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

[Tom Booth]

...


Superposition is a mathematical and engineering tool that allows effects to be added up
....

Like my heat vector sum (alignment) thread.

Resize_20230809_122630_0041.jpg (361.67 KiB) Viewed 195 times

[Tom Booth]

In regard to gas "contracting" at low temperatures, there is a very interesting description of air liquefaction:

Compress_20240421_034139_9784.jpg (189.31 KiB) Viewed 190 times

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What's most interesting is the statement in the second clip, how once enough cold is established, compressing the air to liquify it becomes easier to the point where he says that the air is rushing in and liquifying under atmospheric pressure.

Presumably the attractive force of the extremely cold and compressed air molecules is causing condensation of more liquid air with little additional expenditure of energy, which energy comes from boiling the liquid air in a modified steam engine with ambient heat to drive his compressor.

Elsewhere in the interview he states that he could produce 10 gallons of liquid air for every three gallons he boiled in his liquefier.

Of course, poor Mr. Tripler was publicly denounced as a charlitain and a fraud and driven out of business.

[Tom Booth]

Even now, the smearing of his reputation continues:

http://www.douglas-self.com/MUSEUM/POWE ... uidair.htm

[Tom Booth]

...
That allows us to look at the total energy in the system. So Qhz should have the same relation ship to Qcz that DQh has to DQc,
...

I've been trying to work out what you might mean by this statement.

"Qhz should have the same relation ship to Qcz that DQh has to DQc"


First of all, why "should have"? Is there some question about this?

Looking at this I find

1) Qhz is the "superposition" shall we say? Of the "given" internal energy the engine starts out with plus Qh or "DQh," or. In your example 300 joules plus 100 joules

2) DQh is the energy or "heat" input per cycle and DQc is Qc the portion of DQh that is "rejected" each cycle.

Taking the fuel tank analogy you have a tank 3/4 full.

You fill up, adding an additional 1/4 tank.

If we rewrite the sentence using that analogy:

Qhz should have the same relation ship to Qcz that DQh has to DQc"

"(The full tank of gas) should have the same relation ship to (the gas that was already in the tank) that (the gas added at the last fill-up) has to (the gas added at the last fill-up that doesn't get used)"

In your analogy, however, as much gas as is added is always used up before the next fill-up (next full cycle) so DQc is nothing. Zero. At least as far as measured quantities are concerned. You don't dump 3/4's of each fill-up out of the tank each engine cycle, or even each fill-up.

Now, since the added gas and the 3/4 tank of gas are mixed in the tank, some diminishing residual will always be present from previous fill ups. But how is that relevant to an energy accounting?

I find trying to deduce your meaning something like trying to fit a square peg in a round hole.

Hopefully you can elaborate on what you mean.

In an engine the "fill ups" take place ten times per second. Not to confuse issues but most of the fuel stays in the tank. Small metered amounts are taken in through the carburetor.

Suppose our engine is a stationary generator, so we can dispense with the idea of fuel being wasted by lugging the unused portion of our fuel around as we drive.

Anyway, I've been straining over trying to figure out what parallel relationship you are talking about that we "should" find.

In the Carnot theory there is supposed to be a parallel ratio between "all the heat" as measured by the temperature of Th and how much of the added heat can be utilized for work, but that seems different. That is, I can't work out a one to one correspondence between your variables and the Carnot theory.

I'm hitting something of a roadblock. Maybe you could clarify this. "Should have the same relationship" statement before I go further.

[Tom Booth]

I think I figured it out finally:

Compress_20240421_122627_7772.jpg (21.54 KiB) Viewed 172 times

Drawing out a picture of the two "ratios" described, and adhering to the Carnot theory.

The little rectangle in the upper left of the bottom right rectangle is the "work" or maximum heat input that can be converted.

(Theoretically ala Carnot)

[Tom Booth]

Well, so far at least, the way I look at it is Qcz is like a reserve tank of gas that I don't have a key to unlock so can never use (so far as is generally recognized anyway)

DQh however is high grade fuel put in at 400°K

So there is this 4:3 ratio 300°K to 400°K

I've supplied fresh fuel of the highest grade going in at a temperature of 400°K

By analogy I have this extra fuel tank I have to lug around.

