The TRUTH? η = 1 – (Qc / Qh) = 1 – (Tc / Th)

[Fool]

Basically, plain and simply :

n=(Qh-Qc)/Qh

And :
Q=Cv•M•T

So :

n = (Qh - Qc) / Qh
n = (Cv•M•Th - Cv•M•Tc) / Cv•M•Th

Simplifying :
n = (Cv•M(Th-Tc) / Cv•M•Th

Canceling :

n = (Th-Tc) / Th

If the cycle starts at Qcz, and DQh is added. It is then expanded doing work a maximum of Qhz Joules will be converted to work. The gas will be at T = 0 Kelvin and P=0. Now it must be compressed back to P=atmospheric an Tc=300 K. It will take 300 J to do so.

That makes the machine's efficiency 25%.

The machine will have the same efficiency if the forward work is only 100 J. The compression will take 75 J.

[matt brown]

Indeed, eff = (Wpos-Wneg)/Wpos is the best approach for compression cycles since this is easy to quantify and eliminates Q vs T issue/s. When a cycle is non-compression, then Q=W is the only option.

Even using Q1 to unify quantity of input with Thigh is far from bulletproof.

[Tom Booth]

Basically, plain and simply :

n=(Qh-Qc)/Qh

And :
Q=Cv•M•T

So :

n = (Qh - Qc) / Qh
n = (Cv•M•Th - Cv•M•Tc) / Cv•M•Th

Simplifying :
n = (Cv•M(Th-Tc) / Cv•M•Th

Canceling :

n = (Th-Tc) / Th

If the cycle starts at Qcz, and DQh is added. It is then expanded doing work a maximum of Qhz Joules will be converted to work.
....

How is Qhz the "maximum"?

Qhz is not the "heat" supplied.

Qhz is Qcz, the pre-existing environment in thermal equilibrium before any heat is supplied, added or taken in by the engine. Plus the few additional joules actually supplied.

As you say: "the cycle starts at Qcz, (equilibrium) and DQh (100 joules) is added"

In your derivation 300 joules of ambient heat (Qcz) are already in the engine, in equilibrium with the environment. An additional 100 joules of heat actual heat (DQh) are added.

Qhz is this 300 joules of "given" baseline "internal energy" plus the actual 100 joules of heat supplied. The 300 were never added, never transfered, so don't count as "heat" at all, and don't even meet the definition of heat.

The heat supplied is 100 joules. That is the maximum that can be converted to work to give 100% efficiency. 100 joules supplied, 100 joules of work produced by expansion.

Of course if you want to imagine "available heat" includes the 300 joules that was never "added" never "supplied" never "transfered" and so not really "heat" at all, then you can say Qhz or all 400 joules, "all the way down to absolute zero" is the "maximum".

Then you can say the 100 joules supplied is only 25% of "all the heat" giving 25% "efficiency". Sure. sure,

But that's a crock of bull. Obviously. A complete nonsense measure of efficiency.

At best it's a measure of the quantity of "total internal energy" available to be converted into work. But in reality that 25% of "all the heat down to absolute zero" is 100% of the actual heat supplied above the general background or baseline environmental null, overall ever present energy in equilibrium,

You can throw in your Cv and M so you can pretend your "deriving" something from actual moles and heat capacity of some gas, but that's just a diversion.

[Tom Booth]

...
If the cycle starts at Qcz, and DQh is added. It is then expanded doing work a maximum of Qhz Joules will be converted to work. The gas will be at T = 0 Kelvin and P=0. Now it must be compressed back to P=atmospheric an Tc=300 K. It will take 300 J to do so.

That makes the machine's efficiency 25%.

The machine will have the same efficiency if the forward work is only 100 J. The compression will take 75 J.

This is irrational nonsense.

Rewritten using some common sense:

If the cycle starts at Qcz(300 joules in equilibrium with the environment), and DQh (100 joules of heat) is added. It is then expanded doing work a maximum of [[[Qhz Joules]]] <--- No should be DQh the actual 100 joules added. will be converted to work. The gas will be at [[[T = 0 Kelvin and P=0]]] <--- complete impossible nonsense. Should be 300°Kelvin (back down from 400°Kelvin; 300+100=400, 400 subtract the 100 added then converted to work =300) Pressure? A little under 1 atm probably, not absolute zero pressure. [[[Now it must be compressed back to P=atmospheric an Tc=300 K. It will take 300 J to do so. ]]] <---- more total irrational nonsense based on the previous 0°Kelvin 0 pressure silliness.

