Stirlingengineforum.com

Let me begin by clarifying what I mean by 100% efficiency.

By that I mean; begining with a completely uniform temperature all around, inside and outside the engine, some quantity of heat is supplied to the engine to bring up the temperature of the working fluid.

I am discounting heat which does not ever enter into the engine, such as, for example, a blowtorch aimed at the side of a "test tube" thermal lag engine, 99.99% of the heat simply glancing off the outside of the tube but scarcely any actually finding it's way inside.

To begin, here are a few quotations from various sources for consideration:

A compressed gas spring that is expanding and doing mechanical work is an example of heat being converted into work with 100% efficiency.

https://physics.stackexchange.com/quest ... single-ste

...consider a gas that expands and contracts within a cylinder with a movable piston under a prescribed set of conditions.... As the gas does work against the restraining force of the piston, it must absorb heat in order to conserve energy. Otherwise, it would cool as it expands (or conversely heat as it is compressed). This is an example of a process in which the heat absorbed is converted entirely into work with 100 percent efficiency. The process does not violate fundamental limitations on efficiency, however, because a single expansion by itself is not a cyclic process.

https://www.britannica.com/science/ther ... -processes

Additional authoritative sources concur, it is indeed possible to convert heat entirely into work with 100% efficiency.

This 100% conversion of heat into work happens within a Stirling engine when heat is applied, the gas expands and the piston is driven out.

I don't think any informed, competent authority on the subject would assert otherwise. (Discounting possible loses to friction. In actuality, to produce friction, work is required, so the heat was first converted to work to move the piston, which movement subsequently resulted in friction which converted some of the work back into heat.)

The alleged problem or issue arises, apparently, only when it comes time to have the piston return to the point where it started before any heat was added.

To get the piston all the way back to the starting position requires additional work. Supposedly This return journey is what is supposed to make 100% efficiency of a heat engine "impossible"

And, in much of the literature on the subject, this is the reason heat engines need a flywheel

So, in that scenario, the "work" already put into the flywheel, (by the 100% conversion of heat into work), is used to drive the piston back. This work to return the piston, however, is work that was originally produced by converting heat 100% into work to turn the flywheel in the first place. So how is that work suddenly not work that was produced by converting heat into work?

Aside from that conundrum, by observation, it can be seen that in many circumstances the piston, after being driven out, actually returns even when no flywheel is present.

There is, no logical reason, while carefully observing this whole process, to conclude that heat cannot be converted completely into work In any circumstance, it is the heat that expands the gas that pushes the piston out resulting in it being carried around by the flywheel and back again, or it flies out against atmospheric pressure, and then atmospheric pressure pushes it back. Like pushing against a spring, then the spring pushes back.

But the "push back" is only energy returning that was put into the "spring" by the initial push, and that initial push was a result of the 100% conversion of heat into work. Now some of that ORIGINAL energy has returned to begin the whole process over again.

100% conversion of heat into work, AGAIN, but this time with the addition of the work that was just returned from the first cycle in the form of momentum. Or velocity due to the atmospheric "gas spring",

hmmm ...

So, having reviewed this entire cyclical process all the way around and back to the starting point, can anyone explain to me in some logical coherent terms why it is alleged that this process is only, perhaps 15% efficient?

It is conceded that the first half of the process was 100% efficient, or could be. So 85% of that energy first produced by the complete conversion of heat into work had to be used to push the piston back. If so, how does that work suddenly become work that was not produced by the conversion of heat into work.

I guess then we need to clarify that by saying, "useful" work. But, that return compression work is converted back into heat, is it not? That heat then contributes to the next cyclic revolution.

Now I certainly recognize that there are incidental loses, in the form of friction, noise and so forth, but these can all be accounted for and arise as a RESULT of, or consequence of the conversion of heat into mechanical motion that has already taken place.

