Is Carnot efficiency valid?

[studiot]

 

54 minutes ago, sethoflagos said:

This is the opposite case to most heat engine designs. I can see I wrote minimum pressure when I meant maximum so I've likely got a pair of subscripts reversed somewhere. I'll comb through it later tonight to check. 

Good point, but can I add a thought here ?

I used Th and Tc to try to keep the nomenclature simple.

I also used them as shorthand for source, reservoir etc, perhaps a bit ckeekily.

Most cycle diagrams have more than 2 vertices so are usually numbered 1,2,3,4....

These vertices also correspond to definite states, both in ideal and non ideal machines.

So perhaps V1 and V 2 etc would be better ?

 

A couple of other thoughts,

@Tom Booth  

Beware of sign conventions.

Chemists treat all forms of energy in a positive and all forms of energy out as negative.
Engineers (and most phyicists) treat work done on the system as positive and work done by the system as negative ie (the opposite).

Both systems have their uses and roots in history.

Although Thermodynamic theory was the first discipline to make full use of the new advanced mathematics in the early 1800s I am trying to avoid this part. It is not needed for our purposes.
Thermodynamic theory also pays scant regard to time there is no consideration of how long it takes to reach the mentioned states and most thermodynamic maths in independent of time.

 

I am posting this diagram now as the beginning of the next installment.

I will explain it later but I have other things to attend to over the next few hours.

Meanwhile I'm sure Seth will recognise it.

 

Edited February 3, 2023 by studiot
correct sketch

[Tom Booth]

57 minutes ago, sethoflagos said:

For an ideal Stirling engine maximum compression occurs at the end of the cooling cycle with the working fluid at cold reservoir temperature T_C. Conversely, maximum expansion occurs at the end of the heating cycle with the working fluid at hot reservoir temperature TH.

This is the opposite case to most heat engine designs.

Heating and cooling imply, or more than imply a transfer of heat. Do you agree?

So these statements are incorrect in their entirety as well as the conclusion stated.

Maximum compression and maximum expansion are both preceded by adiabatic processes, in the ideal Carnot cycle.

So I would not say that the Carnot cycle is "opposite" to most heat engine designs. Far from it. Most heat engine designs are intended to approximate the Carnot cycle as closely as possible. Some come close, some don't, but "opposite"???

Can you provide us with an actual example of a heat engine design that is the  opposite of the Carnot cycle, and what is the relevance of all this?

Have you ever actually examined an "ideal Carnot cycle"?

1 hour ago, sethoflagos said:

For an ideal Stirling engine maximum compression occurs at the end of the cooling cycle with the working fluid at cold reservoir temperature T_C. Conversely, maximum expansion occurs at the end of the heating cycle with the working fluid at hot reservoir temperature TH.

This is the opposite case to most heat engine designs. I can see I wrote minimum pressure when I meant maximum so I've likely got a pair of subscripts reversed somewhere. I'll comb through it later tonight to check. 

I'm afraid it's more than that. You have the Carnot cycle turned completely upside down and backwards then declare this is the opposite of most engine designs.

You have completely ignored the adiabatic legs of the cycle which at full compression resolve at T-hot (not Tc) and at full expansion resolve at T-cold (not Th) as with real heat engines.

The main difference between a real engine and a Carnot engine is in the fact that a real engine is nearly all adiabatic expansion and contraction as isothermal processes take place quasistatically (infinitely slowly) which is not possible in reality.

There is a company claiming to have developed a near isothermal heat pump involving dipping numerous thin rods into fluid to effect compression but this is not typical.

Edited February 3, 2023 by Tom Booth

[sethoflagos]

1 hour ago, sethoflagos said:

For an ideal Stirling engine maximum compression occurs at the end of the cooling cycle with the working fluid at cold reservoir temperature T_C. Conversely, maximum expansion occurs at the end of the heating cycle with the working fluid at hot reservoir temperature TH.

This is the opposite case to most heat engine designs. I can see I wrote minimum pressure when I meant maximum so I've likely got a pair of subscripts reversed somewhere. I'll comb through it later tonight to check. 

Compare with Wikipedia

Quote

The idealised Stirling cycle consists of four thermodynamic processes acting on the working fluid:

1. Isothermal expansion. The expansion-space and associated heat exchanger are maintained at a constant high temperature, and the gas undergoes near-isothermal expansion absorbing heat from the hot source.
2. Constant-volume (known as isovolumetric or isochoric) heat-removal. The gas is passed through the regenerator, where it cools, transferring heat to the regenerator for use in the next cycle.
3. Isothermal compression. The compression space and associated heat exchanger are maintained at a constant low temperature so the gas undergoes near-isothermal compression rejecting heat to the cold sink
4. Constant-volume (known as isovolumetric or isochoric) heat-addition. The gas passes back through the regenerator where it recovers much of the heat transferred in process 2, heating up on its way to the expansion space.

Same thing.

38 minutes ago, Tom Booth said:

So these statements are incorrect in their entirety as well as the conclusion stated.

