Is Carnot efficiency valid?

[exchemist]

1 hour ago, Tom Booth said:

It certainly does affect the result.

A flow of "caloric", comparable to the flow of water through a turbine passes through unaltered. The fluid that goes in one side of a turbine comes out the other side.

Heat, as a form of energy on the other hand can be converted to other forms of energy, such as mechanical motion.

With "work" output, there is a corresponding reduction in heat in the working fluid.

Yes, you make a good point!

What Carnot did, as I understand it, was to associate a "work value" with a quantity of caloric, which depended on the temperature of the caloric. So in his analysis, he thought the amount of caloric rejected by a heat engine was the same as the amount absorbed by it from the hot source. Clausius later showed this to be wrong and that work and heat were both energy.

However, one benefit of Carnot's way of thinking was the idea that caloric (heat) has a temperature, just as a fluid like water does, and it is that which determines how much work it can do. It also has the benefit of assuming that caloric (heat) has to be rejected from the cycle at the end, i.e. what a heat engine does is allow caloric(heat) to fall through a temperature gradient, like water in a water mill, and thereby get it to do work.  

So that set the scene for the correct idea that you can't convert all the input heat into work, with no waste heat. 

[sethoflagos]

Okay, let's try and work our way through this step by step.

1 hour ago, Tom Booth said:

How is insulation different from a low temperature?

According to the Carnot formula, an engine with a sink at absolute zero would be 100% efficient.

No it wouldn't. 100% of the enthalpy of the hot working fluid is thermodynamically available for conversion to work, but all real machines have their inefficiencies. So in practice, you may only recover, say, 80% of this as nett work output. We would call this figure the isentropic efficiency of the machine (as opposed to the thermal efficiency). The remaining 20% of the energy input would be discharged to the cold sink with the working fluid at a significantly higher temperature than the cold sink. I've underlined that last part because it is crucially important. It's where the excess entropy is being generated.

1 hour ago, Tom Booth said:

At 100% efficiency, all the heat would be converted to work output so no heat would flow into or out from the sink.

This is were we need to be extremely careful about which efficiency were are talking about - the theoretical Carnot limit or the real world isentropic efficiency. In the theoretical world there could be a near zero heat flow into a cold sink at absolute zero. In the real world, there would be a significant heat flow.

 

1 hour ago, Tom Booth said:

Likewise. Insulating the cold side of the engine mimics the condition of having the cold side at a lower temperature. 

.Only for a machine with an isentropic efficiency of 100% which is not a practical proposition.

1 hour ago, Tom Booth said:

Heat exchange on the cold side is reduced, the same result that would be achieved by reducing the cold side temperature.

For a real world machine impeding the heat exchange is equivalent to heating up the cold sink. Less of the input energy is now available for conversion to work. The two scenarios are not equivalent. In fact they are polar opposites.

1 hour ago, Tom Booth said:

A perfect insulation would, or should have the same effect as having a sink at absolute zero.

Absolutely not. They are diametrically opposed.

1 hour ago, Tom Booth said:

How would the engine know the difference?

From the extreme difference in temperatures on the cold side of the machine.

1 hour ago, Tom Booth said:

If there is heat flowing from the engine into a sink at absolute zero, then there is not 100% efficiency (conversion of the heat to mechanical work output).

 Correct. The work produced is limited by the isentropic efficiency.

1 hour ago, Tom Booth said:

There are, IMO, unacceptable consequences to this whole Carnot limit equation nonsense.

In Carnot's mind, a 100% efficient engine would be an engine that transfers 100% of the heat to the sink the complete opposite of reality.

Reread my first point in this post. You're conflating the Carnot limit with actual machine isentropic efficiency. They are entirely different concepts. Confusing the two leads to absurd conclusions especially at absolute zero. 

2 hours ago, Tom Booth said:

No, 

It is the Carnot limit equation that purportedly tells us the maximum  efficiency of any heat engine with no more information than the temperature difference.

Again focus on the phrase 'maximum efficiency'. Can we agree that this is different from 'actual efficiency'?

 

2 hours ago, Tom Booth said:

Typically, in textbook examples, some actual quantity of heat in Joules is arbitrarily postulated.

Example:

If Carnot efficiency is 20% based on the temperature difference, and 100,000 Joules are supplied to the engine, how many Joules of heat will be transfered to the cold reservoir?

80,000 joules.

Supposing 100 Joules/second as the theoretical maximum that could be delivered by the steamer, 80 Joules/second would be transfered through the engine to the cold side per second, as long as the engine is running. 20 Joules as an absolute maximum could be converted to work output. (According to the Carnot limitation).

In simple terms, nearly all the heat needs to pass directly through the engine to the sink for the engine to operate. (According to the Carnot limit equation).

Here you are allocating an isentropic efficiency of 100% to the machine.

2 hours ago, Tom Booth said:

Simply running one of these engines it can be very easily seen or felt that no such massive heat transfer to the sink takes place.

The cold side of the engine remains relatively cold as long as the engine is running. Just touch it. The hot side is scalding hot. The cold side feels cool to the touch.

Not very "objective", but rather convincing.

I'm finding it difficult to picture 4% of the output of a typical hair dryer as a 'massive heat transfer' and indeed how one would see it. I see no science here.

