Stirlingengineforum.com

The formulas/equations for calculating work and heat flow assume any contribution from the atmosphere to be zero for a cycle. Therefore the full cycle can be calculated from an absolute pressure and temperature sense, ignoring outside pressure. If outside pressure isn't ignored, the forward and return equations must both be modified.

To explain it simpler. Work out of a single forward stroke is calculated by the absolute inside pressure. And the return stroke the same. If you want to add the outside pressure, you must subtract 14.7 x Area of piston x Volume of stroke from the absolute work done by the inside pressure x the same Area x Volume change.

Note: Inside pressure isn't constant, so it is incorrect to subtract a set inside pressure. Outside pressure is constant, so it is acceptable to use a single value for outside pressure.

The forward work, calculated this way for previous examples, will be much less than 100 J.

It is wrong to add an outside pressure/force to one side of the equation as you've done repeatedly.

Forward stroke:
Wf = Inside Forward Work - Outside Work

Return stroke:
Wr = Outside Work - Inside Return Work

Sum the two:
Work Total = Wt = Wf + Wr = (Inside Forward Work - Outside Work) + (Outside Work - Inside Return Work)

Rearranging:
Wt = Inside Forward Work + Outside Work - Outside Work - Inside Return Work

Canceling the Outside Work:
Work Total = Inside Forward Work - Inside Return Work

This equation shows that you will need a smaller Return Work to get any Net Work output. Back work must be smaller than forward work to get work output. That is accomplished by rejecting heat before and or during the return stroke.

In other words, adding something that cancels with itself, like outside pressure, adds nothing. The beauty of cancelation in an equation, allows the equation to be simplified to the point were assumptions become reality. It was a good assumption to ignore the outside pressure. It canceled anyway.

Hence, n = (Qh-Qc)Qh = (Th-Tc)/Th

It is only true for a complete cycle, because of cancellations in the cycle and ratio. The process must be a complete cycle. It will not work for descriptions of a single stroke.

It is possible to have a return stroke without rejecting heat, it just uses more work, the same amount as Forward work. It is called adiabatic bounce, the same as for a metal spring. The processes stay on a single adiabatic line, forward and return strokes, adiabatic.

Observed conservation of energy, the data used to develop the first law, suggests that any energy put into cooling will be the maximum energy that can be gotten back out. Zero improvement, most likely a detriment, if cooling is added.

The first law leads to the second law by considering a full cycle and quantification of the process. And it proves that there are no Calorics, and some thermal energy becomes work, so not all the energy is loss to the sink. Without Carnot, entropy, the second law and the Carnot theorem, we would still be arguing conservation of calorics. The first and second laws have proven the non-existence of calorics.

Well, "fool" has been arguing all along that it is "impossible" for the piston to return without "rejecting" heat.

Oops it was supposed to be this quote.

VincentG wrote: ↑Tue Jun 04, 2024 11:40 am

Well, "fool" has been arguing all along that it is "impossible" for the piston to return without "rejecting" heat.

As far as I am concerned this is still up in the air, I'll reserve judgment until I can test this myself.

Just fixing the quote,

I can't argue with that. It's the same approach I took when confronted with the conflict: Tesla vs. Kelvin.

But I've already done dozens and dozens of experiments, so for me it's no longer "up in the air".

As far as I'm concerned the Carnot efficiency limit is not only a completely baseless theory that emerged from a fallacious concept of the nature of heat, with zero experimental backing whatsoever, it has been empirically demonstrated time and again to be completely false.

It has been disproven in my book and I would like to move on. Instead I have "fool" and others with their relentless attempts to "educate" me about their so-called "science". Which IMO has no scientific basis whatsoever.

It rests entirely on the authority of Sadi Carnot who in actual fact completely changed his mind and recanted his theory and urged others to do likewise.

It was Kelvin who dredged up this old forgotten theory and promoted it as fact at the same time admitting it was known to be wrong.