Maximum compression and maximum expansion are both preceded by adiabatic processes, in the ideal Carnot cycle.

I didn't mention the Carnot cycle in that post.

Given the nature of the remainder of your post, let's close with a proverb.

Quote

Do not answer a fool according to his folly,
Or you will also be like him.
Answer a fool as his folly deserves,
That he not be wise in his own eyes.

 

 

[Tom Booth]

On 2/2/2023 at 9:20 AM, studiot said:

My apologies if that end paragraph was posted before I responded to the beginning of your lengthy post.

 

Unfortunately almost everything you have said in this thread and previously leads to the inevitable conclusion

But you don't understand it. That is the problem.

 

When myself and others tell you that you are misquoting an equation relating to Carnot efficiency you  respond quoting dead philosophers instead of Mathematics.

You clearly have a facility with mechanics and the maths is actually very elementary so you should have no trouble understanding a properly phrased explanation.

 

To answer your question as plainly as possible.

NO it is impossible to buld a material physical 'Carnot Engine'.  It is purely a theoretical concept to explore the theory of Thermodynamics.

It is impossible in theory as well as practice for reasons that Seth and Joigus have hinted at and for reasons exchemist and swansont have tried to explain to do with your misunderstanding of various definitions in thermodynamic theory.

You tell me that we do not need to explore what a 'reservoir' is defined as yet you do not seem to understand that the basic (Th-Tc)/Th  efficiency formula is invalid for any real world heat engine.

 

 Considering the amount of time and effort you put into this, I really cannot understand why you do not want to explore the finer points of this issue.

 

So are you saying that the answer to the opening question is NO.

Quote

the basic (Th-Tc)/Th  efficiency formula is invalid for any real world heat engine.

Is (the) Carnot efficiency [limit] (formula) valid?

No?

My impression has been, that as a limit your answer(s) would certainly be "yes". Even perhaps an overly generous approximation.

I certainly never imagined it was an exact representation.

But certainly as a limit on the actual efficiency of any REAL engine it is considered absolutely valid.

If therefore, no engine can exceed that limit, no engine can exist which does not emit "waste heat".

I've watched dozens of tutorials and solved dozens of sample problems on how to use the Carnot efficiency equation and what it means in terms of real world applications involving joules of heat in and joules of waste heat out and joules converted to work.

So, what do you mean by "invalid".

 

 

[Ghideon]

@Tom Booth did  you see my post regarding an addition to the experiment? https://www.scienceforums.net/topic/128644-is-carnot-efficiency-valid/?do=findComment&comment=1228275

(May have been overlooked since there were some x-posting and editing)

 

 

[Tom Booth]

1 hour ago, sethoflagos said:

Compare with Wikipedia

Same thing.

I didn't mention the Carnot cycle in that post.

Given the nature of the remainder of your post, let's close with a proverb.

 

 

Well thanks for clarifying, but you actually did, by hitching you wagon to Studiots post:

 

Quote

 

studiot said:

So let us return to the OP and explore what Carnot efficiency

 

That was how your post opened. Throughout you never mentioned any other cycle or engine specifically, so it seemed you were adding to.

Anyway my apologies, I assumed, from the way the post opened as an addition to Studiots, that it was about the same.

But thanks for the clarification.

On 2/2/2023 at 11:36 AM, Ghideon said:

  

Let's outline the logical next step by using one addition. Assume the setup works; We have the Stirling engine running and cold plate insulated with an adjacent Stirling engine or good enough insulation. Place the running engine(s) in a well-insulated box. 

All the work performed by the engine(s) will be friction loss in the engine or movement of air inside the box. These losses will heat the air inside the insulated box. Conservation of energy means no energy enters or exits the box and no energy is permanently lost in the box, just changing between heat and mechanical work. The running engine(s) keep the cold side cool, and the losses are heating the air. In principle the box is a sealed system, and the engine will never stop since a permanent difference in temperature is established. This goes against my understaning of physics, but it seems to follow logically from your ideas and your conclusion of experiments?

 

Can you provide a reference? It could add value to the discussion.

(As far as I know it is ok per forum rules to link to further reading)

No, I did not see the first part.

Let me be clear, I'm not attempting to prove or advocate for "perpetual motion" here. Just something Less Than the reciprocal of the Carnot efficiency. The inefficiency or heat transmitted through to the sink.

In this setup, that would be what?

Assuming an arbitrary, but realistic ambient (room temperature) outside and inside the box of 75°F and an ice cube or whatever at typical household freezer temperature at 0°F gives us a Carnot efficiency of what? (Maximum unapproachable efficiency for a real engine of course, not actual efficiency I think that goes without saying)

14% (approximately)

So, we get a minimum heat pass through of 86% but we can assume that 14% efficiency is way too generous. So probably something more like 90% or more heat pass through.

Infact we have Two engines pushing 90% of the heat they take in straight through to the ice, Each.

So, can we assume anything regarding how fast the ice will melt? Are we completely in the dark about how much heat might be entering into the two engines?

Maybe we can't KNOW, not entirely without some really exacting instrumentation and data recording, but generally I think it fairly safe to assume the ice would melt pretty quickly.