Tom - it's how the question is framed which often depends upon fuzzy premise/s. The whole Carnot buzz dominates thinking because most engs are Carnot engs. No, not Carnot cycles, but Carnot engs (recently some German guy attached his name to this class merely to distinguish between engs vs cycles). However, I look at stuff from a historical viewpoint, and would simply say that Carnot engs follow commonly held Carnot conclusions, but would include premise with 4 'interleaving' processes aka compression cycles that we're all familiar with. So, Carnot conclusions are simple (and bulletproof) but only with simple cycles. Adding regen with Stirling or Ericsson Cycles pretty much taps Carnot out ! Anyone who thinks Carnot is the Big Dog needs to expand their thermo knowledge, and a good place is looking at (what some would say) is Carnot eff for a range of Brayton Cycles with vs without regen. Yep, a whimpy low press ratio Brayton with apparent Carnot eff <.20 can approach .70 eff with regen.

So, Carnot rules under 'normal' situations, but forget it when pushing the envelope. A better question everyone should be hashing is why everything uses a compression cycle these days. I mean, consider 3 legged PV of Lenoir cycle with isochoric input, adiabatic expansion, isobaric 'compression' (ambient exhaust). This is the same cycle that ran the Otto-Langen eng and what Otto had his eureka event over. Back in the day, no self respecting engineer would consider 'wasting' energy with a compression process, so what's going on here. Note that even when de Rochas pat'd the 4 stroke in 1861, he never made a working model. The hipshot response is the emerging kinetic theory where (relating to engs) all work can be converted to heat, but all heat can't be converted to work. Engineers pick apart these details, and start with values per process, than compare totals per cycle. But the laymen will look at a 3 legged Lenoir cycle with paltry eff (clueless Carnot) and wonder why this 3 legged Lenoir would gain rad eff by adding a 4th process...'some' adiabatic compression between (on PV plot) part of the isobaric compression and part of the isochoric input, in effect turning a lame Lenoir into a studly Atkinson which trumps Otto (similar PV of course). BTW another interesting early ICE was the 1826 US pat by Samuel Morey, and I'd bet that the only known replica (from the early 1930s) still sits in Dean Kamen's office (he's owned it for yrs).

The problem with the term 'heat engine' is that it's subjective, and conjures up whatever anyone is familiar with. Over the years, I've taken it to basically mean simply single phase gas, and usually some pis/cyl mech. Once you start adding doodads (regen, reheat, inter-cooling, turbo this & that, etc) is starts looking like a utility power plant. Alex Kalina developed an absorption cycle 'scheme' with more eff than most utility steam plants, but was slammed for years since the industry couldn't quite get their head around it (too complex was the buzz for yrs, but I think the big boys were just waiting for his pats to expire). Anyways, I rarely see anyone refer to a steam eng or jet eng as a heat eng.

The only high eff heat eng (of any type) I can think of is geothermal steam eng, since it's only recovering energy. However, it's eff is (again) dependent upon definition, since...if this 'steam' eng has old world water working fluid, steam sucks up ~.50 of heat as latent heat of vaporization thru critical points 700F & 3200psi which is why utility plants favor supercritical steam despite major moola of build/operation. So, everyone, get this straight (engineers know this in their sleep) raising steam to critical points (700F & 3200psi) sucks up as much heat as 'merely' turning water into steam, and this latent heat 'constant' is was limits steam cycle eff (lurking engineers, this is the nickel tour). So, Tom, how could a sub critical geothermal steam eng ever have diddly eff even if it ran all the way down to condensation. It's all perception, knowledge, spin, whatever, and oblivious to latent heat won't cause any issues in building geothermal plant. However, same ignorance would sink a stand alone steam plant in a heartbeat, and remain clueless why.

