neglecting to design the engine according to standard mathematical modeling.
Inability to obtain a patent. Investors warned off from investing in an "impossible" engine designed by a "crackpot" etc. etc.
In fact, if such a person, ignorant of "established science" and the higher math were to wander onto a Science and Physics forum, such as this, and display actual video of an experimental model engine that appeared to operate without need for a cold sink to take away all the "excess heat", he would summarily be banned without recourse or trial or any objective, unbiased evaluation of his machine.
The "scientists" from whom he hoped to receive some help, guidance and support, all turning their backs in distain and implacable ridicule.
Well, exactly! That too.On the contrary, guidance is always forthcoming. You just don't like the form it takes, which is: "Do not waste your time". Nobody is under any obligation to encourage you in delusional pursuits.
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Er no. The second Law is used to derive the Carnot efficiency. The two things are quite different.Well, exactly! That too.
Which no doubt discourages 99.9% of any would be inventors from every trying to do anything.
Anyway, thank you for the assistance and the additional confirmation that the Carnot limit equation is based on circular reasoning. Assuming the second law so as to "derive" the second law.