From Wikipedia:
Work Energy coming out of the engine is positive.

Heat energy going in is positive.

Vt = Volume top dead center.
Vb = Volume bottom dead center.
M Mass of the working gas.
R gas constant for working gas
ln() = Natural log function.
Th and Tc Temperatures hot an cold
W12 work for each process, respectively. Four total. 2 isothermal. Two constant volume.
Q12, Heat transfered for each of four process respectively.

The following is for the ideal Stirling Cycle as depicted in the above graphic.

W12 = M•R•Th•ln(Vb/Vt) positive because work is coming out.
W23 = 0. Zero volume change.
W34 = M•R•Tc•ln(Vt/Vb) negative because work is going in.
W41 = 0. Zero volume change.

Q12 = W12 = M•R•Th•ln(Vb/Vt) positive because the energy is going in.

Q23 = -M•Cv•(Th-Tc) negative because the energy is coming out.

Q34 = W34 = M•R•Th•ln(Vt/Vb) negative because the energy is coming out. Vt smaller than Vb, ln() function negative for values less than one.

Q41 = -M•Cv•(Tc-Th) positive because the energy is going in. Tc smaller than Th, two negatives combined to become a positive.

Q23 and Q41 cancel each other, being an equal and opposite regenerator processes. Ideally.


n = Wout/Qin = (W12 + W34) / (Q12)

Substituting:
n={(M•R•Th•ln(Vb/Vt))+(M•R•Tc•ln(Vt/Vb)}/{M•R•Th•ln(Vb/Vt)}

Using the log identity ln(x) = -ln(1/x), for ln(Vt/Vb) = -ln(Vb/Vt), the equation becomes:
n={(M•R•Th•ln(Vb/Vt))-(M•R•Tc•ln(Vb/Vt)}/{M•R•Th•ln(Vb/Vt)}

Canceling M•R•ln(Vb/Vt) top and bottom:
n=(Th-Tc)/Th
Ideally and a maximum for the temperatures given.

It is direct observable science from the observed relationship between temperature, pressure, volume, energy, mass and the linear coefficients of heat Cv, and ideal gas constant R for the real gas, Rn for Nitrogen, or whatever.

Again this doesn't equate Q to T. The differences just cancel out in the equations of n=W/Q, PV=MRT, and Q=MCvT, for a full cycle. Doesn't work for single strokes. Real engines will be worse.

Fool, I went through your previous "derivation(s)" in good faith, with a fine tooth comb.giving it a fair chance. Keeping open minded

But when I discovered you had essentially "snuck in" the Carnot formula, thinly disguised or altered, right at the start, It seemed to me you were being deceptive, or at best, you argument had no merit. It was all just circular reasoning.

I'm not inclined to bother going through all that again If not being intentionally deceptive and misleading I think this is all self-deception and wishful thinking on your part.

Your previous derivation was entirely self referential and of no value

I can only suppose this new wall of equations is no better. Nevertheless I've got better things to do.

Tom Booth wrote:But I've already done dozens and dozens of experiments, so for me it's no longer "up in the air".

As far as I'm concerned the Carnot efficiency limit is not only a completely baseless theory that emerged from a fallacious concept of the nature of heat, with zero experimental backing whatsoever, it has been empirically demonstrated time and again to be completely false.

So, I take it, you think you have discovered something important. Something that no one else in the whole world has observed. You are the one and only person to know this "true knowledge" that every science teacher has wrong.

Mathematics proves you wrong, but your experiments are more correct, so anything contradicting you is wrong. Even though you have no valid counter mathematical proof, your experiments must be correct, and your conclusions are firmly based on those experiments with no other possible conclusion.

Right?

Therefore there is no reason to respect another poster enough to study, standard mathematical derivations.

Fool wrote: ↑Thu Jun 06, 2024 11:23 pm

Tom Booth wrote:But I've already done dozens and dozens of experiments, so for me it's no longer "up in the air".