While on my soapbox, here's a similar tidbit that demonstrates lame science. So many goofballs are all hyped about hydrogen fuel for ICE, yet are oblivious to LHV and HHV. Yep, in a 'high tech' age of fancy protocols and such, these guys have missed that the high heat value (HHV) is the heat of combustion but the low heat value (LHV) is the available heat, the difference being what's lost to latent heat. Now, it shouldn't take a rocket scientist to recognize that latent heat sounds like something to do with water, and it is. Yep, the more hydrogen in your fuel, the more latent heat loss upon combustion, and the lower the LVH. Bottom line, gasoline has 8% loss from HHV, but hydrogen has 18%, so nearly 1/5 of total hydrogen fuel energy is trapped in latent heat. Meanwhile, solid carbon (think coal) has LVH=HHV, max cluck to buck, and why kicking the carbon habit will be a tough nut to crack.

Don't get me wrong, I still think there's various solutions to this energy mess, but I often feel like King Midas grabbing at rocks while trying to avoid being turned into a pillar of salt...

Not sure what you mean by "Carnot engs"

most engs are Carnot engs

.

I'm scratching my head over that. Not Carnot Cycle?

So, Carnot conclusions are simple (and bulletproof)

Some clarification of the distinction is needed, and your sense behind those statements.

I don't think that there ever was or ever will be a Carnot engine. It's hypothetical nonsense.

As far as "Carnot conclusions" being "bulletproof", or even vaguely applicable to any real heat engine of any kind: I don't think Sadi Carnot contributed much of anything whatsoever of any worth towards the advancement of much of anything other than the proliferation of ignorance and silly ideas about how engines might work

Carnot was completely clueless. In particular, in regard to hot air engines, expressing doubt that any such thing could even exist.

He never laid eyes on even any actual steam engine, and anything he ever imagined about them was not just wrong, but so divorced from actual reality as to be laughable.

The water wheel was about the extent of his experience. So he thought a heat engine was literally a water wheel.

I imagine the only reason anyone ever felt they had to take him seriously was due to the political influence of his family, largely in charge over who's head got chopped off

The guy's name I was looking for is Reitlinger who is quasi redefining cycle buzz as if a grant meister. I get his point, but more needless mumbo-jumbo, and taken just a tad further we'd have all conv'l compression cycles under his Reitlinger umbrella. In the grand scheme of energy, all 5 of the 'major' cycles are very similar, despite most guys stress their differences more than their similarities. Ya know, pis vs turbine, open vs closed, regen vs non, etc.

Looks like you never read "Reflections' and a tad fuzzy on Carnot family. Yep, the Carnots were well connected and Sadi's dad was Napoleon's logistics guru. Napoleon was always seeking advantage, and being an artillery nut, gave a contract to Sadi (an army engineer) to study cannon 'ballistics' (for lack of a better description), but Waterloo (1815) nixed this. Post Napoleonic Europe was a mess, and within 5 years Sadi was back in school without a future. Then he reckons that the English are eclipsing continental Europe with 'their' steam engine, and ponders whether he can beat them at their own game. BTW at this time, even the Germans referred to the steam engine as the 'English Engine', since it was so poorly understood. So, Sadi studies the expansion_and_contraction of steam as a cycle vs previous expansion only for cannon balls. This is what made Carnot famous...he nailed the cycle concept. However, despite getting cycle concept, with requisite temp diff, AND describing current 4 process cycle, AND suggesting single phase gas vs steam, everyone blew him off due to his compression process. This all took place during the caloric theory, and our compression cycles would have to wait for the kinetic theory.

As I said previously, Carnot only counts when simple (tho that's where most stuff is these days). Check out this pic of Brayton Cycle with vs without regen. Note eff on left and how LP nonregen cycles with whimpy eff get studly with regen.

The PDF that can be downloaded here:

https://www.researchgate.net/publicatio ... mic_cycles

Regarding the Reitlinger cycles is interesting to me in that it references Senft's "Mechanical Efficiency of Heat Engines" which I've just finished reading recently. The PDF also reproduces one of Senft's diagrams, which I also posted to the forum here recently.

Senft, however went a step further than what's asserted in this article, saying that not only does the Stirling engine's efficiency equal, but surpasses Carnot efficiency.