That's OK as an analogy, but what actual physical mechanism is that supposed to represent?

Supposedly it is a "Tax" or "penalty". Or "entropy". For some reason that's just the "rule" or "law".

So I add my 1 part high grade DQh at 400°k and that gets diluted with three parts of the lower grade Qcz at 300°k

300x3 + 400 = (900 + 400)

1300/4 = 325

So my high grade 400° "fuel' has been diluted down to 325 which is only 25 above the 300 "baseline"

Maybe kinda makes sense, but has this raised the "baseline" to 325°K?

Have I added fuel to the "reserve tank", the regenerator maybe?

How do we account for the "lost" heat?

"Entropy"? The "cold reservoir" ?

If DQh has been "diluted" with Qcz then hasn't Qcz also been upgraded by 25 joules?

I mean the 75 joules of "waste heat" haven't been "rejected". Yet. Qcz is INSIDE the engine, right?

[Tom Booth]

So next cycle.

Again add heat at 400°K but if heat is not "rejected" our ∆T quickly diminishes. We have a bottleneck. After a few rotations the ∆T should get completely washed out.

Well, what if ∆T doesn't matter?

Suppose by "upgrading" the quality of Qcz DQh is less diluted?

Suppose in reality we have access to the alleged "reserve" tank.

If fuel going in gets mixed up with Qcz, then there must not really be any separation.

Maybe the hotter Qcz gets, eventually the fuel added is not diluted at all.

Experimentally, insulating the "sink" on my engines has sometimes increased the RPM markedly. Creating a "bottleneck" to destroy the ∆T so the engine grinds to a halt, experimentally, turns out to be impossible. Or at least apparently so.

Smothered by every kind of insulation to block every possible heat exit, the engines just keep going and going and going...

https://m.youtube.com/playlist?list=PLp ... Q9pQZzY7Eu

[Tom Booth]

I mean, this engine is ALL acrylic. Sides top, power cylinder, everything but the bottom hot heat input plate.

It is sitting on a 100 Watt ceramic heating element.

With all that heat, potentially going in at the bottom and nowhere else to go, the engine is running like a bat out of hell and just kept going. It had already been running like that for I forget how long before getting the camera.

It kept running at super high RPM, (super high for this little plastic engine anyway) Not only made of all acrylic which makes a. very poor heat outlet, but blanketed with Aerogel just for good measure.

It apparently only slowed down because the glue or silicone holding the bottom plate on started melting.

The bottom plate was searing hot, as can be heard in the video when it is touched by the wet knife. The water SIZZLES.

https://youtu.be/WCNsmE-Evbc

One thing I've noticed though.

When running engines in this way, with no heat outlet. They seem to have to keep running to keep running.

The seal on the engine had given out and was obviously leaking, but probably not so bad that it couldn't run if I pressed down on it to hold it together, but once idle, it wouldn't re-start while hot.

No cooled down working fluid to expand.

But if kept running, it can run for hours.

To me that indicates the heat is being converted, but for that the engine has to keep running. Once it stops it quickly becomes "heat soaked".

It will need the ∆T restored to start up again. It needs the cold to expand from to get started, but that is all. Once running the work output restored the ∆T each cycle, but if it stops, good luck getting it going again.

[VincentG]

Vincent, I don't know what you want or are striving for, but to get 50% efficiency out of any heat engine would be a very good feather in someone's cap.

Carnot efficiency of 50% with DQh of 100 could be done between 100 K and 200 K. However, a real engine at those temperatures probably wouldn't get much better than about 25%, and it would have to be run on a much colder planet.

It could also run at 300 K and 600 K, for the same efficiencies, but a larger DQh.

If run at 300 K and 1200 K the Carnot Efficiency would be 75% and a real engine might be 37.5%.

We have previously determined that buffer pressure has no effect on efficiency, and that charge pressure has little to no effect. So what parameters would have to be changed to reach "super-carnot" (thanks Matt) efficiency?