[[[That makes the machine's efficiency 25%.]]]. <--- ditto, more nonsense.

[[[The machine will have the same efficiency if the forward work is only 100 J. The compression will take 75 J.]]] <--- ditto

[Tom Booth]

Sorry but using "all" of Qhz, all the "internal energy" down to absolute zero, all 100 joules added PLUS all the "given" 300 joules of "environmental heat" already inside the engine before heat was added, before the engine started, would be like 400% efficiency.

Sometimes I think maybe the engine's working fluid might drop down a half a degree below ambient, and you think I'm crazy!

Your talking about going all the way down to absolute zero and back up again each cycle, 10 times per second. LOL

How is that not ridiculous?

[Fool]

Yes. It's like being at a gas station. Adding a 1/4 tank of fuel. Driving for 400 miles. And saying wow, great milage on 1/4 tank 400%. Then putting 75% back in, to get to your starting point, and saying, "Ugh! I only got 25% percent." 100 out of 400.

The difference for a heat engine is that, to fill the tank back to 75%, the miles must be reversed and taken off. So with a full tank it has a range of 100 miles. Fuel tank empty.

But burning only 1/4 tank round trip, will have a range of 25 miles. Still at efficiency 25%. You can't refill a heat engine in a cycle without resupplying it with work and removing heat. Instructor pulling a vacuum to get it back up the hill, or pushing it and removing heat.

This only applies to heat engines supplying work. If no work is produced, the total work will go back in, and if frictionless and adiabatic, it will uselessly keep spinning, as a frictionless flywheel does. Zero work in, zero work out. This last point is why LTD'S appear to shed little heat, because very little work is produced. Drinking bird power levels.

Have you tried to measure the temperature difference on a drinking bird? Have you tried to heat the bottom of a drinking bird? Neither have I.

[Tom Booth]

Well, like I said before, you have some imagination.

[Tom Booth]

Yes. It's like being at a gas station. Adding a 1/4 tank of fuel. Driving for 400 miles. And saying wow, great milage on 1/4 tank 400%. Then putting 75% back in, to get to your starting point, and saying, "Ugh! I only got 25% percent." 100 out of 400.

The difference for a heat engine is that, to fill the tank back to 75%, the miles must be reversed and taken off. So with a full tank it has a range of 100 miles. Fuel tank empty.

But burning only 1/4 tank round trip, will have a range of 25 miles. Still at efficiency 25%. You can't refill a heat engine in a cycle without resupplying it with work and removing heat. Instructor pulling a vacuum to get it back up the hill, or pushing it and removing heat.

This only applies to heat engines supplying work. If no work is produced, the total work will go back in, and if frictionless and adiabatic, it will uselessly keep spinning, as a frictionless flywheel does. Zero work in, zero work out. This last point is why LTD'S appear to shed little heat, because very little work is produced.

I think that might be a contradiction, but anyway...

You keep repeating this, that my little Stirling engines produce such a small amount of work output, that is why little or no heat can be detected passing through the engine to the sink.

Yet you consistently support the Carnot limit theory that says the less "efficient" the engine, the MORE heat will have to be rejected to the sink. The less "efficient" the less heat converted to work, the more "waste heat" passing through.

Theoretically, then, according to the Carnot efficiency limit nonsense, applying more and more heat at a higher temperature to a little LTD engine should result in less and less heat passing through to the sink a higher temperature means greater ∆T, less "waste heat".

LTD engines can run at very high temperatures and also have considerable work output for their size.

LTD's intended to run on "heat of your hand" are made of plastic and foam rubber and simply can't take high heat. That's a materials issue, not a thermodynamic property inherent in the engine design.

LTD's have enormous big flat heat exchangers. That means MORE heat going in per degree temperature, not less.

That's the problem with conflating/confusing heat and temperature. More surface area means more joules of heat crossing the boundary at the same temperature. More surface area, more joules, more potential for work output at the SAME, or even lower temperature. That's why an LTD CAN run at low "heat of your hand" temperature, it has more surface area, so takes in more heat at a much lower temperature. That doesn't mean it CAN'T run at higher temperatures if made of more heat resistant materials.

https://youtu.be/zD5vCIBQz8Q?si=hNfBHl5GaShKR0pB

Drinking bird power levels.