That a regenerator can reclaim "waste heat" increasing efficiency is all well and good and everything and I have no particular problem with that, or Reitlinger, but I think it goes deeper than that.

Not only doesn't "Carnot efficiency" account for any potential efficiency gain due to regeneration, it fundamentally does not account for the conversion of heat into work.

Obviously, or maybe not so obviously I guess actually, but anyway, if the heat going into a heat engine is converted to mechanical output, that same heat energy that went in cannot be stored in the regenerator for later use, nor can it be "rejected" to a "sink" or "cold reservoir".

In a way, that heat has become, in a sense "latent".

That is, the heat/energy is no longer measure able with a thermometer, pretty much in the same way heat can become latent due to a phase change, (or come out of latency), the "sensible heat" that is, the heat that can be felt by our physical senses as warmth, or that can be measured with a thermometer, that went INTO the engine becomes latent in the form of momentum and velocity, the "heat" has BECOME, part of the rotating mass of the crankshaft and flywheel, the heat no longer exists as heat at all.

The heat energy, having become "latent" in the form of mass mechanical motion, can then be removed from the system" as such, that is, transfered to a load, by gears and pulleys and further, perhaps transformed into electricity by being used to turn a generator.

"Efficiency" is a measure of how complete is the transformation of heat, into the "latent" form "work".

That heat that went in is GONE. There is no point in trying to account for it by looking for it in the regenerator, or waiting for it to emerge out the other side of the engine into the "sink".

The heat is not "rejected" to a "cold reservoir". It simply no longer exists as heat at all.

Carnot had no means of even conceptualizing the idea of heat energy being transformed or becoming "latent" in the form of mechanical motion, momentum or velocity.

Carnot believed that heat was simply transported through a heat engine in toto, every bit of it, entirely, completely. None being transformed or becoming latent, none going out as "work" or gross mechanical motion

The entire concept of "Carnot efficiency" as the "height of the fall" or temperature difference is completely incomparable with the modern concept of efficiency as the quantity of heat actually transformed.

There is no reconciling these two diametrically opposite concepts. Heat cannot be transformed into work and simultaneously be "rejected to the cold reservoir".

The mathematical formula for "Carnot efficiency" is based on the principle that heat is transported from source to sink entirely, just like all the water that goes over the top of a water wheel is transported down to a lower level and comes out the other side unchanged.

This does not take into account the "disappearance" of heat within the engine. It does not take into account that heat is transformed.

In reality, the Carnot "efficiency" equation is not any measure of efficiency at all. It is completely meaningless. All it is is temperature difference.

The temperature difference has nothing whatsoever to do with how much heat energy has actually become latent, having been transformed by the engine into "work" output.

Yet, "efficiency" is still calculated on the basis of temperature difference alone. No account whatsoever being taken of how much heat goes into the engine and how much heat actually comes out the other side, or rather DOESN'T come out the other side, by any kind of actual measurement.

Well, the "hot reservoir is T-h and the "cold reservoir" is T-c therefore the efficiency of the engine is:

1 - Tc/Th

That's nothing more than the temperature difference. It tells us nothing whatsoever about the actual efficiency of the engine. Nothing about the heat going in vs the heat going out. Nothing whatsoever about the amount of heat that has been TRANSFORMED by the engine, which is the ACTUAL efficiency of the engine.

If the Carnot efficiency" is calculated by the above formula to be 20% that is not the efficiency. That's the temperature difference

So academia continues to teach that of every 100 Joules going into an engine, at 20% "Carnot efficiency" as determined by the temperature difference 80 Joules must be "rejected" to the sink.

This does not at all take into account the heat transformed into work The only thing the formula 1 - Tc/Th represents is the temperature difference. which has no bearing whatsoever on how much heat goes in and how much comes out and what percentage of the 100Joules that went in were actually transformed into work.