2 hours ago, Tom Booth said:

It seems to me, in my experience that a Stirling engine is literally a kind of heat pump. Not a heat pump that transfered heat from the hot side to the cold side, but just the opposite. The engine is always transferring heat from the cold side and concentrating it back at the hot side, then using that concentration of heat to expand the gas and drive the piston.

You've gone a long way down a rabbit hole and need to find your way back.

It's taken me quite a while to wade through all the steps in your thinking so I'd be grateful if you spent a similar amount of effort in trying to understand what I've presented here. Obviously, I'm only too happy to assist with further clarification.

[Ghideon]

15 hours ago, swansont said:

But you’ve insulated the device. Which means the hot side can be hotter and stay hot. Before insulation the heat differential is likely smaller.

Good question. A few years back I think I think I asked the same thing:

Quote

Is there any chance that the observed effect is caused by the insulation on the hot side?...

Reference: https://www.scienceforums.net/topic/122721-heat-engine-experiments-and-2nd-law-of-thermodynamics/?do=findComment&comment=1149108

 

What is the difference between the 2020 setup and the new one above @Tom Booth? 

 

[Tom Booth]

20 hours ago, exchemist said:

Yes, you make a good point!

What Carnot did, as I understand it, was to associate a "work value" with a quantity of caloric, which depended on the temperature of the caloric. So in his analysis, he thought the amount of caloric rejected by a heat engine was the same as the amount absorbed by it from the hot source. Clausius later showed this to be wrong and that work and heat were both energy.

However, one benefit of Carnot's way of thinking was the idea that caloric (heat) has a temperature, just as a fluid like water does, and it is that which determines how much work it can do. It also has the benefit of assuming that caloric (heat) has to be rejected from the cycle at the end, i.e. what a heat engine does is allow caloric(heat) to fall through a temperature gradient, like water in a water mill, and thereby get it to do work.  

So that set the scene for the correct idea that you can't convert all the input heat into work, with no waste heat. 

You say I make a good point. Thanks. But then repeat the old Carnot water wheel fallacy. Which was my point. That is a fallacy.

 

Heat is not anything like any fluid. No energy can be derived from it's so-called "fall".

Carnot's idea that "caloric (heat) has to be rejected from the cycle at the end" is no "benefit", it's utter nonsense.

The water wheel "analogy" (which Carnot did not consider an analogy at all, but a literal description, literally true, that heat is a "fluid" that "falls" in temperature) implies the existence of some unknown force apart from "heat" (or caloric) itself, similar to gravity.

What is the outside "force" that compels heat to "flow" between an elevated high temperature "reservoir" and a low temperature one?

Water flows down hill due to an "outside" force acting on it: gravity.

So water can flow into, through and out of a turbine and energy can be extracted due to gravity.

There is, as far as I know, no corollary to gravity compelling heat to "flow" from hot to cold. No outside force pushing or pulling or otherwise compelling "heat" to "flow" up, down or sideways from which energy could be extracted.

Heat itself is the energy.

When heat is converted to "work" the heat/energy has not "fallen" due to some kind of heat-gravity to then continue along on its way to a lower level where it then "has to be rejected" . That would violate conservation of energy.

"Heat" in a heat engine is just the random motion of the air particles trapped inside the engine colliding with each other, colliding with the inner walls of the heat engine chamber and colliding with the piston.

When gas particles collide with the piston and the piston moves, the motion of the particles is transfered to the piston.

There is no outside force, (some unknown form of heat-gravity) compelling this interaction from which energy can be extracted, is there?

When the air particles transfers their motion, (energy), to the piston the motion of those particles stop or slow down. Now the air particles will not have as much energy to transfer to our temperature probe. They have been rendered "cold". No heat flowed out to any "reservoir".

The "heat" of the particle does not need to be subsequently removed to a sink after this "fall" in temperature. The heat (motion/kinetic energy) has already been transfered to the piston and transformed into mechanical motion.

The whole Carnot water mill idea is juvenile and should be completely discarded once and for all. There is no "benefit" in it whatsoever.

 

18 hours ago, sethoflagos said:

Okay, let's try and work our way through this step by step.

No it wouldn't. 100% of the enthalpy of the hot working fluid is thermodynamically available for conversion to work, but all real machines have their inefficiencies. So in practice, you may only recover, say, 80% of this as nett work output. We would call this figure the isentropic efficiency of the machine (as opposed to the thermal efficiency). The remaining 20% of the energy input would be discharged to the cold sink with the working fluid at a significantly higher temperature than the cold sink. I've underlined that last part because it is crucially important. It's where the excess entropy is being generated.

This is were we need to be extremely careful about which efficiency were are talking about - the theoretical Carnot limit or the real world isentropic efficiency. In the theoretical world there could be a near zero heat flow into a cold sink at absolute zero. In the real world, there would be a significant heat flow.

 

.Only for a machine with an isentropic efficiency of 100% which is not a practical proposition.

For a real world machine impeding the heat exchange is equivalent to heating up the cold sink. Less of the input energy is now available for conversion to work. The two scenarios are not equivalent. In fact they are polar opposites.

Absolutely not. They are diametrically opposed.

From the extreme difference in temperatures on the cold side of the machine.

 Correct. The work produced is limited by the isentropic efficiency.