What would be the expected outcome?

A perpetual motion machine?

Hardly.

 

As for the other question, I assume you already received the references.

There is the drinking bird of course, which I'm pretty sure everyone here has seen but also there are heat engines that can run on the ∆T from simple evaporative cooling. Nothing remarkable in that IMO.

Edited February 3, 2023 by Tom Booth

[Ghideon]

The ice just complicates the scenario; would it be possible to discuss an ice-less scenario? I can't follow your descriptions, sorry.

Can we agree that you expect a cooling effect on the cold side? I mean, if ice does melt slow in your experiment then, according to your description, the running engine is keeping the temperature lower that ambient at the cold side? 

On 2/1/2023 at 12:10 AM, Tom Booth said:

colder than ambient temperature reached by the working fluid

If so we can discuss the consequences and a simplified experiment without the errors and failures that the ice will cause.

[Tom Booth]

Let's say we dip a coin of known heat capacity into liquid nitrogen and put the coin in a circle cut out of a silicone mat the same thicknes as the coin.

1) Put that between the two engines. Not running.

2) Repeat with one running

3) Repeat with both running

 

What would be the outcome in order of melting (or running) time?

 

Edited February 3, 2023 by Tom Booth

[Ghideon]

3 minutes ago, Tom Booth said:

What would be the outcome in order of melting (or running) time?

According to established science or your ideas?

[studiot]

2 hours ago, Tom Booth said:

So are you saying that the answer to the opening question is NO.

Quote

the basic (Th-Tc)/Th  efficiency formula is invalid for any real world heat engine.

Is (the) Carnot efficiency [limit] (formula) valid?

No?

My impression has been, that as a limit your answer(s) would certainly be "yes". Even perhaps an overly generous approximation.

I certainly never imagined it was an exact representation.

But certainly as a limit on the actual efficiency of any REAL engine it is considered absolutely valid.

If therefore, no engine can exceed that limit, no engine can exist which does not emit "waste heat".

I've watched dozens of tutorials and solved dozens of sample problems on how to use the Carnot efficiency equation and what it means in terms of real world applications involving joules of heat in and joules of waste heat out and joules converted to work.

So, what do you mean by "invalid".

Just a quick answer before I turn in for the night.

This is a much better way of arguing your challenge.

You are actually asking why someone says something.

 

First we start with the premise that

Every real world engine has an efficiency.

So the issue becomes  "How to calculate that efficiency ?"

I have established that the Carnot formula only applies to an imaginary engine.

So why would anyone expect it to be valid for any real world one  ?

 

What you will calculate if you use the Carnot formula will be incorrect for a real world engine.

So I have begun the long process of delving into which leads on to "How should we calculate it instead ?"

 

 

 

[Tom Booth]

14 minutes ago, Ghideon said:

The ice just complicates the scenario; would it be possible to discuss an ice-less scenario? I can't follow your descriptions, sorry.

Can we agree that you expect a cooling effect on the cold side? I mean, if ice does melt slow in your experiment then, according to your description, the running engine is keeping the temperature lower that ambient at the cold side? 

If so we can discuss the consequences and a simplified experiment without the errors and failures that the ice will cause.

What do you mean by "ice-less"?

The "colder than ambient" temperature of the working fluid is at best a brief "flash in the pan" near full BDC.

Without insulating the cold side of the engine such a brief instant of sub-ambient cold would be completely overwhelmed by the immediately adjacent ambient heat, being generally or probably  undetectable by slow responding thermal measuring instruments.

Carnot's original declaration, and I can only call it that, not a scientific theory was that ALL the heat going in was "transported" through the engine, like a bucket of water carried down by a water mill wheel.

Later this was modified, IMO arbitrarily to harmonize more closely with new findings. Heat could be converted to work, and also the absolute temperature scale came along.

If Carnot ever talked about the zero of temperature he meant 0°C

Personally I think this efficiency limit equation attributed to Carnot, whomever came up with it, and I haven't been able to say for sure who, probably originally meant the engine could take in a quantity of heat at T-hot and convert that quantity into work only as far as bringing the temperature of the working fluid down to T-cold or the surrounding ambient or coldest "reservoir" available. Period.

That makes perfect sense to me as a general rule of thumb.

But the modern interpretation seems to be that if a quantity of heat is taken in at T-hot, it can only be converted into work as far as bringing the temperature down to... ... To what?

Not T-cold.

Instead, if the distance between T-hot and T-cold happens to be 15% of the distance down to absolute zero on the Kelvin scale, then with that ratio in hand we are going to now say that taking in a quantity of heat at T-hot, we can only convert a small portion of that quantity of heat into work. So the temperature can only be reduced something less than 15% not on the absolute scale now, but only 15% of that limited quantity of heat actually added.

By what actual physical mechanism do we make that transposition? Someone got the percentage of the absolute scale mixed up with a percentage of the actual heat supplied.