IOW, does the atmosphere have to be absolute zero? So in that case any atmospheric pressure will do, so long as the temp is 0k?

So if an artificial atmosphere of 0k was maintained, the efficiency of the (ideal)engine itself would be 100%?

Is that the only hold up?

[matt brown]

We have previously determined that buffer pressure has no effect on efficiency, and that charge pressure has little to no effect. So what parameters would have to be changed to reach "super-carnot" (thanks Matt) efficiency?

IOW, does the atmosphere have to be absolute zero? So in that case any atmospheric pressure will do, so long as the temp is 0k?

So if an artificial atmosphere of 0k was maintained, the efficiency of the (ideal)engine itself would be 100%?

Is that the only hold up?

0k is only an advantage when a heat engine needs a heat sink which is what Tom is trying to circumvent. However, if you can recycle would be sink heat to source then you don't need a heat sink. Think of this kinda like cooling a steam engine condenser with alcohol that feeds boiler source whereby sink heat returns to source vs ambient.

So far, here's what I'm finding about Super-Carnot cycles:

(1) Tom is right about adiabatic compression vs isothermal compression since the retained (or is that conserved - lol) heat of adiabatic compression is more important to cycle eff than the lost work, thus gaining eff over power

(2) the trick is scheming PV plot where the temperature after expansion is as HIGH as possible, not as low as possible to maximize regen heat

(3) thus, gaming thermal ratios vs volume ratios while ignoring charge and buffer pressures (for now)

(4) in the "S-C" Otto I posted, the thermal ratio = 3.5 and the volume ratio = 2.0 so this scheme has Tr/Vr = 1.75

(5) approaching "one-one" (think common LTD) where thermal ratio = 1 and volume ratio = 1, then Tr/Vr also approaches 1, so there's no single T/Vr ratio that maximizes regen

(6) the S-C Otto has ideal eff = .85 thanks to Tr = 3.5 but eff = .90 appears possible with enough wiggle room for credible power from a much lower thermal ratio (work in progress)

(7) when you shrink PVT values down...way down...you approach eff = 1.0 but are left with only common LTD toy

(8) once you have a credible thermal scheme, you then need a credible mech...

[Tom Booth]

...
0k is only an advantage when a heat engine needs a heat sink which is what Tom is trying to circumvent. ....

Not to be overly picayune, but I guess I'm overly sensitive about mischaracterizations.

Anyway, again, I'm not "trying to circumvent" anything. Just trying to determine the facts of the matter. Does a Stirling engine "need"" or require a heat sink or "cold reservoir".

Carnot, Kelvin and company said/say ABSOLUTELY it's a "LAW" of the universe.

Tesla suggested, well, not necessarily.

To me it seems like an important question that has never been conclusively resolved by any convincing empirical evidence.

So really I'm just trying to fill what seems to me to be a void. The argument is never going to be settled by debate., theorizing, number juggling or name calling.

I'm just doing some experiments in an effort to answer the question in, I think, a rather impartial manner, not "trying to circumvent" what may be an illusion. Or deny what could be a reality.

[Tom Booth]

....
... So Qhz should have the same relation ship to Qcz that DQh has to DQc, in other words, 'n' is the same. Basically this says that Qcz can be calculated from 'n' and Qhz,
or:
Qcz = Qhz•(1-n)

Substituting that equivalence for Qcz into the 'DQh' equation:
DQh = Qhz - Qcz (DQh equation)
Qcz = Qhz•(1-n)

Substituting and distributing:
DQh = Qhz - Qhz(1-n)
DQh = Qhz - Qhz + n•Qhz

Subtracting:
DQh = n•Qhz (#2)

Combining #1 and #2
n = n•(Qhz - Qcz) / DQh (#1)
DQh = n•Qhz (#2)

#2 into #1:
n = n•(Qhz - Qcz) / n•Qhz

The n's on the right side, of the equals sign, cancel becoming one, and rewriting:
n = (Qhz - Qcz) / Qhz (#3)

Equation #3 shows that DQh and DQc have now become Qhz and Qcz. In retrospect, it seems logical that the efficiency profile should be the same regardless of absolute scale. Substituting in Qhz and Qcz straight across for DQh and DQc makes sense, and would have been faster. That was the mathematical derivation/proof. Note also, that it tends to maximize efficiency by equating DQc with Zero. DQc is not zero, it is just the amount of inevitable heat rejection and with maximum work out.