Reread my first point in this post. You're conflating the Carnot limit with actual machine isentropic efficiency. They are entirely different concepts. Confusing the two leads to absurd conclusions especially at absolute zero. 

Again focus on the phrase 'maximum efficiency'. Can we agree that this is different from 'actual efficiency'?

 

Here you are allocating an isentropic efficiency of 100% to the machine.

I'm finding it difficult to picture 4% of the output of a typical hair dryer as a 'massive heat transfer' and indeed how one would see it. I see no science here.

You've gone a long way down a rabbit hole and need to find your way back.

It's taken me quite a while to wade through all the steps in your thinking so I'd be grateful if you spent a similar amount of effort in trying to understand what I've presented here. Obviously, I'm only too happy to assist with further clarification.

Thanks, but I should apologize. My main intent in that post was to point out some of the absurd conclusions and contradictions that result from the Carnot theory generally. Like all the heat flowing to the sink at absolute zero resulting in 100% efficiency. Among other things you pointed out, that would be a violation of conservation of energy.

As far as your opinion that my  considering a heat engine operating similarly to a heat pump has taken me "a long way down a rabbit hole" I consider the whole Carnot theory infecting the minds of so many the actual "rabbit hole" we've been in for two centuries and need desperately to find our way out of.

To reiterate, heat engines are nothing like water mills or turbines. There is no HEAT-gravity.

Edited January 26, 2023 by Tom Booth
Clarification of plurality "particle"(s)

[sethoflagos]

59 minutes ago, Tom Booth said:

As far as your opinion that my  considering a heat engine operating similarly to a heat pump has taken me "a long way down a rabbit hole".....

That's not what I said at all. I said that you persistently confuse actual machine efficiency with the Carnot limit. 

1 hour ago, Tom Booth said:

To reiterate, heat engines are nothing like water mills or turbines. There is no HEAT-gravity.

However, hot surfaces transmit more momentum than cold surfaces. So although it is entirely possible for a cold body to transmit a quantum of heat to a hot body, it is overwhelmed by the momentum flow in the opposite direction. The nett direction of heat flow is determined by force of numbers.

 

[Tom Booth]

18 hours ago, Ghideon said:

Good question. A few years back I think I think I asked the same thing:

Reference: https://www.scienceforums.net/topic/122721-heat-engine-experiments-and-2nd-law-of-thermodynamics/?do=findComment&comment=1149108

 

What is the difference between the 2020 setup and the new one above @Tom Booth? 

 

It is a continuation of the same line of research.

Previously I used insulation on engines that had metal plates for the heat exchangers on both the hot and the cold sides.

Back then I had planned on using acrylic (plexiglass) on the cold side to block the supposed "flow" of "waste heat" out of the engine, but my plexiglass was brittle and kept cracking and breaking when I tried cutting it. Then that thread was locked before I could do any more, or address yours or anyone else's ideas or suggestions. Sorry.

I think I may have also been banned from the forum, or just saw no point in continuing here.

So the only difference is finding a means of more effectively insulating the engine. I came across these little engines with only a metal plate on the bottom, I believe intended as the "sink". The idea being to let the sun shine in through the acrylic top the heat going out the metal plate on the bottom.

I could reverse that. Heat the metal plate on the bottom and "trap" the heat under the non-heat conducting acrylic dome.

This, IMO should be impossible, (according to Carnot theory) the engine was not designed to run that way.

But it ran just fine.

To block even more heat I added the Aerogel blanket and glass dome.

These additions were not included in any previous experiments.

I thought the addition of all this insulating material would impress the forum members here, more than the previous use of ordinary styrofoam or house insulation.

The metal cold side heat exchanger has been replaced with non-heat conducting acrylic, blanketed with silica Aerogel, covered with a glass dome.

But does all that make any impression on anyone here?

Apparently the invincible "caloric" is unstoppable and can pass right through anything as if there were nothing there at all. No different than the open air.

Your idea or theory is as plausible as any other. Maybe the insulation on the cold side is causing an elevation in temperature on the hot, heat input side, thus maintaining a temperature difference.

The temperature probes should reveal something.

 

10 minutes ago, sethoflagos said:

That's not what I said at all..

 

Sorry, my mistake I guess, but:

(Screenshot attached)

You quoted my statement about the engine acting as a heat pump then immediately afterward made your statement about my falling down a rabbit hole.

Not sure how else to interpret that. But OK.

Edited January 26, 2023 by Tom Booth

[sethoflagos]

19 minutes ago, Tom Booth said:

Not sure how else to interpret that. But OK.

So you are just going to ignore the true context intended:

21 minutes ago, sethoflagos said:

... that you persistently confuse actual machine efficiency with the Carnot limit. 

Which would be a pity, because all your misunderstandings appear to stem from this single root cause.

[Tom Booth]

53 minutes ago, sethoflagos said:

That's not what I said at all. I said that you persistently confuse actual machine efficiency with the Carnot limit. 

However, hot surfaces transmit more momentum than cold surfaces. So although it is entirely possible for a cold body to transmit a quantum of heat to a hot body, it is overwhelmed by the momentum flow in the opposite direction. The nett direction of heat flow is determined by force of numbers.