If T-hot is 80°F and T-cold is 0°F without heat "rejection" somewhere we can only reduce the working fluid what? 12°F and the temperature must be reduced the other 68° through rejection of all that heat to the sink. Our ice or whatever. Why?

So if the ice is a small finite "reservoir" it should melt pretty quickly, if we have to put all that waste heat into it in order to bring the temperature of the working fluid down another 68°F in the fraction of a second it takes for the piston to round TDC or BDC or wherever this impossible "rejection" of heat to the "cold reservoir" is supposed to happen.

If ALL or nearly all the heat added can be utilized to bring the temperature all the way down to T-cold then how do we actually "reject" any heat to the cold reservoir at T-cold?

We can't. They are the same temperature!

But that is what the "Carnot cycle" proposes we do.

How?

Why, we can utilize an isothermal process.

We just have to very very slowly move the piston. Infinitely slowly, so that no temperature changes take place. After an eternity of time, eventually all the heat will transfer one way or the other.

No it won't.

We are suppose to inject this rather large quantity of heat (relative to the heat converted to work) nearly instantaneously over an eternity.

It's so much nonsensical bullocks it could make your head spin.

1 hour ago, Ghideon said:

According to established science or your ideas?

According to the Carnot limit equation. That is what we are trying to validate.

14 minutes ago, studiot said:

Just a quick answer before I turn in for the night.

This is a much better way of arguing your challenge.

You are actually asking why someone says something.

 

First we start with the premise that

Every real world engine has an efficiency.

So the issue becomes  "How to calculate that efficiency ?"

I have established that the Carnot formula only applies to an imaginary engine.

So why would anyone expect it to be valid for any real world one  ?

 

What you will calculate if you use the Carnot formula will be incorrect for a real world engine.

So I have begun the long process of delving into which leads on to "How should we calculate it instead ?"

 

 

 

You haven't clarified what you mean by "invalid".

Do you mean it is only a limit and not a precise measure? As is already universally understood afaik, or it is complete hogwash?

1 hour ago, Ghideon said:

The ice just complicates the scenario; would it be possible to discuss an ice-less scenario? I can't follow your descriptions, sorry.

What words or phrases, sentences or paragraphs exactly can't you follow? Of which post?

What is hard to understand or complicated about putting some cold object between two engines?

[swansont]

1 hour ago, Tom Booth said:

But that is what the "Carnot cycle" proposes we do

And the Carnot cycle is unachievable. It’s an idealized case, like frictionless surfaces and elastic collisions in classical mechanics. The Carnot cycle assumes reversible processes, which don’t physically happen.

It’s like calculating the maximum speed of a dropped object by ignoring air resistance. 

Similar to what studiot said, these idealized analyses apply to imaginary situations. 
 

 

[Tom Booth]

 

1 hour ago, swansont said:

And the Carnot cycle is unachievable. It’s an idealized case, like frictionless surfaces and elastic collisions in classical mechanics. The Carnot cycle assumes reversible processes, which don’t physically happen.

It’s like calculating the maximum speed of a dropped object by ignoring air resistance. 

Similar to what studiot said, these idealized analyses apply to imaginary situations. 
 

 

Not just "imaginary" within the realm of possibility. The processes as described are literal impossibilities.

There is no possibility of an engine using "isothermal expansion" to draw heat away from some object  while maintaining thermal equilibrium with that same object. Certainly not in the time a piston moves from BDC to TDC.

What's the point of contemplating something that has no correspondence to the real world. No practical application.

It only had a seeming reality if heat were actually a fluid you could draw out as if sucking up gravy with a turkey baster. Today we know better.

 

Let's entertain the Carnot scenario (as typically interpreted in online tutorials, textbook problems etc.)

Two heat engines. 20% Carnot efficiency (determined by the ∆T, each sharing a finite "cold reservoir" (the ice or cold object between them.

If it is true the 20% efficiency figure can be applied to supplied heat above the baseline ("baseline" = everything at some one ambient temperature before the quantity of heat in question was added) we put 10,000 joules of heat into the engine each cycle in some measurable way, watts of electricity or whatever. After one cycle 8,000 joules of "waste heat" should be found added to the sink helping warm up a cold plate, melt ice or whatever.

Idle engines should transmit the heat the fastest. 1 engine running should transmit less heat (because 20% is converted to work) 2 engines running should reduce the heat input more if the 10,000 joules is divided between them or transmit more if each engine receives 10,000 joules and "rejects" 8,000 each to the same sink. But In each case the ice should melt quickly as each engine is only reducing the heat flow marginally.

If on the other hand the engines are converting a much higher percentage of the heat, more than the Carnot limit predicts, then with the two engines acting as  "insulation" with the ice (or whatever cold thing) between them,  the object should require a very long time to heat up or melt.

In other words, if there really is a kind of slight refrigerating action by the engines, nothing (no engine at all) or non-operating engines should melt the ice quickly.

One engine would be like a refrigerator with the door open. The ice will still melt, but maybe aittle slower.

Two engines together would be like two refrigerators with the doors off  but using each other to enclose the refrigerated space.