Have you tried to measure the temperature difference on a drinking bird? Have you tried to heat the bottom of a drinking bird? Neither have I.

Maybe the bird has too much "blow by".

Apples to oranges

[Fool]

a2+b2=C2 would be pretty useless if it only worked for equilateral triangles.

Pythagoras is spinning in his grave.

There is of course, no such thing as an equilateral right triangle. Which is the point.

There is no such thing as a "perfect" Carnot engine either

An algebraic formula should be able to accept any "real" parameters from the domain to which the equation is supposed to apply that actually exist in the real world or what's the point?

When you write things like that, it calls into question your motives and ethics. There's no perfect circle, but we use 3.14 as if it is the perfect number, when it isn't.

You don't prove a math equation wrong by putting in incompatible numbers that won't balance. All you accomplished by doing that is proving you don't have a right triangle. 3^2+4^2=5^2, works. But 3^2+3^2=3^2 doesn't, and only proves that a triangle with sides of lengths 3,3,3 is not a right triangle. It doesn't disprove the formula.

Pythagorean Theorem describes a perfect right triangle. Give it two sides and it will calculate the third. Algebra will be necessary.

Pi can be calculated to extreme precision, far more accurate than can be built or measured, but it is still valid.

The Carnot theorem, based on a description of a perfect engine, and when reversed, a heat pump, is a theoretical maximum that every real engine can't, never will, and never has, obtained. The only way to prove it wrong is to build an engine that exceeds the efficiency. It must be tested and retested by independent laboratories. You have not done this. All your bashing is moot.*** The fact that a better engine could prove it wrong is enough for falsifiability. It is science.

You may be on to something by insulting the cold plate, I doubt it, but you might be. But, that doesn't prove the Theorem wrong, it may just improve real engine efficiency closer to Carnot, I doubt that too, but you might be on to something. Wasting your time here claiming Carnot is wrong without proof, is pointless. Instead of asking for Carnot proof, so you can dispute it by inserting bogus numbers and theories, spend that time constructing engines. I know you can turn that around and point it at me. But I'm just supporting 200 years of thermodynamics theory and successful engines. It seems to me that should be helpful for people constructing engines. Your theory, unproven, not so much. Unfortunately it seems to permeate almost every thread here like this is some kind of Tom blog or soapbox. And I will be spending more time constructing now that the weather is getting better.


*** You will try to deny that you are bashing anything. We will laugh.

[Tom Booth]

a2+b2=C2 would be pretty useless if it only worked for equilateral triangles.

Pythagoras is spinning in his grave.

There is of course, no such thing as an equilateral right triangle. Which is the point.

There is no such thing as a "perfect" Carnot engine either

An algebraic formula should be able to accept any "real" parameters from the domain to which the equation is supposed to apply that actually exist in the real world or what's the point?

When you write things like that, it calls into question your motives and ethics. There's no perfect circle, but we use 3.14 as if it is the perfect number, when it isn't.

You don't prove a math equation wrong by putting in incompatible numbers that won't balance. All you accomplished by doing that is proving you don't have a right triangle. 3^2+4^2=5^2, works. But 3^2+3^2=3^2 doesn't, and only proves that a triangle with sides of lengths 3,3,3 is not a right triangle. It doesn't disprove the formula.

Pythagorean Theorem describes a perfect right triangle. Give it two sides and it will calculate the third. Algebra will be necessary.

Pi can be calculated to extreme precision, far more accurate than can be built or measured, but it is still valid.

The Carnot theorem, based on a description of a perfect engine, and when reversed, a heat pump, is a theoretical maximum that every real engine can't, never will, and never has, obtained. The only way to prove it wrong is to build an engine that exceeds the efficiency. It must be tested and retested by independent laboratories. You have not done this. All your bashing is moot.*** The fact that a better engine could prove it wrong is enough for falsifiability. It is science.

You may be on to something by insulting the cold plate, I doubt it, but you might be. But, that doesn't prove the Theorem wrong, it may just improve real engine efficiency closer to Carnot, I doubt that too, but you might be on to something. Wasting your time here claiming Carnot is wrong without proof, is pointless. Instead of asking for Carnot proof, so you can dispute it by inserting bogus numbers and theories, spend that time constructing engines. I know you can turn that around and point it at me. But I'm just supporting 200 years of thermodynamics theory and successful engines. It seems to me that should be helpful for people constructing engines. Your theory, unproven, not so much. Unfortunately it seems to permeate almost every thread here like this is some kind of Tom blog or soapbox. And I will be spending more time constructing now that the weather is getting better.