The refrain that it is "impossible" for a heat engine to use all 100 Joules that were supplied without the exhaust being at ABSOLUTE ZERO, is complete and utter idiocy.

If all of the 100 Joules supplied to the engine are transformed into work, the "exhaust" will simply be back at ambient. Which, is to say, for a Stirling engine that has no actual "exhaust". No heat will be left over to be transfered to the sink.

Carnot efficiency, as presented and taught is entirely wrong.

To say that Carnot "nailed the cycle concept" is, IMO overly generous.

Carnot's "cycle concept" never took any account of heat as energy that could be changed from one form into another.

Transported from the Stirling 1 thread:

Nobody wrote: ↑Wed Feb 16, 2022 6:54 am I still don't see what the Carnot Limit has do with it?

Carnot said a running engine will convert 20% of the heat coming in to work out. Think:

Percentages-

For a running engine, 100 in, 80 out to melt the ice, 20 out on shaft.

Carnot says nothing of a non-running engines, nor about the rates of influx of energy, just the efficiency.

One can infer from others and using simple logic that:

For a stalled engine, 100 in, zero out on the shaft, so by default- 100 out to melt the ice.

The question as to which will melt ice faster Isn't answered by Carnot. In fact Carnot's Limit seems to be supported by your experimental findings.

The thought that a stopped or stalled engine will suddenly have zero energy flowing in is just wrong.

All heat engines to date have experimental data that have efficiencies far below the Theoretical Carnot Limit calculated for their situation. None have broken that prediction. Not even close. And when all the mechanical and peripheral losses are added in, far worse.

To be clear, I did not ever say "a stopped or stalled engine will suddenly have zero energy flowing in", though someone on the Science forums had made that assertion, at least in regard to an engine that was,.. well I don't recall, "reversible" or 100% efficient?

Anyway, I disagreed, though perhaps there was some logic behind that, I don't know.

For a running engine, 100 in, 80 out to melt the ice, 20 out on shaft....

For a stalled engine, 100 in, zero out on the shaft, so by default- 100 out to melt the ice..

. In fact Carnot's Limit seems to be supported by your experimental findings.

What I was testing was not what we have today, which is a kind of re-definition of Carnot, but rather Carnot's original belief that ALL the heat would be "transported" through the engine.

If the experiment was not otherwise flawed in some way, then it indicated at least that the Caloric theory is unfounded.

I agree with you that the experiment did not necessarily disprove the formula that has come down to us through, perhaps Clausius or someone else:

efficiency = 1 - Tc/Th

I have not been able to actually trace that back to Carnot who knew nothing of "absolute zero".

My estimate was that the ice under the running engine melted about 15% more slowly, rather consistently.

So, I was rather puzzled why the moderators on the science forum started insisting I was trying to present the engine as a "perpetual motion machine".

All heat engines to date have experimental data that have efficiencies far below the Theoretical Carnot Limit calculated for their situation. None have broken that prediction. Not even close. And when all the mechanical and peripheral losses are added in, far worse.

I have not been able to locate any such experimental data. Certainly not for "All heat engines". Not for any, actually, except my own experiments, which I only initiated in the first place because there was no record of any such experiments that I was able to locate.

I've asked repeatedly to be shown such experimental results, any account of any previous experiment, on all the science and physics forums.

I've infact asked you several times previously, I believe.

I'm still waiting.

Simply asserting there is experimental data, doesn't prove there is.

Well, you have my experiment

Where is the record of all the others?


My experiment was intended to establish, if any of the heat, converted to work by the engine, infact "disappeared" due to having been converted, so as to not reach the sink (the ice).

I don't think the experiment proves anything really. But it did indicate that a difference could be measured, and that difference was consistently on the side of showing that when a Stirling engine is "running on ice" the ice tends to melt more slowly.

That was the expected result, if at least SOME fraction of the heat was converted to "work".

The results thus far do not overturn the fundamental assumptions of thermodynamics. Not at all.

