Is Carnot efficiency valid?

[Ghideon]

15 hours ago, Tom Booth said:

Small flat ceramic heating elements.

Could slip that right inside the engine above the bottom plate to heat the working fluid directly.

Quick note; have you been thinking about adding identical heating elements to both the hot plate and cold sink? A small element under the insulation on the cold side could add control to the temperature difference? I don't mean you should crank up the heat, just add a way to tune the temperature and observe how behaviour depends on temperature. Maybe in combination with the probes you posted above? https://www.scienceforums.net/topic/128644-is-carnot-efficiency-valid/?do=findComment&comment=1227752

 

(Sorry if this already discussed, I may have missed some nuances of the experimental details)

 

 

[studiot]

10 hours ago, Tom Booth said:

So how does melting ice, or warming cold water help answer that question?

 

How does that address my point right at the beginning of my post immediately above your answer ?

 

11 hours ago, studiot said:

I agree that playing around with ice water / electric heaters / and other devices opens too many cans of worms for satisfactory simple experimentation.

 

I also asked you a serious and important question which you did indeed ignore which was designed to help create a simple block diagram to show where you need to concentrate your efforts and why what you are currently doing will not achieve your stated aims.

 

10 hours ago, Tom Booth said:

The purpose behind the experiment, originally, is to see what happens to the engine with the "sink" blocked.

 

10 hours ago, Tom Booth said:

My question I want answered is where is the "waste heat" that the Carnot (so-called) equation suggests should be there.

 

9 hours ago, Tom Booth said:

What "cold reservoir"?

 

An ideal reservoir is an object that does not change in temperature however much heat is added to it or extracted from it.

This is true for both hot and cold reservoirs. But as swansont says they are imaginary ideals.

If the if the heat transfer causes a change in temperature it (dramatically) changes the thermodynamics of the system.

There are two ways around this in practical reality. One is the very difficult way you are attempting.

The other is to find an object with very large heat content compared to the amount of heat transfer. But you did not answer my question as noted above.

 

Verbal sparring with swansont is in my opinion what in the UK we call a 'hiding to nothing'. I think I have only known him being wrong once since I have been a member.

 

[Tom Booth]

4 hours ago, Ghideon said:

Quick note; have you been thinking about adding identical heating elements to both the hot plate and cold sink? A small element under the insulation on the cold side could add control to the temperature difference? I don't mean you should crank up the heat, just add a way to tune the temperature and observe how behaviour depends on temperature. Maybe in combination with the probes you posted above? https://www.scienceforums.net/topic/128644-is-carnot-efficiency-valid/?do=findComment&comment=1227752

 

(Sorry if this already discussed, I may have missed some nuances of the experimental details)

 

 

I think it would be great!

Having additional control over the temperatures of both source and sink to dial the temperatures up or down would be fantastic.

To begin with, seems like years ago now, (July 2020 just checked my YT uploads) I just put a piece of 1/4" foil face styrofoam over another engine, recalling an "argument" on the Stirling Engine forum from back around 2012 I think (February 2010 actually, it's still there.) about insulating the cold side of the engine.

I had theorized that if expansion work had a cooling effect on the working fluid. Perhaps the working fluid was getting colder than the "sink" itself (sink = ambient outside the engine) and insulating the sink could, perhaps, increase the ∆T by blocking heat infiltration by ambient heat. That is, if the engine could increase its own temperature differential as it ran, insulation might actually help it to do that BETTER!

Well, this was too radical an idea for the forum at that time. Everybody basically laughed and tried to "educate" me on how a Stirling engine absolutely MUST have a way to dump unused/excess heat or it would overheat and stop immediately.

But... But...

I was reading books on thermodynamics, refrigeration, gas law, gas liquefaction etc. at the time.

The BOOKS said having a compressed gas expand to push a piston was an effective method of reaching cryogenic temperatures. The gas would liquefy right in the cylinder. Typically at very high compression, like 100 bar or whatever to get down to -250° or whatever to liquefy oxygen or nitrogen or some such thing, but...

A Stirling engine, in principle, does the same thing. The piston compresses a gas, then the gas expands doing work to drive the engine,... Just like a compressor/expander liquefies  air. How could it NOT be producing a very marked cooling effect. To me the conclusion seemed inescapable.

Turn the engine over with a motor and it immediately becomes a Cryocooler/air-liquefier. Known fact.

There are heat driven heat pumps as well, so why is this so inconceivable?

Anyway I gave up and pretty much forgot about that debate.

Ten years later I'm fooling around to see how long a Stirling LTD will run on ice or hot water and what difference insulation would make, then recalled that old idea I had pondered on and argued about 10 years earlier, and with the materials there on hand already I decided to settle the argument and put a piece of insulation over the cold side of an engine running on hot water. I had cut the insulation out previously for some other reason, don't recall what.

I thought, I might as well record whatever happened and post it on the forum.

I fully expected that the engine would stop almost immediately. I'd go back to the forum and admit I had been wrong. Everybody was right. I was wrong.

So I watched and waited for the inevitable. The engine would overheat and stop.

But it kept running. ... And running. 

It didn't even slow down as far as I could tell.

Reviewing the recording I found that instead of slowing down, the engine actually ran a little faster. Nothing dramatic, but counting the revolutions with a stop watch, the engine was running faster AFTER the sink was insulated. It also, I found, ran longer and seemed, by the clatter it made, to have more torque and power causing an audible "knock" like the piston was being jerked inward with more force. (The knock was on the contraction stroke).

If the engine had just stopped that time, that would have been the end of it and I wouldn't be here now.

 

4 hours ago, studiot said:

 

How does that address my point right at the beginning of my post immediately above your answer ?