*** You will try to deny that you are bashing anything. We will laugh.

This thread only exists because of your continuously hounding me on other threads where I simply post videos of my experiments or try to have normal conversations on other topics not related to YOUR obsession with Carnot and your obsession with following me from thread to thread hounding me and trying to debunk and discredit me

In my opinion, ANY Stirling engine beats the "Carnot Limit"

I've demonstrated this a dozen times ON VIDEO, by showing near ZERO heat "rejection" through the engine's working fluid.. Emphasis on THROUGH. and WORKING FLUID. Not heat that didn't go in to begin with, went around, got conducted through bolts or got re-created through friction from mechanical work output.

I'm just reporting my experiments. Stop attacking and trying to discredit and slander me and I won't be forced to defend myself.

There are a million engines that exceed "Carnot efficiency". Take any toy Stirling engine available and test the "heat rejection" and compare it to what the Carnot formula predicts. The "waste heat" isn't there.

You may not agree, I don't care. We can agree to disagree.

As long as you and Matt, and "nobody" and whomever else continue bringing up my name I'll continue defending myself. Keep trying to debunk my experiments, I'll defend myself, or if you make a valid point, try to run another experiment.

Start your own thread and leave me alone. If you didn't keep bumping all my topics up, I"d probably post a video about once a month.

My "motives and ethics"?

I'm interested in facts and reality and truth regarding how Stirling engines operate, that's it.

You keep trying to cram obsolete, 200 year old long ago invalidated "calorics" nonsense down my throat and keep hitting me over the head with unproven Carnot Limit b/s every time I turn around, along with long rambling essays and so-called "proofs".

I'm just giving you my honest opinion.

Why don't you address the fact that your so-called "derivation" begins with a thinly veiled version of the Carnot limit formula, which you insert at the start, that informs everything that follows.

All your calculations depend on this equation.

You start with the Carnot limit equation, thinly disguised, run it through all kinds of mathematical manipulations, then pretend you "derived" the Carnot limit equation from gas moles and heat capacity.

What's your motive for such a deception?

[Tom Booth]

...

The Carnot theorem, based on a description of a perfect engine, and when reversed, a heat pump, is a theoretical maximum that every real engine can't, never will, and never has, obtained. The only way to prove it wrong is to build an engine that exceeds the efficiency. It must be tested and retested by independent laboratories. You have not done this. All your bashing is moot.*** The fact that a better engine could prove it wrong is enough for falsifiability. It is science.

...

It is impossible to build an engine that "exceeds the Carnot limit".

The reason for that is, the "Carnot limit" has nothing to do with engines. It's a calculation based on temperatures OUTSIDE the engine. The so called "hot and cold reservoirs".

It says that the energy is limited by the "fall of Caloric" down the temperature scale. Based ONLY on the hot and cold temperature.

Of course, the high temperature and the low temperature will be the same regardless of the actual engine thermal efficiency. So it is impossible to beat the Carnot limit on its own terms.

You cannot measure the Carnot efficiency of any engine, you can only measure the temperatures of the heat sources. You can't "beat" a theory that has no connection with physical reality or the actual object to which it is supposed to apply.

The Carnot limit has nothing to do with efficiency. It's a temperature reading.

I was very patient and open minded, very willing to consider your "proof".

Your proof turned out to be an intentional deception.

No "proof". No "derivation". Just deceptive psychological manipulation in a pretended attempt to demonstrate a "proof" for a theory that there is no proof for, no experimental evidence, no sound mathematics. Nothing.

I've pointed out before, claiming that your theory cannot be disproven is not a valid argument.

How would you or anyone else determine that an engine exceeded the "Carnot Limit"?

Measure the temperature of the heat input and the temperature of the sink? The hot and cold "reservoirs"?

That has nothing to do with the actual engine efficiency.

You can accept the Carnot Limit nonsensical theory based on the "grandfather clause" if you want. It's so old it managed to escape modern standards of scientific validation, but I don't have to adhere to your standards of acceptance.