What I do question is what seems to me the arbitrary nature of the so-called Carnot efficiency limitation, represented by this equation:


efficiency = 1 - Tc/Th

Where is the experimental data that established this exact formula?

That a toy engine running on ice with imperfect insulation got somewhat close to the theoretical maximum efficiency limit is somewhat suspicious.

It shouldn't have been that good.

The ice under the running engine took, what was it, five hours longer to melt? Or was it three?

Well it depended on the quantity of ice used actually. But for the engine that was used, the difference in melt time between the running and not running was around 15%

But, there are many identifiable inefficiencies that could be improved upon.

Better insulation, perhaps a regenerator could be added. That engine had no regenerator. The most interesting test might be to add a load. The engine was running no-load, so, whatever heat was being converted was used only to spin its own wheels. Adding a load might make a huge difference one way or the other.

What I hear repeatedly from various quarters is that measuring heat input and output is "too difficult".

Really?

Well it could be difficult if people are trying to measure something that isn't there.

You say: "All heat engines to date... have efficiencies far below the Theoretical Carnot Limit calculated for their situation. None have broken that prediction. Not even close..."

My toy engine came pretty close, actually.

Hopefully Alphax will follow through and do some experimenting, tightening up controls, doing better measurements and such I look forward to it.

Alphax wrote: ↑Wed Feb 16, 2022 8:04 am @ nobody

I still don't see what the Carnot Limit has do with it?

I have tried to encourage Tom to forget all about Carnot, but he struggles to do that.

As far as I can tell, Tom doesn't "like" Carnot's limit and thinks it is "wrong" yet cannot satisfactorily articulate his dislike or his objection in a single sentence.



As far as I am able to understand Tom's objection to Carnot, it seems (to me) to rest on the use of Absolute zero implicit in Carnot's equation. But he has yet to articulate his objection in a single sentence. I think I can put his argument for him, and will start by restating Carnot's limit/theorem in a single sentence. Then I'll attempt to express Tom's objection to it in a single sentence and allow Tom to correct or adjust my interpretation of Tom's objection so that we may all better understand what Tom is trying to say.

Here goes:

Carnot's efficiency says that the efficiency of a heat engine is given by: one minus (the temperature of the cold working fluid divided by the temperature of the hot working fluid).

And that is basically it - one simple sentence. Mathematically it is usually expressed as E = 1-(Tcold/Thot).


Tom objects to it, and I think he doesn't actually object to that sentence (I could be wrong - Tom will say if I am).

What I think he objects to in Carnot's theorem/Limit/efficiency is the use of Absolute zero implicit in degrees Kelvin (or Rankine if you are American and prefer your delta Ts to be Fahrenheit compatible rather than Centigrade compatible).

My objection is simply that the so-called "Carnot efficiency formula" does not appear to have ever been scientifically established.

There is no experimental data to indicate such an exacting absolute, not to mention paltry and exceedingly low or restrictive "limit".

That equation is nothing but a derivation based on the temperature difference. Infact, all it is is the temperature difference expressed as a ratio on the Kelvin scale.

If it was derived by Carnot, likely he was using the Celsius scale. His zero, was simply the freezing temperature of water, which makes sense for Steam engines. Ice doesn't run a steam engine. There was no such thing as absolute zero in Carnot's time. Not before he wrote his book anyway.

Why should this particular ratio dictate how much of the heat supplied to a heat engine can be utilized?

Heat is not "Caloric" that falls from a high temperature down to a low temperature like a waterfall, is it?

This equation has no valid theoretical basis.

Take this article as a reference for example:

This simplest heat engine is called the Carnot engine, for which one complete heating/cooling, expanding/contracting cycle back to the original gas volume and temperature is a Carnot cycle, named after Sadi Carnot who in 1820 derived the correct formula for the maximum possible efficiency of such a heat engine in terms of the maximum and minimum gas temperatures during the cycle.