As far as I'm concerned the Carnot efficiency limit is not only a completely baseless theory that emerged from a fallacious concept of the nature of heat, with zero experimental backing whatsoever, it has been empirically demonstrated time and again to be completely false.

So, I take it, you think you have discovered something important. Something that no one else in the whole world has observed. You are the one and only person to know this "true knowledge" that every science teacher has wrong.

Mathematics proves you wrong, but your experiments are more correct, so anything contradicting you is wrong. Even though you have no valid counter mathematical proof, your experiments must be correct, and your conclusions are firmly based on those experiments with no other possible conclusion.

Right?

Therefore there is no reason to respect another poster enough to study, standard mathematical derivations.

What "standard" mathematical derivations?

As far as the Carnot efficiency limit equation, it, afaik, is not derived from anything. It's just a supposition that the temperature difference imposes some limit on engine efficiency. As such, it is nothing more than the temperature difference itself written out as a ratio or percentage. It's nothing more or less than the difference between Tc and Th.

As for example: if Th = 400 and Tc = 300 the ∆T is 100 which is 25% of 400.

That's your "derivation" plane and simple.

If that was as far as it went, I'd have no issue

Add 100 joules, you can't do any better than to use the 100 joules. Perfectly logical.

But the Carnot limit has been INTERPRETED to mean: add 100 joules and 75 joules of what you supplied get magically set aside for the "cold reservoir". So just by supplying 100 joules of heat 75% is deducted right off the top for no reason.

You are left with 25% of your original 100 joules and then have to deduct friction, parasitical heat loses through conduction, radiation, vibration etc.

Based on absolutely nothing.

No one has ever observed the supposed 75% "waste heat" traveling magically to the mythical "cold reservoir". If they have, YOU please cite that experiment. Tell me when it was conducted, and by whom.

I at least have my own actual experiments. In 200 years the Carnot limit camp has nothing. No experimental evidence to validate this nonsensical "Carnot efficiency limit" assumption whatsoever.

You don't need to "derive" a temperature difference. You just need a thermometer.

So where oh where is this "standard derivation"?

Aside from your own made up off the top of your head so-called "derivation" that starts with the Carnot limit assumption using the Carnot limit to supposedly "prove" the Carnot limit using circular reasoning.

I'd like to see this "standard derivation"

Matt Brown made a similar claim not too long ago:

Turning this Carnot limit into a mystery is ridiculous, since it's only a simple mathematical derivation of how PV=mRT plays out.

viewtopic.php?p=20312#p20312

Though asked, he could not produce this "simple mathematical derivation" or any references thereto.

You glibly refer to some "standard derivation". But these are empty words with nothing whatsoever to back them up. So what exactly is it I'm supposed to "study" or "respect". A imagined "standard derivation" that doesn't exist?

If it exists, it should be a simple matter for you to produce dozens of textbook references, online sources, YouTube videos, etc etc. in no time, without any effort at all.

Simply empty lies. False assumptions. I hear these claims over and over about how the Carnot limit has been "proven", or experimentally validated, hundreds of times, but funny, not one person making such a claim over the MANY years I've been researching this, has been able to produce a single reference. Not one.

No "standard derivation", no experiment, nothing.

Pure fiction.

https://physics.stackexchange.com/quest ... ts-theorem

Matt was talking Carnot derivation. Links have been provided.

https://unacademy.com/content/jee/study ... cle-proof/

https://homework.study.com/explanation/ ... eorem.html

https://people.ohio.edu/trembly/mechani ... ter3b.html

Fool wrote: ↑Wed Jun 05, 2024 12:42 am From Wikipedia:

Stirling_cycle_pV.svg.png

Work Energy coming out of the engine is positive.

Heat energy going in is positive.

Vt = Volume top dead center.
Vb = Volume bottom dead center.
M Mass of the working gas.
R gas constant for working gas
ln() = Natural log function.
Th and Tc Temperatures hot an cold
W12 work for each process, respectively. Four total. 2 isothermal. Two constant volume.
Q12, Heat transfered for each of four process respectively.