The two engines "helping each other" should produce a dramatic lengthening in time before the engines ever stop running, before the sink fills up with heat. But only if the Carnot limit is a complete fallacy.

If the Carnot limit is true, and at least 80% of the heat supplied to the engines passes straight through to the ice, then putting the cold sides of the engines together should 't make much difference.

If the Carnot limit is a rather grotesque error or misunderstanding and in reality virtually all the heat supplied can be converted to other forms of energy, which is no violation of conservation of energy, there should be a dramatic lengthening in the time it takes for any heat to reach the sink cradled between the engines.

Edited February 4, 2023 by Tom Booth

[Tom Booth]

2 hours ago, swansont said:

And the Carnot cycle is unachievable. It’s an idealized case, like frictionless surfaces and elastic collisions in classical mechanics. The Carnot cycle assumes reversible processes, which don’t physically happen.

It’s like calculating the maximum speed of a dropped object by ignoring air resistance. 

Similar to what studiot said, these idealized analyses apply to imaginary situations. 
 

 

Ok, so if I drop an object in a vacuum, that's an actual possibility. It could be proven that even without air resistance there is a limit or potentially real measure of how things fall in the absense of air.

A frictionless surface is actually achievable. Magnetic levitation of a superconductor. Not a surface exactly, but it certainly approximates a frictionless surface.

Perfectly elastic collisions between gas particles seems real enough to me.

Carnot efficiency is, IMO a completely arbitrary construct invented based on a fallacy regarding the nature of heat, has no actual physical basis whatsoever, has never been empirically tested,  verified or demonstrated in any way shape or form, it's just a hold over from the caloric theory.

There is no caloric. There are no pools or "reservoirs" of this supposed fluid, it is admittedly all complete fantasy. No falling down like a waterfall to a "lower" temperature. Heat is not "flowing" through a heat engine. It's all a misconception an illusion a mistake.

That's what I honestly think anyway.

I've been doing experiments looking for the "waste heat" supposed to be emanating from the cold side of my Stirling engines and there is scarcely anything there.

There is no rational or material reason why a ratio based on a temperature difference determines anything.

Anyway the power of a waterfall depends on the height AND the quantity of water, like volts and amps. What Carnot actually said was that the utilization of heat depends on only the temperature difference and the quantity. Carnot never said temperature ONLY period afaik, that was somebody's misreading of a bad translation or something probably.

There is no historical account of this formula having ever been proven that I could ever find. It has no basis. Not the way it's being taught anyway.

 

Edited February 4, 2023 by Tom Booth

[Ghideon]

5 hours ago, Tom Booth said:

What words or phrases, sentences or paragraphs exactly can't you follow? Of which post?

What is hard to understand or complicated about putting some cold object between two engines?

I''m thinking as an experimenter. When ice is added, for instance under insulation between two engines, I find it complicated to see when all the ice actually melts; I may disturb the experiment. Instead I prefer to use only a thermometer. 

Thinking again, this is a good idea:

7 hours ago, Tom Booth said:

Let's say we dip a coin of known heat capacity into liquid nitrogen and put the coin in a circle cut out of a silicone mat the same thicknes as the coin.

What if you instead of ice have a thermometer probe pre-cooled and inserted at the cold side? Then you can see the temperature all the time and the pre-cooled probe takes the role of the ice? If something more massive than the probe is required you can attach the probe to some object of suitable size and shape (The probe may heat too quick when moved from freezer to engine setup). Maybe a thin sheet of metal? 

 

[studiot]

8 hours ago, Tom Booth said:

You haven't clarified what you mean by "invalid".

Do you mean it is only a limit and not a precise measure? As is already universally understood afaik, or it is complete hogwash?

Actually I did, but you didn't completely read what I said, any more than you did the first time round.

I didn't mention 'limit' or 'hogwash' and most importantly I didn't say that the Carnot formula is invalid full stop.

I even quoted the exact passage for you and I am not going to do that again if you can't bothered to read that short passage to the end.

The standard engineer's formula and analysis for elastic beam deflections is invalid for wide beams.

In other words it only applies to narrow beams.

That is why engineers use a different analysis and formula for the deflection of wide beams and narrow beams.

 

No the Carnot formula is not hogwash if used for the purpose for which it was intended.

I don't like to use the word limit because the word limit has a variety of meanings, some of which would be contradictory if used in the wrong place. A limit may be achievable or unachievable in both mathematics and other sciences.
The only place it is used in Thermodynamics that I can think of is in the thermodynamics of chemical reaction rates and is used to define something called 'the limiting rate step'. In this instance it does not indicate the unachievable.
So, if we were to call the Carnot formula a limit then would would be using limit in two contradictory ways within one discipline (thermdynamics). 

And that would require the reader to make the distinction.

 

[joigus]

17 minutes ago, studiot said:

I don't like to use the word limit because the word limit has a variety of meanings, some of which would be contradictory if used in the wrong place. A limit may be achievable or unachievable in both mathematics and other sciences.

Perhaps "upper bound" are the words to look for here? 