Carnot's result was that if the maximum hot temperature reached by the gas is Th, and the coldest temperature during the cycle is Tc, (degrees kelvin, or rather just kelvin, of course) the fraction of heat energy input that comes out as mechanical work , called the efficiency, is

Efficiency = Th - Tc/Th.

This was an amazing result, because it was exactly correct, despite being based on a complete misunderstanding of the nature of heat!

Well, there are a few inaccuracies there, perhaps. But, the last statement is quite remarkable;

OK, so, how do we know that ".. it was exactly correct, despite being based on a complete misunderstanding of the nature of heat! ".

????

I would like to see the experimental data that actually established conclusively that this formula is actually correct, "exactly correct".

I've made this request many times on many Science and Physics forums. No answer.

Then, there are additional indications, that there may be something going on, different from the assumptions implied by E = 1-(Tcold/Thot)

If 85% of the heat going into the engine passes through to the ice, on a hot summer day, I would not expect that the ice the engine was running on would re-freeze while the engine was running, after it had already started melting.

Above, I suggested that different results might be obtained with the engine under a load, perhaps MORE heat would be converted to work by being diverted into the load.

Accidently, I did infact see indication that this might be true.

This engine is under a load, because I decided to use the power of the running engine to hone down the piston and cylinder with grinding paste. I was trying to fit the engine with a new epoxy piston I made, but it was too tight with too much friction.

If it would run with grinding paste on the cylinder, I didn't need to do the work myself. I could just let the engine run.

The weird thing, though, something that had never happened before, and I had already done more than half a dozen experiments running engines on ice...

The ice, when I went to check the progress, kept re-freezing under the engine


Well, I thought this was really really strange, as the ice had already started to melt on the surface before I even started the engine .running.

So after the second time this happened, having to literally break the engine loose from the ice, and the ice freezing again, I got my phone and after letting the engine run for another fifteen minutes or so checked again with the phone recording.


https://youtu.be/2b2dIR8Eql8


After making this video, the ice re-froze a Fourth time while I was writing the video description.

After that I decided to let the engine run but fell asleep.

By the time I woke up, the engine had stopped running, apparently due to the piston getting ground down too much.

So maybe this could be another experiment for Alphax. Run a Stirling engine on ice with a load. Maybe the ice will take even longer to melt, because of more heat being diverted into work.

Tom,

- you are like the proverbial dog with a bone!



This is a line of reasoning that undergrads might enjoy hassling their lecturers with (ask me how I know). It goes like this.......

There are two avenues down which you might achieve 100% efficiency, and none down which you might achieve more than 100% efficiency.


Before we consider these two avenues, you will have to settle for an approximation of 99.9998% efficiency. But as that is 100% when rounded up to two decimal places, I'm assuming you are OK with that. So don't get picky on me!


Avenue 1: Assume that Carnot's efficiency equation is acceptable (notice I am not saying "correct") for the purpose. Under what circumstances would you approach 100% efficiency? The answer is simple, since E=1-(T_cold/T_hot) we simply have to satisfy the condition T_hot>>T_cold. A fusion reactor gas plasma reaches 150 million degrees Centigrade, give or take a few degrees. (That number is so large that using Kelvin or Centigrade makes no material difference to the calc). So the quantity (T_cold/T_hot) is 0.000002. Therefore E= 0.999998, or 99.9998% or 100% to 2 decimal places.

Students tend to like that sort of reasoning, and in fairness, experimental fusion reactors do achieve plasma temperatures that high and the output from future working reactors will be heat (just not plasma heat!).


Avenue 2: Rembering that the word "proof" applies only to mathematical expressions (science never "proves" things, it simply tries to find the best current explanation amongst many), then you - Tom Booth, must supply an alternative mathematical proof that shows how 100% efficiency might be achieved. I'm not saying that such a proof can't be found, by the way. I'm saying, though, you haven't come up with the Booth Expression and all we are left with is the Carnot Expression (i.e. 1-(T_cold/T_hot).