The following is for the ideal Stirling Cycle as depicted in the above graphic.

W12 = M•R•Th•ln(Vb/Vt) positive because work is coming out.
W23 = 0. Zero volume change.
W34 = M•R•Tc•ln(Vt/Vb) negative because work is going in.
W41 = 0. Zero volume change.

Q12 = W12 = M•R•Th•ln(Vb/Vt) positive because the energy is going in.

Q23 = -M•Cv•(Th-Tc) negative because the energy is coming out.

Q34 = W34 = M•R•Th•ln(Vt/Vb) negative because the energy is coming out. Vt smaller than Vb, ln() function negative for values less than one.

Q41 = -M•Cv•(Tc-Th) positive because the energy is going in. Tc smaller than Th, two negatives combined to become a positive.

Q23 and Q41 cancel each other, being an equal and opposite regenerator processes. Ideally.


n = Wout/Qin = (W12 + W34) / (Q12)

Substituting:
n={(M•R•Th•ln(Vb/Vt))+(M•R•Tc•ln(Vt/Vb)}/{M•R•Th•ln(Vb/Vt)}

Using the log identity ln(x) = -ln(1/x), for ln(Vt/Vb) = -ln(Vb/Vt), the equation becomes:
n={(M•R•Th•ln(Vb/Vt))-(M•R•Tc•ln(Vb/Vt)}/{M•R•Th•ln(Vb/Vt)}

Canceling M•R•ln(Vb/Vt) top and bottom:
n=(Th-Tc)/Th
Ideally and a maximum for the temperatures given.

It is direct observable science from the observed relationship between temperature, pressure, volume, energy, mass and the linear coefficients of heat Cv, and ideal gas constant R for the real gas, Rn for Nitrogen, or whatever.

Again this doesn't equate Q to T. The differences just cancel out in the equations of n=W/Q, PV=MRT, and Q=MCvT, for a full cycle. Doesn't work for single strokes. Real engines will be worse.

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Your response is unresponsive.

My request was "..please cite that experiment. Tell me when it was conducted, and by whom"

Referencing yourself from earlier in the thread is not referencing any "standard" derivation. Your dissertation that begins with the words "from Wikipedia", other than the PV diagram, appears to be entirely your own invention:

viewtopic.php?p=23159#p23159

If any of that is from an actual Wikipedia article, please provide a link.

The remaining links, I believe, like your own "proof" are self referencing or similarly circular reasoning.

That is, they conclude by saying: "that would violate the second law/Carnot theorem".

But maybe I overlooked something. So please provide these two things, if possible:

1) Which if any of your links provides actual empirical/experimental evidence? This should have some historical setting such as James Joule (or whomever) demonstrated the Carnot efficiency limit in such and such year with experiment such and such.

2) Which of your links provide a widely accepted "Standard" derivation that derives the Carnot limit, preferably from real data or actual measurements taken.

Needless to say, if the "derivation" or "proof" depends on some conclusion such as,

"if a heat engine could run on the heat from a heat pump while powering the heat pump THAT WOULD VIOLATE THE SECOND LAW"

Such a proof is itself a fallacy. Self referential circular reasoning and amounts to saying that: Violating the Carnot limit is impossible because that would be a violation of the Carnot limit/2nd Law.

Using a proposition to prove itself is circular reasoning and proves nothing.

As far as I can see, all of the links you've provided fall into that category, or simply provide general information about Stirling engines without any experiment, proof or derivations at all.

Fool wrote: ↑Thu Jun 06, 2024 11:23 pm

Tom Booth wrote:But I've already done dozens and dozens of experiments, so for me it's no longer "up in the air".

As far as I'm concerned the Carnot efficiency limit is not only a completely baseless theory that emerged from a fallacious concept of the nature of heat, with zero experimental backing whatsoever, it has been empirically demonstrated time and again to be completely false.