It definitely sets a theoretical upper bound in terms of energy obtained to energy invested ratio, having nothing to do with time --how long the machine is running, as you pointed out before--, or with whether the machine will eventually stop or keeps going forever --as Swansont pointed out.

Because the Carnot cycle is defined in terms of state variables --due to all intermediate states beeing equilibrium ones-- and because an ideal gas has no internal mechanism to hide energy other that its pressure, volume, and temperature, no matter how many contraptions or intermediate complications we introduce, this upper bound cannot be overcome.

The dynamics of this discussion does remind me of that of a Carnot engine, with a reservoir full of an inexhaustible resource, and the corresponding sink that can take any amount of such resource without in any way changing its state.

[studiot]

1 hour ago, joigus said:

Perhaps "upper bound" are the words to look for here? 

It definitely sets a theoretical upper bound in terms of energy obtained to energy invested ratio, having nothing to do with time --how long the machine is running, as you pointed out before--, or with whether the machine will eventually stop or keeps going forever --as Swansont pointed out.

Because the Carnot cycle is defined in terms of state variables --due to all intermediate states beeing equilibrium ones-- and because an ideal gas has no internal mechanism to hide energy other that its pressure, volume, and temperature, no matter how many contraptions or intermediate complications we introduce, this upper bound cannot be overcome.

The dynamics of this discussion does remind me of that of a Carnot engine, with a reservoir full of an inexhaustible resource, and the corresponding sink that can take any amount of such resource without in any way changing its state.

Of course it does.

I am not saying that invalid means useless (see hogwash).

But my development is to show that it forms an upper bound.

Lots of posters here have offered various parts of the thinking development of this, including yourself.

Since Tom rejects the whole caboodle, I am trying to offer these parts in a logical step by step order.

Sadly everyone but Tom seems to understand that. And if he is genuinely doing all that work over decades then it is a shame for him it will ultimately be to no avail.

I have not yet got into state variables, reversibility or the quasi-static concept and their implications for the discussion.

Edited February 4, 2023 by studiot

[swansont]

7 hours ago, Tom Booth said:

There is no caloric. There are no pools or "reservoirs" of this supposed fluid, it is admittedly all complete fantasy

Yes. So why do you keep bringing it up? Nobody else has used caloric in their explanations.

The thing is, while caloric was abandoned, the thermodynamic principles it attempted to explain are still there. Heat is transferred. Some of it can be converted to work. It just isn’t because of caloric moving about.

9 hours ago, Tom Booth said:

 

Not just "imaginary" within the realm of possibility. The processes as described are literal impossibilities.

There is no possibility of an engine using "isothermal expansion" to draw heat away from some object  while maintaining thermal equilibrium with that same object. Certainly not in the time a piston moves from BDC to TDC.

Yes, I just explained that.

9 hours ago, Tom Booth said:

What's the point of contemplating something that has no correspondence to the real world. No practical application.

Physicists do idealized systems all the time when discussing theory.

 

9 hours ago, Tom Booth said:

Let's entertain the Carnot scenario (as typically interpreted in online tutorials, textbook problems etc.)

Why? There is no real engine that follows the Carnot cycle. You just agreed to that.

9 hours ago, Tom Booth said:

The two engines "helping each other" should produce a dramatic lengthening in time before the engines ever stop running, before the sink fills up with heat.

Fill up with heat? I would think someone railing against caloric theory would avoid treating heat as a substance.

 

 

 

[swansont]

8 hours ago, Tom Booth said:

I've been doing experiments looking for the "waste heat" supposed to be emanating from the cold side of my Stirling engines and there is scarcely anything there.

There is no rational or material reason why a ratio based on a temperature difference determines anything.

I recall trying to run my stirling engine on a hot day. I put it on a mug of hot water and it would barely run - too much friction. When I put ice cubes on the top plate, it ran pretty well. Since the source of heat was the same, the only way this could be the case is if I was converting more heat to work - the efficiency increased.

 

[exchemist]

9 hours ago, Tom Booth said:

Ok, so if I drop an object in a vacuum, that's an actual possibility. It could be proven that even without air resistance there is a limit or potentially real measure of how things fall in the absense of air.

A frictionless surface is actually achievable. Magnetic levitation of a superconductor. Not a surface exactly, but it certainly approximates a frictionless surface.

Perfectly elastic collisions between gas particles seems real enough to me.

Carnot efficiency is, IMO a completely arbitrary construct invented based on a fallacy regarding the nature of heat, has no actual physical basis whatsoever, has never been empirically tested,  verified or demonstrated in any way shape or form, it's just a hold over from the caloric theory.

There is no caloric. There are no pools or "reservoirs" of this supposed fluid, it is admittedly all complete fantasy. No falling down like a waterfall to a "lower" temperature. Heat is not "flowing" through a heat engine. It's all a misconception an illusion a mistake.

That's what I honestly think anyway.

I've been doing experiments looking for the "waste heat" supposed to be emanating from the cold side of my Stirling engines and there is scarcely anything there.

There is no rational or material reason why a ratio based on a temperature difference determines anything.