 

I have no major disagreement with that ("the direction of heat flow is determined by force of numbers"). True enough, but incomplete. (Not force of numbers exclusively. Also energy level).

You are also neglecting to address the fact that heat, as a form of motion or kinetic energy, may also be converted to some other form of energy entirely. At that point any "flow" of "heat" (in the form of sensible/measurable heat) comes to an abrupt end. The heat is gone having been replaced by the wheels of the engine turning and the subsequent clatter, friction and any other work output (load on the engine), electricity, if the engine turns a generator etc.

The "heat" has already left AS these other forms of energy so does not need to be removed again via a heat sink.

29 minutes ago, sethoflagos said:

So you are just going to ignore the true context intended:

Which would be a pity, because all your misunderstandings appear to stem from this single root cause.

Feel free to elaborate. How do I:

"persistently confuse actual machine efficiency with the Carnot limit. "

 

A limit on efficiency is not efficiency itself, any more than a fence around a cow is a cow.

My understanding is that the "Carnot limit" or efficiency equation is a limit on heat utilization, by any heat engine.

Nothing more or less than that.

If the Carnot efficiency be 20% then supposedly, only 20% of the heat supplied (above the ambient baseline) will be available to convert into "work" output. The other 80% of the heat supplied MUST be eliminated, "rejected" to the sink or "cold reservoir". (According to generally accepted theory ala Carnot limit)

So where is the misunderstanding?

Edit: The above percentages derived from the presumed temperatures in my experiment via the Carnot limit equation and would vary according to circumstance, of course.

 

 

Edit: also it is understood that an upper "limit" is just that; a limit not the actual efficiency, which is generally presumed to be within that limit. The actual heat utilization being less than the (20% or whatever) calculated limit 

Edited January 26, 2023 by Tom Booth

[studiot]

24 minutes ago, Tom Booth said:

I have no major disagreement with that ("the direction of heat flow is determined by force of numbers"). True enough, but incomplete. (Not force of numbers exclusively. Also energy level).

 

Well I have a major disagreement with the claim I have emboldened.

 

This is a fine example of what two experts (+1 each) have been trying to tell you.

You do not know enough to understand exactly what they are saying to you.

The energy level has exactly zero bearing on the direction of heat flow.

This is a simple case of.

If A > then B heat flows from A to B.

If A = B no heat flows.

[sethoflagos]

39 minutes ago, Tom Booth said:

Feel free to elaborate. How do I:

"persistently confuse actual machine efficiency with the Carnot limit. "

I listed them for you in this post. Read it carefully from the beginning.

[Tom Booth]

7 minutes ago, studiot said:

 

Well I have a major disagreement with the claim I have emboldened.

 

This is a fine example of what two experts (+1 each) have been trying to tell you.

You do not know enough to understand exactly what they are saying to you.

The energy level has exactly zero bearing on the direction of heat flow.

This is a simple case of.

If A > then B heat flows from A to B.

If A = B no heat flows.

Not sure where the problem is.

I'm thinking primarily in terms of the gas particles zipping around inside a heat engine, or outside for that matter.

Some particles are "high energy", by that I mean HOT fast moving, some are low energy COLD slow moving.

When a fast moving high energy particle collides with a slow low energy particle heat (kinetic energy) is transmitted from the higher energy particle to the lower energy particle.

The propagation of heat can continue (or "flow") by subsequent particle collisions

11 minutes ago, sethoflagos said:

I listed them for you in this post. Read it carefully from the beginning.

OK.

I've already responded; I said:

"Thanks, but I should apologize. My main intent in that post was to point out some of the absurd conclusions and contradictions that result from the Carnot theory generally. Like all the heat flowing to the sink at absolute zero resulting in 100% efficiency. Among other things you pointed out, that would be a violation of conservation of energy."

Sorry for the confusion but you are trying to address "my thinking" in a post that was apparently a failed attempt at refuting Carnot by reductio ad absurdum.

[sethoflagos]

26 minutes ago, Tom Booth said:

Sorry for the confusion but you are trying to address "my thinking" in a post that was apparently a failed attempt at refuting Carnot by reductio ad absurdum.

You refuted something by this means, but it wasn't Carnot. 

Well, I tried. 

[Tom Booth]

1 minute ago, sethoflagos said:

You refuted something by this means, but it wasn't Carnot. 

Well, I tried. 

There is the assertion all over:

Example:

Carnot knew something else: there was an absolute zero of temperature.  Therefore, he reasoned, if you cooled the fluid down to absolute zero, it would give up all its heat energy.  So, the maximum possible amount of energy you can extract by cooling it from TH to TC is, what fraction is that of cooling it to absolute zero? 

It’s just TH−TC/TH ! 

I believe the equation originated with Clausius but has been attributed to Carnot.

It is infact just a reiteration of Carnot's "fall of Caloric" water wheel nonsense formalized as a mathematical formula.

[studiot]

48 minutes ago, Tom Booth said:

Not sure where the problem is.

I'm thinking primarily in terms of the gas particles zipping around inside a heat engine, or outside for that matter.

Some particles are "high energy", by that I mean HOT fast moving, some are low energy COLD slow moving.

When a fast moving high energy particle collides with a slow low energy particle heat (kinetic energy) is transmitted from the higher energy particle to the lower energy particle.