Now using the equations above for Qhz and Qcz:
Qhz = M•Cv•Th (The equations above)
Qcz = M•Cv•Tc (The equations above)

Substituting the above two lines into equation #3:
n = (Qhz - Qcz) / Qhz (#3)
Here:
n = (M•Cv•Th - M•Cv•Tc) / (M•Cv•Th)

Rearranging and removing the distributed 'M•Cv':
n=M•Cv•(Th-Tc) / (M•Cv•Th)

Canceling 'M•Cv' top and bottom because they become one:

n=(Th-Tc)/Th <<<The final solution.

That shows the logical step by step progression for the mathematical derivation or proof.

Basically we took relative scale Delta heat:
n=(DQh-DQc)/DQh
Converted it to absolute temperature scale heat:
n=(Qhz-Qcz)/Qhz
Then converted it to temperature calculated heat:
n=(Th-Tc)/Th
They are all the same value of n, because they are all the same heat-in heat-out ratios. They are just three different ways of obtaining the same thing.

It's logical to think that higher temperature differences produce higher pressure differences, that make greater power to weight and size ratios, ease of construction, operation, and efficiency increases.

1/10 degree temperature, would be like trying to move a piston with 1/10 of a psi. How can that possibly be as efficient as trying to move a smaller piston with 100 psi.

It would take a piston 1000 times larger in area to develop the same force. Power and efficiency sucking bad bulk would be the down fall. I hope this makes sense in regard to the Carnot Theorem.

Hopefully that is a little easier to follow. Whomever said this was easy, or simple, has my complete disagreement. LOL

And it still probably has little errors. I'm hoping the little errors we've found are it. I don't think they spoil the overall proof, but a proof isn't a proof until all the errors are eliminated. Your help has been much appreciated.

The underlined sentence is, I think, clearly an assumption rooted in the Carnot efficiency limit notion, idea, concept, theory, so-called "LAW".

Without having gone through all that follows again, with a fine tooth comb, I suspect this is, as pointed out before, a case of circular reasoning, or using the theory itself as the proof of the theory.

In this case the assumption "Qhz should have the same relation ship to Qcz that DQh has to DQc" is an assumption based on the Carnot limit theory, it seems more than likely then, that all that follows is simply a restatement in mathematical terms of the initial postulate.

Now, perhaps this is just some preliminary calculations and some actual "proof" independent of the Carnot assumption follows, but at first glance, there seems little point in going further. But I will.

Again, there is nothing in error mathematically. It is just permutations of the Carnot limit equation.

What it proves, so far, is; the Carnot limit equation is the Carnot limit equation, and as such it can be rewritten in various and sundry ways as can any mathematical equation.

Do we ever break out of this self referential loop further down?

[Fool]

We have previously determined that buffer pressure has no effect on efficiency, and that charge pressure has little to no effect. So what parameters would have to be changed to reach "super-carnot" (thanks Matt) efficiency?

IOW, does the atmosphere have to be absolute zero? So in that case any atmospheric pressure will do, so long as the temp is 0k?

So if an artificial atmosphere of 0k was maintained, the efficiency of the (ideal)engine itself would be 100%?

Is that the only hold up?

There is no such thing as "Super Carnot Efficiency". The Carnot engine is an example of a perfect engine. Run one backwards as a heat pump and you will return 100% of the heat to the hot plate, ideally. Anyone telling you differently is mistaken. If they have a working device, it will need to proven by independent testing in a reputable laboratory.

The temperature needs to be 0 K to theoretically obtain 100%. In reality, that won't even work. Pressure is temperature dependent. At 0 K pressure will be zero. And all gasses will be frozen. Theoretically, we don't need zero Kelvin to get close to 100%, if you are willing to live on Pluto and use nuclear fuel, and are satisfied with 70 80 percent, theoretically. Can't say for a real engine until one has been built.