Anyway the power of a waterfall depends on the height AND the quantity of water, like volts and amps. What Carnot actually said was that the utilization of heat depends on only the temperature difference and the quantity. Carnot never said temperature ONLY period afaik, that was somebody's misreading of a bad translation or something probably.

There is no historical account of this formula having ever been proven that I could ever find. It has no basis. Not the way it's being taught anyway.

 

You have been told over and over again that the Carnot efficiency formula is good science, for at least two excellent reasons.

One is that its derivation does not depend on anything other than the gas laws, which are well confirmed. (It does not depend on the old idea of caloric, even though you are pretending as hard as you can that it does. If you really think that modern science would justify a formula by means of a derivation based on a false model for heat, then you are a total moron.)

The other reason is that over 150 years of practical experience has confirmed that, however hard we try to make the most efficient heat engine we can, it never manages to surpass the efficiency limit predicted by the Carnot cycle.  That's what it does: it predicts a limiting efficiency. 

You are now simply sticking your fingers in your ears and saying "lalalala". You are wasting everybody's time, frankly. 

Edited February 4, 2023 by exchemist

[iNow]

14 minutes ago, exchemist said:

You are wasting everybody's time, frankly. 

That’s their entire reason for posting here 🤷‍♂️

[Tom Booth]

8 hours ago, Ghideon said:

I''m thinking as an experimenter. When ice is added, for instance under insulation between two engines, I find it complicated to see when all the ice actually melts; I may disturb the experiment. Instead I prefer to use only a thermometer. 

Thinking again, this is a good idea:

What if you instead of ice have a thermometer probe pre-cooled and inserted at the cold side? Then you can see the temperature all the time and the pre-cooled probe takes the role of the ice? If something more massive than the probe is required you can attach the probe to some object of suitable size and shape (The probe may heat too quick when moved from freezer to engine setup). Maybe a thin sheet of metal? 

 

Seems we are in the same page. A "coin" is a "thin piece of metal" commonly used for monetary exchange.

On the WWW spanning the globe I understand there are different dialects, language barriers, some might be using translators. I'm American my wife is from "down under" and we often can't get through the day without some mix up. On an international forum, X10.

It's to be expected, can't be helped really. I'm one person trying to respond to comments and questions from half a dozen other people from I know not where. An occasional misunderstanding is to be expected and is inevitable.

Add cross posting, late edits, stupid spell check programs, typos, the existence of words with dozens of shades of meaning, different in different regions etc. It's something of a wonder we can potentially collaborate on some experiment at all.

We are at an early stage of at least making some attempt at cooperation and mutual understanding here. That seems like a major breakthrough to me.

8 hours ago, Ghideon said:

Maybe a thin sheet of metal? 

 

Thinking on it a bit more, the cold heat exchanger of the engine(s) are simply thin sheets of metal.

A plate could be removed from the bottom of one engine and the other plate shared.

That is, the two engines would both be mounted on the same cold heat exchanger.

In fact, on the Stirling engine forum we have contemplated eliminating the cold plate entirely. As someone on the forum said, this would allow the mounting bolts to pass from hot side to hot side without contacting, and potentially conducting heat to the cold center plate.

Maybe have a cold disk suspended between the displacers.

Theoretically (my own tentative theory) no cold object would be required if the two engines could be driven mechanically for some time with an auxiliary motor, if they are truly acting as heat pumps. The shared bottom (bottom/top) plate would be chilled by running the engines as heat pumps.

 

Edit: and of course temperature probes. Probes everywhere.

6 hours ago, studiot said:

Actually I did, but you didn't completely read what I said, any more than you did the first time round.

I didn't mention 'limit' or 'hogwash' and most importantly I didn't say that the Carnot formula is invalid full stop.

I even quoted the exact passage for you and I am not going to do that again if you can't bothered to read that short passage to the end.

invalid for any real world heat engine. 

I certainly did read that.

You also made the claim:

Quote

 

I have established that the Carnot formula only applies to an imaginary engine.

So why would anyone expect it to be valid for any real world one  ?

 

I'm not convinced that you have actually established this claim at all.

There are untold numbers of educators teaching students that the formula does very well apply to every engine ever built and every engine that could conceivably ever be built.

There are textbooks, tutorials, videos, example problems etc.doing that very thing. Applying the formula to real every day situations and engines of all types.

Yes the Carnot engine is imaginary but it stands as a very real theoretical LIMIT to each and every REAL engine that ever existed or ever could exist.

I think this is basically very true IF interpreted strictly on the absolute scale. Raise the temperature to supply heat 10% on the absolute scale. In that case the temperature can only be brought back down the same 10% to the same ambient baseline temperature. The other 90% down to absolute zero is unavailable. Makes perfect sense.

That only 10% of the 10% is available is unsupportable and has no basis in reality. It does not even apply to the imaginary Carnot engine itself. It is a misunderstanding and misapplication of the formula IMO, that has been happily transmitted down through the generations.

There is no reason why raising the temperature 10% on the absolute scale should somehow magically render 90% of the added heat locked up somewhere or swept away to the mythical "cold reservoir".