The propagation of heat can continue (or "flow") by subsequent particle collisions

There you go again.

Preaching fallacies, to those who know more than you do,

Instead of reading properly what they are saying.

 

Seth has told you and I have highlighted what he told you and tried to reinforce that he specified the direction not the amount of heat transferred.

And yet here you go again trying to change the subject to the amount.

 

A total waste of others' time and effort.

[Tom Booth]

43 minutes ago, studiot said:

There you go again.

Preaching fallacies, to those who know more than you do,

Instead of reading properly what they are saying.

 

Seth has told you and I have highlighted what he told you and tried to reinforce that he specified the direction not the amount of heat transferred.

And yet here you go again trying to change the subject to the amount.

 

A total waste of others' time and effort.

I'm not trying to "change the subject" I was just clarifying what I meant by "energy level".

In a gas in a heat engine the collisions are basically random in all directions, there is no particular "flow" in any one direction, except perhaps as dictated by the geometry and mechanics. The effort of an engine designer should be to direct the "flow" in such a way as to impact the piston (not a heat sink).

That is the tragedy of adherence to the Carnot theory. Even NASA designs their Stirling engines with active water cooling 2 inches from the heat input. indirect channeling of the expanding hot gas through a cold regenerator before it can impact the piston, heat robbing steel construction, all because Carnot thought heat had to be thrown away to a sink for an engine to complete a cycle. All this cooling and "heat rejection" is just wasting FUEL.

Heat is the heat engines FUEL. Transferring it to a cold heat exchanger is like putting a big hole in your cars fuel tank.

A heat engine is nothing like a water wheel where the liquid driving the engine must pass through and out the opposite side.

Carnot theory is the reason there has been little advancement in Stirling heat engine design in 200 years.

1 hour ago, sethoflagos said:

You refuted something by this means, but it wasn't Carnot. 

Well, I tried. 

Maybe you could try addressing my questions to you in the second part of this post where I provided my actual understanding of the carnot efficiency limit:

 

Is there anything there that you have any disagreement with? Starting with: "My understanding is ..."

I hesitate somewhat to bring this up because I'm not entirely certain of the validity, who uploaded it, what type of Stirling engine was involved etc.

But for the sake of reviewing other work and maybe not reinventing the wheel or something.

Someone on the Stirling engine forum a while back pointed out a graph on Wikipedia that is supposed to be actual temperature readings of the heat exchangers as well as the hot and cold side working gas from inside a running Stirling engine.

The straight blue and red lines are the hot and cold "heat exchangers". The curved lines represent the temperatures of the working fluid on the hot and cold sides of the engine.

 

"The gas temperature fluctuations are caused by the effects of compression and expansion in the engine"

Edited January 26, 2023 by Tom Booth

[Tom Booth]

I'm skeptical of this being from a "real" engine as stated in the Wikipedia article. The "heat exchanger" lines are absolutely straight which seems unrealistic or unlikely. The image info page calls it a "simulation".

Nevertheless, what I find interesting is that the working fluid on the respective hot and cold sides exceeds the temperature of the heat exchangers periodically.

That is, the gas on the hot side increased above the temperature of the hot, heat input heat exchanger. And on the cold side the working fluid temperature dips below the temperature of the "sink".

The hot peak is presumably full compression and the cold dip full expansion, the cooling effect being due to adiabatic expansion of the gas.

Regardless if this represents real readings or just a computer generated simulation, it corresponds with my own research and findings. That is, it is what I would expect to see from real temperature readings from inside a real engine.

I also don't know that taking such real time temperature readings would be possible using ordinary probes.

 

[studiot]

1 hour ago, Tom Booth said:

I'm not trying to "change the subject" I was just clarifying what I meant by "energy level".

 

What amazes me is your total refusal to pay attention to important matters others say to you.

 

For instance, what do you actually know about the history of the subject ?

Do you actually hate the French ?

 

You have persisted with some incredible slurs upon Carnot.

Why slurs ?

Because your version is not possible.

 

Carnot published his cycle in 1824, when Clausius was exactly 2 years old.

Clausius published his most famous thermodynamic work in 1850, in which he discussed Carnot's earlier work mathematically and indeed provided a mathematical basis for it, replacing Sadi's Physics basis.

Do you know either of their reasoning ?

 

This stuff is a matter of Historic record.

Quote

When Lazare Carnot died in August 1823, Hippolyte Carnot returned to Paris and there he helped Sadi Carnot to make the book on steam engines that he was working on at the time more understandable to the general public. In 1824 Carnot published this work, the only one he published during his lifetime, Réflexions sur la puissance motrice du feu et sur les machines propres à développer cette puissanceⓉ which includes his description of the "Carnot cycle". This book only became well known after Clapeyron published an analytic reformulation of it in 1834. Carnot's ideas were later incorporated into the thermodynamic theory of Clausius and Thomson.

https://mathshistory.st-andrews.ac.uk/Biographies/Clausius/

https://mathshistory.st-andrews.ac.uk/Biographies/Carnot_Sadi/

 

 

 

[Tom Booth]

How could these working fluid  temperature fluctuations take place?

Well, it's simple.

During the first part of the compression stroke the hot heat exchanger is blocked. During compression the temperature of the gas increases due to adiabatic compression. (We are talking about a real engine running at high speed, so isothermal compression is not actually possible).