You could get high efficiency from a heat engine by running it on an artificial cold sink, but overall efficiency will be even worse. Artificial low temperatures are very energy costly. Think about how much AC and refrigerator appliances cost to run. Both those are at the top of a homes energy consumption, those and electric heat. Now imagine trying to cool off a 100 hp engine in your living room.

Remember one more thing a heat pump operating at zero Kelvin will have a COP no grater one, 1, uno, 100%. Matching a perfect Carnot engine getting 100% efficiency as well.

No, there is plenty more holding us back. That is just the ideal thermodynamic part, initial part. After that, we start subtracting. Subtract non ideal path, Delta to to get heat to flow, friction, etc...

Matt, I'd like to see a PV diagram of your "(2) the trick is scheming PV plot where the temperature after expansion is as HIGH as possible", scheme. A full cycle, please. I know it is proprietary.

Tom, magnets don't work that way.

I've been trying to work out what you might mean by this statement.

"Qhz should have the same relation ship to Qcz that DQh has to DQc"


First of all, why "should have"? Is there some question about this?

The ratio is the same.

Qcz/Qhz = DQc/DQh = 300/400 = 75/100

Should, could, is, will be, has to be, needs to be, is set by mathematical precision, by definition. All just semantics. Look at the equations.

[Quite=Tom Booth]Anyway, I've been straining over trying to figure out what parallel relationship you are talking about that we "should" find.[/Quote]

I've been exploring parallel analogies for quite some time too. It always ends with, it's an analogy and not reality. One must understand that heat is energy, and work is energy, that is in transit. Storing energy can be done by motion/kinetic, height/potential, and by internal-energy/temperature.

Putting work into a system that will store it as temperature has two possibly routes.

Irreversible, friction gives rise to equal work for equal internal energy storage.

Or reversible, squeezing, gives rise to more temperature gain and that is dependent on starting and ending temperatures, for a complete cycle.

There is nothing in the world that I've come up with that is a perfect parallel, hence analogies will be more confusing than helpful.

I find it interesting that you tend to put faith into stories that are aligned with what you want rather than what research and logic indicates. Mr. Tripler's compression pump was run by a 85 hp steam engine and boiler. Yet that part is strangely missing, a sign of faith, I guess.

Mr. Tripler's comment about 'air rushing in to fill the vacuum and suddenly liquifying', doesn't seem to happen for a pool of liquid air, or an open thermos bottle of it, even when under elevated pressure.

The process being described as a "Hampson-Linde process", seems missing too. I'm sure your faith will come up with a miss applied way around these points. I don't see any reason to believe either way. The second law counters any claim of perpetual motion, so far there isn't any valid theory for it, and there appears to be zero operational devices ousting the second law. Perhaps that is why his company went bankrupt an no one has been able to repeat the claims.

I doubt you can actually back up that statement. Or what you mean, or are trying to imply I don't know.

Do you suppose that if there is a compression stroke after an isothermal expansion 90% of the joules go back in time so instead of being transformed into work they can go to the "cold reservoir"?

Let's not bring time travel into this. It is fairly straightforward to use the equivalent of heat and work. How are they get stored is more complicated, and how the conversion proportions are calculated is abstract, but not too bad. Maybe the following link will help :

https://www.thoughtco.com/isothermal-process-2698986

There is a good graphic showing the shaded area under the curve going all the way to zero pressure. Zero pressure and zero Kelvin are the same condition. That shaded area would be the 100 Joules.

https://en.m.wikipedia.org/wiki/Isothermal_process

Gas molecules always attract. That attraction gets stronger as they get closer. They "stick" to each other if their velocity is lower than the escape velocity. Liquid molecules evaporate when the kinetic energies/velocities get higher than escape velocity. In space they will continue away forever. Contained, they will bounce against the walls making a positive pressure.

Gasses to not succumb to their attraction unless slowed down below escape velocity by energy removal. They don't all slow down. There is always a pressure, even when very low.