Feel free to propose a better way of calculating real efficiency but that does seem to be veering off topic a bit.

Edited February 4, 2023 by Tom Booth

[joigus]

So the answer to the question is a resounding yes! Carnot's efficiency formula is valid. There's no reason to believe its validity depends on heat being a fluid or not* --with our modern understanding being it's not, and Carnot's reasoning being the 1st stepping stone towards understanding it must somehow be quantifying elementary dynamical processes, which leads to the concept of entropy. There's no reason to believe the engine eventually grinding to a halt has anything to do with efficiency calculations**. There's no reason to believe the time it takes to complete a cycle --or thousands of them-- has anything to do with efficiency calculations. And finally, there's no reason for me to believe super-busy OP --with 113 comments at the time I'm writing these lines-- will ever even bother to address any of my comments.

 

* If the fluid happened to correspond to a conserved quantity, it wouldn't make much of a difference, TBH. It's a conserved quantity that must go somewhere --for all that Carnot's reasoning is concerned. "Phlogiston" is a place-holder for a concept that was better understood later.

** Mind you, if the engine lost 0.00000000000001 usable energy every cycle, it would eventually grind to a halt anyway. Mind you also, @swansont's observation that,

3 hours ago, swansont said:

I recall trying to run my stirling engine on a hot day. I put it on a mug of hot water and it would barely run - too much friction. When I put ice cubes on the top plate, it ran pretty well. Since the source of heat was the same, the only way this could be the case is if I was converting more heat to work - the efficiency increased.

 

already gives you another clue: Under otherwise fixed conditions, re-scale T_c/T_h, and things will get better in terms of efficiency. That's not direct proof, but certainly a good "thermometer" --allow me the conceptual pun-- that Carnot's reasoning is spot on.

PD:

1) I said before something to the effect of "entropy leaking out." That wasn't quite right. You see, entropy is not a conserved quantity, so that was, strictly speaking, incorrect. But it can certainly go up and up for the whole universe, and it does reflect a loss in usable energy --something that can be exactly quantified by means of Gibbs or Helmholtz free energy, as the cases may be. And it will, as soon as you deviate in any way from the case of a 1-phase ideal gas ideally separated from the heat reservoir --and thereby exchanging both reversible work and heat-- by means of these "ghostly," non-existent walls that Carnot once imagined.

2) @Tom Booth In every reasoning you've deployed so far, you're counting irreversible work bluntly as "work" in the sense of Carnot. That's a blunder of such proportions that I don't wanna get involved in your reasoning any more. It will only lead to one mistake after another. When irreversible work is done, and you don't do anything to store it in any way in the form of state of the system, IOW, it leaves no record, it's as good as lost. Gone, forever, bye-bye. It's there, but you no longer know where it is. Nothing in the system's state reflects it's been done, or whether it came from work or from heat transfer. So you're tampering with concepts that are ambiguous if you try to interpret them in terms of Carnot's formula, and thereby, reversible thermodynamics.

 

Edited February 4, 2023 by joigus
minor correction

[Tom Booth]

7 hours ago, studiot said:

(...) No the Carnot formula is not hogwash if used for the purpose for which it was intended.

I don't like to use the word limit because the word limit has a variety of meanings, some of which would be contradictory if used in the wrong place. A limit may be achievable or unachievable in both mathematics and other sciences.
The only place it is used in Thermodynamics that I can think of is in the thermodynamics of chemical reaction rates and is used to define something called 'the limiting rate step'. In this instance it does not indicate the unachievable.
So, if we were to call the Carnot formula a limit then would would be using limit in two contradictory ways within one discipline (thermdynamics). 

And that would require the reader to make the distinction.

 

Who says any word must be limited in use to some one specific application? Your assertions here is bewildering to me.

Try using an internet search engine (ie Google et al) and perform a search for "Carnot efficiency limit" in quotes. There is no end to thermodynamics and general scientific references using that exact phrase, routinely the majority of which are applied in the same way I have been doing here and to the same formula.

You are apparently not very well read on the subject of thermodynamics is about the only conclusion I'm able to draw from your above attestation.

6 hours ago, joigus said:

The dynamics of this discussion does remind me of that of a Carnot engine, with a reservoir full of an inexhaustible resource, and the corresponding sink that can take any amount of such resource without in any way changing its state.

LOL

5 hours ago, studiot said:

Of course it does.

I am not saying that invalid means useless (see hogwash).

But my development is to show that it forms an upper bound.

Lots of posters here have offered various parts of the thinking development of this, including yourself.

Since Tom rejects the whole caboodle, I am trying to offer these parts in a logical step by step order.

Sadly everyone but Tom seems to understand that. And if he is genuinely doing all that work over decades then it is a shame for him it will ultimately be to no avail.

I have not yet got into state variables, reversibility or the quasi-static concept and their implications for the discussion.

Read, but skipped as not calling for a response. (So Studiot does not feel ignored and petition to have the thread closed).

Edited February 4, 2023 by Tom Booth