The displacer is 90° ahead of the piston.

Half way into the compression stroke while the gas temperature is increasing the displacer uncovers the hot heat exchanger delivering a blast of heat to the working fluid as it is being compressed and already increasing in temperature by heat of compression.

At full compression the heat from the heat source and the heat of compression combine and for a brief moment the working fluid gets very hot. Hotter even than the heat source (the hot heat input heat exchanger).

At TDC (top dead center or full compression) the crank rounds the corner and the piston changes direction and the hot gas expands rapidly driving the piston.

The displacer, 90° ahead of the piston will uncover the cold heat exchanger just as the working fluid drops in temperature due to the rapid expansion and conversation of the heat into work output.

The working fluid is now colder than the supposed "sink". So, which way would the heat be flowing?

The working fluid is now very cold and contracts causing a rapid drop in pressure within the engine so that now outside atmospheric pressure drives the piston inward for the compression stroke.

The process repeats.

The engine is not dumping any heat into the cold side. It is pulling additional heat out of it.

[sethoflagos]

39 minutes ago, Tom Booth said:

Is there anything there that you have any disagreement with? Starting with: "My understanding is ..."

 

2 hours ago, Tom Booth said:

My understanding is that the "Carnot limit" or efficiency equation is a limit on heat utilization, by any heat engine.

Nothing more or less than that.

 'Heat utilisation' is a bit woolly and ambiguous, but arguably okay.

2 hours ago, Tom Booth said:

If the Carnot efficiency be 20% then supposedly, only 20% of the heat supplied (above the ambient baseline) will be available to convert into "work" output.

What do you mean by 'above the ambient baseline'? You appear to be confusing 'heat' and 'temperature'. They can certainly be related but they are not the same thing - their units are never interchangeable.

The amount of heat absorbed from the hot sink in the ideal Carnot cycle Is represented by Q_H = T_H(S_B - S_A) and at the cold sink Q_C = T_C(SA - SB) - These arise from simple application of the 2nd Law for reversible heat exchange.

Neither of these terms reference any 'ambient' condition. From W = Q_H - Q_C we then get

Carnot cycle efficiency = W/Q_H = (Q_H - Q_C)/Q_H = 1 - Q_C/Q_H = 1 - T_C/T_H 

There is a huge body of work and experimental data that is in agreement with the absolute nature of this limit.

3 hours ago, Tom Booth said:

The other 80% of the heat supplied MUST be eliminated, "rejected" to the sink or "cold reservoir". (According to generally accepted theory ala Carnot limit)

Naturally.

3 hours ago, Tom Booth said:

So where is the misunderstanding?

It's one thing to say something. It's another to understand what you are saying. 

[Tom Booth]

33 minutes ago, sethoflagos said:

 

 'Heat utilisation' is a bit woolly and ambiguous, but arguably okay.

What do you mean by 'above the ambient baseline'? You appear to be confusing 'heat' and 'temperature'. They can certainly be related but they are not the same thing - their units are never interchangeable.

The amount of heat absorbed from the hot sink in the ideal Carnot cycle Is represented by Q_H = T_H(S_B - S_A) and at the cold sink Q_C = T_C(SA - SB) - These arise from simple application of the 2nd Law for reversible heat exchange.

Neither of these terms reference any 'ambient' condition. From W = Q_H - Q_C we then get

Carnot cycle efficiency = W/Q_H = (Q_H - Q_C)/Q_H = 1 - Q_C/Q_H = 1 - T_C/T_H 

There is a huge body of work and experimental data that is in agreement with the absolute nature of this limit.

Naturally.

It's one thing to say something. It's another to understand what you are saying. 

"What do you mean by 'above the ambient baseline'?"

I mean simply that the engine exists in an ambient environment (our earth atmosphere) at roughly 300° Kelvin.

The surrounding pre-existing heat in the environment around the engine is what I'm calling the ambient baseline.

To get the engine to operate additional heat must be added above the ambient heat in the surrounding atmosphere supplied by the sun.

I don't agree with it (the interpretation) but the "carnot limit" is generally interpreted as representing a percentage of the added heat we supply to get the engine to operate, not all the heat, including the pre-existing heat in the atmosphere all the way down to absolute zero.

If you object to referring to "heat" call it the kinetic energy of the surrounding air molecules or whatever you like, but I don't mean "temperature"

There is certainly "heat" on a molecular level being supplied from the ambient environment. The engine is bombarded with hot air molecules bouncing off it continually on all sides, though the engine is equally hot, so the exchange is mutual.

Mathematically the carnot limit is derived from the difference in temperature produced as a result of adding heat (raising the temperature) above the existing baseline of 300k. (Approximately, depending on location).

 

If the carnot limit means anything, (what makes some sense) is if it is applied to All the heat down to absolute zero.

Then the heat we add is the limit of heat that is available to convert back into useful work. All of it, not some meager percentage or ratio.

 

Edited January 26, 2023 by Tom Booth

[exchemist]

6 hours ago, Tom Booth said:

You say I make a good point. Thanks. But then repeat the old Carnot water wheel fallacy. Which was my point. That is a fallacy.

 

Heat is not anything like any fluid. No energy can be derived from it's so-called "fall".