So, I take it, you think you have discovered something important. Something that no one else in the whole world has observed. You are the one and only person to know this "true knowledge" that every science teacher has wrong.

Mathematics proves you wrong, but your experiments are more correct, so anything contradicting you is wrong. Even though you have no valid counter mathematical proof, your experiments must be correct, and your conclusions are firmly based on those experiments with no other possible conclusion.

Right?
...

Wrong.

In researching heat engines in general, at some point I came across a conflict between Kelvin and Nichola Tesla regarding the nature of heat and the functioning of heat engines.

Kelvin said rejecting heat to a "sink" or "cold reservoir" is necessary. Tesla suggested it is not necessary because heat is energy that can be converted.

I conducted some simple experiments that I thought might help resolve this long standing disagreement and help sort out the truth of the matter one way or the other.

I recorded the experiments on video and simply presented the objective results for anyone that might be interested.

I don't have and never did have any preconception or preference about the outcome of any experiment. I'm just interested in how Stirling engines actually work.

My experiments are simple experiments anyone can perform and decide whatever they want for themselves, making their own observations.

I'd be interested to know why, if you think they are so "inconclusive" and insignificant, why you waste so much time in here following me around from thread to thread obsessively fixating on me and my kitchen table experiments.

You seem to attach a great deal more importance to them than I do.

Maybe it's my ignorance, but I fail to see what math proves.
Math is what we use to understand nature. To make it calculable for us. It's not what runs nature. So if our math is off because it's based on a wrong theory, what can we prove with that?
Again, I'm horrible at math, so I might just not get it.

Jack wrote: ↑Fri Jun 07, 2024 7:55 pm Maybe it's my ignorance, but I fail to see what math proves.
Math is what we use to understand nature. To make it calculable for us. It's not what runs nature. So if our math is off because it's based on a wrong theory, what can we prove with that?
Again, I'm horrible at math, so I might just not get it.

Well, IMO mathematics can be used to prove, or at least lend some strong evidence to support some ideas or theory.

In this case however, there is no mathematics that supports the Carnot limit theory.

It is purely supposition.

Carnot theorized that if heat (caloric) is a fluid, like water, then it must run downhill from a high to a low temperature.

If true than it can be supposed that the difference in temperature, to one degree or another influences heat engine efficiency. The greater the "height'" the greater the fall in temperature, so the stronger the "flow' of heat.

Not entirely unreasonable IF heat is actually a fluid.

But, as it turns out, heat is NOT a fluid, heat is just a form of energy so the entire theory falls flat and no longer has any sound theoretical basis whatsoever, mathematical or otherwise.

At some point in history though, apparently Kelvin put Carnot's theory about heat running down hill into mathematical form.

Basically, the equation is just the temperature difference, or how far the heat will "fall down" from hot to cold.

Mathematical equations are pretty hard to argue with and most people consider math to be iron clad and set in stone.

Further, the Carnot equation is very easy.

How an engine works is actually quite complicated involving a great deal of precision engineering and practical knowhow, and engine efficiency depends on innumerable factors, some known and well understood and some unknown, but the Carnot formula is very simple so that any nincompoop who knows the formula can consider themselves an authority on engines and an expert engineer even though they might not know a piston from a crankshaft. So the Carnot nonsense is very attractive to wannabe "engineers" and deletant "scientists".

Jack wrote: ↑Fri Jun 07, 2024 7:55 pm Maybe it's my ignorance, but I fail to see what math proves.
Math is what we use to understand nature. To make it calculable for us. It's not what runs nature. So if our math is off because it's based on a wrong theory, what can we prove with that?
Again, I'm horrible at math, so I might just not get it.

Warfare involves more logistics than combat. Imagine how easy it would be to defeat the Roman army by sheer advantage of our decimal system vs their lacky Roman Numeral system. A classic case where the pen is mightier than the sword...