I don't think "pulling" is often included in a definition of "contract".

Some definitions from some online dictionaries:
"to cause to draw more closely together"
"to reduce to smaller size by or as if by squeezing or forcing together."
Gases have attractive forces and when cooled or brought closer together by being compressed, the attractive forces get stronger and this can moderate or ebate the pressure.

The word "Draw" has the synonym "pull".

Squeeze is to compress.

A stretched rubber band, spring, or guitar string, will contract/pull/Draw inward when released, and will pull that which it is attached with it. It is a feature mostly found in solids, usually not in gasses or liquids.

Contraction is often misused in gas descriptions. It confuses things.

Magnets attractive force is maximum when touching, when oriented N-S-N-S.

If oriented N-S-S-N or S-N-N-S, maximum repulsive force is when they are touching too.

[Quite=Tom Booth]Do we ever break out of this self referential loop further down?[/Quote]

Probably not. Thermal internal energy is correlated to temperature. Temperature is correlated to energy. Work and heat are just energy coming in or out. Work and heat are the change in internal energy.

The Carnot theorem is a concatenation of, conservation and conversion of energy, work, heat, temperature, mass, conversion between these, coefficient of heat, and absolute temperature and pressure, and calculus and other mathematics. It will circle around these things. It is not a coincidence that efficiency is related to energy, absolute energy, heat, heat's relation to energy, temperature energy, and other energies, and their proportions.

DQ = M•Cv•DT

PV = MRT

M mass
R gas constant
DQ heat coming or going, Delta energy
Cv coefficient of heat temperature and energy
DT change in temperature, Delta T
P absolute pressure
T absolute temperature

One leads to another. Another leads back to one. That's the way theories are. Then comes all attempts to disprove it.

[Tom Booth]

....
Tom, magnets don't work that way.

....

What way? I don't think I said anything about how magnets work.

If you hang two magnets from strings or just push them across a table you have to apply some pressure, is all I said. Then eventually, as the magnets get closer the pressure between your finger and the magnets will decrease as the magnets get closer and closer. Eventually the attractive force will pull the magnets together.

It's an analogy of how gas molecules behave under pressure. Did you read the link I provided?

I've been trying to work out what you might mean by this statement.

"Qhz should have the same relation ship to Qcz that DQh has to DQc"


First of all, why "should have"? Is there some question about this?

The ratio is the same.

Qcz/Qhz = DQc/DQh = 300/400 = 75/100

Only because you set it up that way so your equations adhere to the Carnot limit theory, from what I can see so far. I'm not all the way through though, so I'll reserve judgement and take another look, however it appears the supposition "should have the same relationship" leads to your arranging the mathematical "proof" accordingly.

Should, could, is, will be, has to be, needs to be, is set by mathematical precision, by definition. All just semantics. Look at the equations....

I have.

Do we ever break out of this self referential loop further down?

Probably not. ...

Didn't think so, however I'll continue looking it over.

99% of your "proof" however, appears to be mere obfuscation, completely redundant number juggling. Writing the same Carnot formula over and over in dozens of different ways simply to demonstrate your mathematical prowess and hopelessly obscure the fact that all this is nothing more than the same old Carnot formula based on temperature difference and is not any actual "proof" of anything. Just a very elaborate exercise in starting out with the Carnot assumption, giving it a new mathematical expression and then juggling the numbers to arrive back where you began, with an assumption, a theory. Nothing more.

[Tom Booth]

...
One leads to another. Another leads back to one. That's the way theories are. Then comes all attempts to disprove it.

Round and round we go.

Circular reasoning.

Modern science considers theories that depend on failure of "attempts to disprove it" pseudoscience. Popper's principle of falsifiability.

The Carnot theory has survived primarily due to the fact that it is nearly unfalsifiable.

For example you cannot disprove my claim that I have sixteen guardian angels. Eight on each shoulder.

Simply making an assertion that can't be disproven does not make it true or valid science. The Carnot efficiency limit is just that. A claim or assertion with no empirical backing whatsoever.