Carnot's idea that "caloric (heat) has to be rejected from the cycle at the end" is no "benefit", it's utter nonsense.

The water wheel "analogy" (which Carnot did not consider an analogy at all, but a literal description, literally true, that heat is a "fluid" that "falls" in temperature) implies the existence of some unknown force apart from "heat" (or caloric) itself, similar to gravity.

What is the outside "force" that compels heat to "flow" between an elevated high temperature "reservoir" and a low temperature one?

Water flows down hill due to an "outside" force acting on it: gravity.

So water can flow into, through and out of a turbine and energy can be extracted due to gravity.

There is, as far as I know, no corollary to gravity compelling heat to "flow" from hot to cold. No outside force pushing or pulling or otherwise compelling "heat" to "flow" up, down or sideways from which energy could be extracted.

Heat itself is the energy.

When heat is converted to "work" the heat/energy has not "fallen" due to some kind of heat-gravity to then continue along on its way to a lower level where it then "has to be rejected" . That would violate conservation of energy.

"Heat" in a heat engine is just the random motion of the air particles trapped inside the engine colliding with each other, colliding with the inner walls of the heat engine chamber and colliding with the piston.

When gas particles collide with the piston and the piston moves, the motion of the particles is transfered to the piston.

There is no outside force, (some unknown form of heat-gravity) compelling this interaction from which energy can be extracted, is there?

When the air particles transfers their motion, (energy), to the piston the motion of those particles stop or slow down. Now the air particles will not have as much energy to transfer to our temperature probe. They have been rendered "cold". No heat flowed out to any "reservoir".

The "heat" of the particle does not need to be subsequently removed to a sink after this "fall" in temperature. The heat (motion/kinetic energy) has already been transfered to the piston and transformed into mechanical motion.

The whole Carnot water mill idea is juvenile and should be completely discarded once and for all. There is no "benefit" in it whatsoever.

 

Thanks, but I should apologize. My main intent in that post was to point out some of the absurd conclusions and contradictions that result from the Carnot theory generally. Like all the heat flowing to the sink at absolute zero resulting in 100% efficiency. Among other things you pointed out, that would be a violation of conservation of energy.

As far as your opinion that my  considering a heat engine operating similarly to a heat pump has taken me "a long way down a rabbit hole" I consider the whole Carnot theory infecting the minds of so many the actual "rabbit hole" we've been in for two centuries and need desperately to find our way out of.

To reiterate, heat engines are nothing like water mills or turbines. There is no HEAT-gravity.

This is all mere assertion on your part and I'm afraid that 150 years of physics and engineering says you are wrong. The fluid analogy - and of course it is only an analogy - is very useful. A temperature gradient for heat is like a gradient on a riverbed for water. Heat is a flow of internal energy and the steeper the thermal gradient the faster it flows.

Yes, you are of course right that heat is due to the motion of the molecules of the substance in question, but the way that motion spreads itself out through a body, along temperature gradients, is analogous to a flow of a physical fluid. People of Carnot's time were not morons. They were groping towards the understanding we now have. Caloric was an intelligent idea, even if it proved to be a defective model. My point is that it provided useful insight for those that came later.

As to the idea of heat being entirely converted to motion of a piston, it is quite interesting to think about that for a moment. There is no way that heat can give up all its energy to make a piston move. Why? Because molecules don't move all at the same speed. There is a bell-shaped velocity distribution* among the molecules. So at whatever speed the piston moves when molecules hit it, it will be moving faster than some and slower than others. So some motion will always be left, among most of the molecules, after the interaction. Furthermore, in order to exert a force on the piston to make it move, molecules have to rebound from it. So they leave the piston surface still in motion.  

This is the whole point about heat. It is disordered, random kinetic energy. There is no way to order all the molecules neatly, so that they all move together, at one speed, towards the piston in order to exactly give up all their momentum to push it. That is the reason why it is impossible to convert all heat to work. (This inherently disordered character of molecules in motion is captured in the concept of entropy.) 

* In fact not quite a bell curve: a Maxwell-Boltzmann distribution: https://en.wikipedia.org/wiki/Maxwell–Boltzmann_distribution     

 

[Tom Booth]

42 minutes ago, studiot said:

 

What amazes me is your total refusal to pay attention to important matters others say to you.

 

For instance, what do you actually know about the history of the subject ?

Do you actually hate the French ?

 

You have persisted with some incredible slurs upon Carnot.

Why slurs ?

Because your version is not possible.

 

Carnot published his cycle in 1824, when Clausius was exactly 2 years old.

Clausius published his most famous thermodynamic work in 1850, in which he discussed Carnot's earlier work mathematically and indeed provided a mathematical basis for it, replacing Sadi's Physics basis.

Do you know either of their reasoning ?

 

This stuff is a matter of Historic record.

https://mathshistory.st-andrews.ac.uk/Biographies/Clausius/

https://mathshistory.st-andrews.ac.uk/Biographies/Carnot_Sadi/

 

 

 

I respect Carnot. In the end he recognized the error he originally helped perpetuate and finally rejected the caloric theory and all that it implied. but unfortunately nobody read about that for many years to come.

My contention is with the theory Carnot represents generally, not the person or any people.