Students tend to not like the second avenue so much as it requires them to think about what they have conjectured and then express it in mathematical terms (preferably as an equation).

Tom,

So maybe this could be another experiment for Alphax

I have been running initial experiments for a few days (not full time, I hasten to add!). As is often the case with experiments, what appears to be a simple, elegant experiment turns out to take a great deal of care to do properly. I like "done properly", and so none of this will be fast to report.

My advice - for now - is to not push your findings too hard until someone else (doesn't have to be me, though I would recommend they take considerable care setting the experiment up) can confirm your findings. It is all about other people being able to reproduce your experimental results. Patience is the key.

I'll put my advice a little stronger than that, actually - just remember what happened to Pons and Fleischmann's claim.......

Avenue 1: Assume that Carnot's efficiency equation is acceptable (notice I am not saying "correct") for the purpose.

Well, that's out. I don't "assume" anything

That is the problem or issue, for me anyway.

I follow scientific methodology Though for some reason I'm called a pseudoscientist by those who have chosen not to. Who just want to blindly follow the corriculum.

Everyone has "assumed" this formula, pulled out of thin air, based on completely erroneous fundamental theorizing must be absolutely correct, simply because nobody has ever bothered doing any experiments to demonstrate otherwise.

I believe what I can see. Well, actually, I take that back as I recognize that human perception is notoriously fallible.

The Carnot formula originated in an era when it was fashionable to discover universal "Laws" rather than the less glamorous approach of postulating "theories", as you put it: "science never "proves" things, it simply tries to find the best current explanation amongst many".

Yet, today, if anyone dares to make the assertion that they have developed an engine that gets better than the paltry amount allowed by "Carnot" they will be labeled a pseudoscientist or worse, a fraud, a liar and a fool. No wonder none dare risk their reputation by so much as questioning the authority of Carnot or dabbling in this area of better than Carnot efficiency.

The issue could be very quickly and easily resolved, just show me some of, ANY of the alleged cumulative data that has piled up over the past century supporting this absolutely iron clad efficiency formula

But the formula, based on NOTHING of any substance whatsoever has gone completely unchallenged since somebody pulled it out of their hat 100 some odd years ago.

So what is this now dueling equations?

You want me to invent an equation that shows how 100% efficiency might be achieved?

That's easy: efficiency = W/Qh

I'm not even talking about 100% efficiency. I'm just asking, or rather pointing out that there seems to be no rational basis for assuming the correctness of the so-called "Carnot limit" which typically, is a tiny tiny fraction of that. Maybe 10%, 20%, 25...

What does temperature have to do with Qh ?

Temperature is not a quantity of heat.

All the Carnot so-called formula does is take a temperature reading.

Does temperature say anything about the number of Joules passing through at Qh? The heat exchange surface area ? Flow rate of any heat transfer fluid, heat capacity, working fluid properties, anything?

I'm just supposed to accept on what, FAITH in the almighty power of Sadi Carnot to have gotten one thing right while getting everything else wrong?

In the appendix of Carnot's book he wrote:

There have been made, it is said, recently in
England, successful attempts to develop motive
power through the action of heat on atmospheric
air. We are entirely ignorant in what these at-
tempts have consisted-if indeed they have really
been made

So, even if someone wants to accept Carnot as applicable to the steam engine, or engines generally,what reason do we have to assume the formula is applicable to a type of engine Carnot expressed doubt, even existed at all ?

You keep talking about "claims" I'm supposed to have made, but I make no claims. I'm just not swallowing the Carnot efficiency "claims" hook line and sinker, presented with ZERO supporting evidence and ZERO supporting documentation. ZERO empirical data, ZERO experimental evidence.

Why such dire warnings: "remember what happened to so and so..." Give me a break.

Try dredging up some kind of actual supporting evidence for assuming that temperature difference has any controlling influence over engine efficiency in exactly the way Carnot or whomever extrapolated from the flow of Caloric through a water wheel "analogy".