I've done my own common sense evaluations of the "Carnot Limit" and found it to be complete junk. No experiments I've done give it any credence whatsoever. Any engine I've ever tested exceeds the Carnot Limit by miles and miles, based on the fact I have not been able to measure the "waste heat" predicted by the theory.

You may think that is not a valid test, and say: "The only way to prove it wrong is to build an engine that exceeds the efficiency. It must be tested and retested by independent laboratories."

That's your opinion.

I think measuring the heat output or lack thereof is a perfectly valid proof and a simple experiment anyone can perforn for themselves using their own engine, so there can be no mistake.

[Stroller]

How would you or anyone else determine that an engine exceeded the "Carnot Limit"?

Measure the temperature of the heat input and the temperature of the sink? The hot and cold "reservoirs"?

It's not hard to measure the combustibles expended in transferring energy to the working fluid. Just put the gas canister on an electronic scale.

Likewise, it's not hard to measure the work extracted from the system with a simple brake or some modern electronic monitoring of magnetic resistance for small systems.

Most of the generators I've been looking at online seem to be struggling to get more than 5% work out of the input energy.

Quite a way to go before we worry ouselves too much about Carnot and his half baked conceptualisations then...

[Fool]

Lying and twisting my arguments won't help you understand thermodynamics.

That's your opinion.

No. It's science, and backed by years of refinement. Your opinion is that your experiments are valid. Scientific practice requires independent verification. Since you've destroyed most of the engines you've tested, you will be hard pressed to get verification.

I've tried making suggestions. I've given mathematical proofs, that no one has found any flaws. I don't see this ending.

I still don't understand why people keep trying to run LTD's at higher temperatures than they are designed for. There is a reason for there shape.

Styrofoam cups are barely able to hold boiling water. And that is because they are constantly cooled by the air around them.

Styrofoam won't stand up well to an oven at 200 degrees F.

[Tom Booth]

Lying and twisting my arguments

"Lying and twisting" how?

All you did is rewrite the Carnot equation with a new set of symbolic variables. What does that prove?

That's your opinion.

No. It's science, and backed by years of refinement.

Nonsense. The Carnot equation is backed by exactly nothing.

Your opinion is that your experiments are valid. Scientific practice requires independent verification. Since you've destroyed most of the engines you've tested, you will be hard pressed to get verification.

More nonsense.

Try Amazon.

I said ANY off the shelf model Stirling engine exceeds the Carnot limit as far as "heat" entering the working fluid and being converted to work rather than passing through.

There is a virtually infinite array of Stirling engines you or anybody could use. Most cost less than $50

I've tried making suggestions.

Your suggestions are almost invariably nonsensical. Put the engine in an oven. Great idea!

I've given mathematical proofs

Rewring the Carnot formula 20 different ways proves what exactly?

, that no one has found any flaws.

I've found several flaws. The same logical flaws inherent in the Carnot formula itself, which you have only repeated not resolved.

Making added heat into "all the heat down to absolute zero" is a major flaw.

100 joules does not equal 400 joules.

I don't see this ending.

I still don't understand why people keep trying to run LTD's at higher temperatures than they are designed for. There is a reason for there shape.

Styrofoam cups are barely able to hold boiling water. And that is because they are constantly cooled by the air around them.

Styrofoam won't stand up well to an oven at 200 degrees F.

The LTD design using a large surface area is a great design, and also disproves the Carnot Limit, proving that efficiency is not limited by temperature. You can easily increase the heat input in joules without increasing the temperature difference by just increasing the surface area.

[Tom Booth]

How would you or anyone else determine that an engine exceeded the "Carnot Limit"?

Measure the temperature of the heat input and the temperature of the sink? The hot and cold "reservoirs"?

It's not hard to measure the combustibles expended...

As I've said, combustibles outside the engine are not the issue.

The Carnot efficiency limit concept relates only to heat actually passing into and expanding the working fluid or actually passing through the working fluid to the cold side without expanding the gas, if that's possible.

Though admittedly there is a great deal of confusion and disagreement on that subject.

It's all I'm concerned about anyway.

The question is, can a Stirling engine "run on ice" without passing heat through to the ice.?

I could care less about heat that stays over on the hot side.

IMO the Carnot equation applies to STEAM passing through a steam engine carrying "latent heat" that is returned to the condenser, not a Stirling engine that admits only energy in what is arguably its purest form with no mass. There is no "combustion" or "exhaust" in a Stirling engine.