[swansont]

 

7 hours ago, Tom Booth said:

The water wheel "analogy" (which Carnot did not consider an analogy at all, but a literal description, literally true, that heat is a "fluid" that "falls" in temperature) implies the existence of some unknown force apart from "heat" (or caloric) itself, similar to gravity.

What is the outside "force" that compels heat to "flow" between an elevated high temperature "reservoir" and a low temperature one?

Water flows down hill due to an "outside" force acting on it: gravity.

So water can flow into, through and out of a turbine and energy can be extracted due to gravity.

There is, as far as I know, no corollary to gravity compelling heat to "flow" from hot to cold. No outside force pushing or pulling or otherwise compelling "heat" to "flow" up, down or sideways from which energy could be extracted.

It’s an energy analysis, not a force analysis. You can do this in mechanics, too. You use the tools that get you to the answer.

An object falls; you can say it’s because of a force, but also say it’s because things go to their lowest potential energy.

 

7 hours ago, Tom Booth said:

Heat itself is the energy.

Heat is the flow of energy.

7 hours ago, Tom Booth said:

When heat is converted to "work" the heat/energy has not "fallen" due to some kind of heat-gravity to then continue along on its way to a lower level where it then "has to be rejected" . That would violate conservation of energy.

No, it doesn’t. Q_H is not equal to Q_c

7 hours ago, Tom Booth said:

"Heat" in a heat engine is just the random motion of the air particles trapped inside the engine colliding with each other, colliding with the inner walls of the heat engine chamber and colliding with the piston.

When gas particles collide with the piston and the piston moves, the motion of the particles is transfered to the piston.

There is no outside force, (some unknown form of heat-gravity) compelling this interaction from which energy can be extracted, is there?

Nobody is claiming it’s an outside force. 

7 hours ago, Tom Booth said:

When the air particles transfers their motion, (energy), to the piston the motion of those particles stop or slow down. Now the air particles will not have as much energy to transfer to our temperature probe. They have been rendered "cold". No heat flowed out to any "reservoir".

The gas at the end is colder than the gas before the piston moves. The cold reservoir heats up. If you disagree, then where does the energy come from that appears as mechanical work?

 

7 hours ago, Tom Booth said:

The "heat" of the particle does not need to be subsequently removed to a sink after this "fall" in temperature. The heat (motion/kinetic energy) has already been transfered to the piston and transformed into mechanical motion.

All of it has been removed? The gas is at absolute zero?

 

[Tom Booth]

25 minutes ago, exchemist said:

This is all mere assertion on your part and I'm afraid that 150 years of physics and engineering says you are wrong. The fluid analogy - and of course it is only an analogy - is very useful. A temperature gradient for heat is like a gradient on a riverbed for water. Heat is a flow of internal energy and the steeper the thermal gradient the faster it flows.

Yes, you are of course right that heat is due to the motion of the molecules of the substance in question, but the way that motion spreads itself out through a body, along temperature gradients, is analogous to a flow of a physical fluid. People of Carnot's time were not morons. They were groping towards the understanding we now have. Caloric was an intelligent idea, even if it proved to be a defective model. My point is that it provided useful insight for those that came later.

As to the idea of heat being entirely converted to motion of a piston, it is quite interesting to think about that for a moment. There is no way that heat can give up all its energy to make a piston move. Why? Because molecules don't move all at the same speed. There is a bell-shaped velocity distribution* among the molecules. So at whatever speed the piston moves when molecules hit it, it will be moving faster than some and slower than others. So some motion will always be left, among most of the molecules, after the interaction. Furthermore, in order to exert a force on the piston to make it move, molecules have to rebound from it. So they leave the piston surface still in motion.  

This is the whole point about heat. It is disordered, random kinetic energy. There is no way to order all the molecules neatly, so that they all move together, at one speed, towards the piston in order to exactly give up all their momentum to push it. That is the reason why it is impossible to convert all heat to work. (This inherently disordered character of molecules in motion is captured in the concept of entropy.) 

* In fact not quite a bell curve: a Maxwell-Boltzmann distribution: https://en.wikipedia.org/wiki/Maxwell–Boltzmann_distribution     

 

Of course "some" motion will be left. Otherwise the temperature of the gas molecules hitting the piston would reach absolute zero and cease to exist, or perhaps reduce to the form of a Bose-Einstein condensate, but we exist at 300k which is very hot already and we are not talking about utilizing "all the heat" down to absolute zero, just the added heat we supply to the engine.

Some of the gas molecules, I believe, might indeed drop well below the ambient baseline. As in the Claude method of air liquefaction. (Which includes having the gas do work by expanding in an engine pushing a piston to reach cryogenic temperatures).

 

Edited January 26, 2023 by Tom Booth

[swansont]

3 minutes ago, Tom Booth said:

Of course "some" motion will be left. Otherwise the temperature of the gas molecules hitting the piston would reach absolute zero and cease to exist, or perhaps reduce to the form of a Bose-Einstein condensate, but we exist at 300k which is very hot already and we are not talking about utilizing "all the heat" down to absolute zero, just the added heat we supply to the engine.

The engine’s energy source is the hot reservoir. How you get it to be hot is not included in the analysis.

The hot reservoir heats up the gas. That’s the Q_H. The gas heats up the cold reservoir. Q_c