 

 

I also asked you a serious and important question which you did indeed ignore which was designed to help create a simple block diagram to show where you need to concentrate your efforts and why what you are currently doing will not achieve your stated aims.

 

 

 

 

An ideal reservoir is an object that does not change in temperature however much heat is added to it or extracted from it.

This is true for both hot and cold reservoirs. But as swansont says they are imaginary ideals.

If the if the heat transfer causes a change in temperature it (dramatically) changes the thermodynamics of the system.

There are two ways around this in practical reality. One is the very difficult way you are attempting.

The other is to find an object with very large heat content compared to the amount of heat transfer. But you did not answer my question as noted above.

 

Verbal sparring with swansont is in my opinion what in the UK we call a 'hiding to nothing'. I think I have only known him being wrong once since I have been a member.

 

Sorry but I just got up. I only have time to respond to so many posts, usually in the order they appear.

I was responding to a post by someone else before yours.

Nothing personal, but I don't have time now.

What was your vitally important question/statement again? Specifically ?

I did go back and start reviewing your posts from the begining of the thread. You repeatedly insulted me and said this thread was a waste of everybody's time. I'm still working my way forward.

I'm not offended BTW, my character is often questioned and I have thick skin. Skepticism is a must really, and I'm not here to have my ego stroked, obviously, I should think.

Keep your pants on. Have some patience and try not to act like a sniveling spoiled punk that wants to be the center of attention of throws a fit like some 2 year old and BTW some of your posts make no sense. Be glad I DON'T  respond in most cases.

As my mother used to say, if you don't have anything nice to say, don't say anything at all. If you think this thread is a waste of time, I'm sure there must be other threads in this forum somewhere.

 

Edited January 30, 2023 by Tom Booth

[Tom Booth]

17 hours ago, studiot said:

I agree that playing around with ice water / electric heaters / and other devices opens too many cans of worms for satisfactory simple experimentation.

You need to arrange both reservoirs so that the heat transferred through the fluid is les than 1% - preferably less than0.1% - of the heat content ofeach reservoir.

Do you understand the difference between specific heat (also called heat capacity) and heat content ?

For instance using the ocean or a lake etc as the cold reservoir would be really good.

Stirling in his original devices used a blast furnace as the hot reservoir.

You don't seem to comprehend the actual aim of the experiment 

To completely eliminate all possibility of transfer of any heat from the engine into any sink or "cold reservoir" outside the engine.

What you propose is the complete opposite of that: "...using the ocean or a lake etc as the cold reservoir would be really good."

Not! 

I've often wondered; IF the engine is actually pulling some heat from the cold side (less hot side) of the engine, as well as the hotter side, (In a manner similar to a Vuilleumier machine (a heat driven heat pump very similar to a Stirling engine) what would happen if the temperature of the "sink" side (theoretically really just another heat SOURCE or less hot side) were gradually increased after the engine was up and running 

An additional heating element on the cold side as Ghideon suggested would make it possible to investigate that.

The Vuilleumier heat pump draws heat from both hot and cold sides using heat as it's power source as well.

Edited January 30, 2023 by Tom Booth

[joigus]

I've been reading the arguments back and forth and I'm still missing something here. I have to confess I need more reading.

Carnot's argument about the efficiency of heat engines is, from a logical POV, based on two assumptions --correct me anybody if I'm wrong:

1) Conservation of energy

2) Existence, to a reasonable degree of approximation, of heat reservoirs, ie, systems so big and thermodynamically static* that they can exchange any amount of thermal energy necessary --or irreversible work-- for the engine to work between the higher-temperature reservoir and the lower-temperature one.

As one famous argument by Sagan goes, extraordinary claims require extraordinary proof. Because for Carnot's argument to be flawed it would require either 1) or 2) to be wrong, extraordinary evidence that either one of them is the case is required. It seems that the OP leans on the side that heat reservoirs are nothing but monumental abstractions with no basis on real physics. A claim that seems ludicrous to me.

A further qualification could be necessary, which is the distinction between reversible work and irreversible work. Carnot's argument, AFAIR, relies only on the concept of reversible work. Irreversible work is, to all intents and purposes concerning thermodynamic arguments, pretty much indistinguishable from heat losses or gains, and can only be detected by means of precise calorimetric measurements, in principle. After a short time, any irreversible work will have leaked into the "worked upon" system in the form of heat.

But --and it's a big 'but' implied, I think, by other members too--, the more a system resembles a heat reservoir, the more difficult it becomes to make precise measurements of heat loss --never mind it coming from irreversible work done. If a system can absorb or release any sizeable amount of heat --or irreversible work, like eg the motion of a blender-- without significantly changing its temperature, how can you be sure of the amount of energy it has received or released by means of calorimetric measurements based on known heat capacity/specific heat of such reservoir?

What's more, how can you be sure that the conclusion to be drawn is that Carnot's efficiency formula is not correct? Wouldn't it be reasonable to demand from you that you design an engine that improves that? I mean, build a heat engine that delivers an efficiency better than that provided by Carnot's argument --kitchen availability pending.

Also --and no minor point:

On 1/25/2023 at 2:02 PM, sethoflagos said:

Other than demonstrate that industrial machines are tested by professionals up to their thermodynamic limits on a daily basis contrary to your claims.

I apologise if I've misunderstood any of the points under discussion. I need more time to get up to speed.

* Both as compared to the engine.

[Tom Booth]

The Vuilleumier machine however produces only an elevated heat output, It does not generate very much mechanical power output, just enough to operate it's regenerative displacers, if that. Some are driven by a small motor that takes very little outside power but others drive the displacers by their own internal pressure changes and are entirely heat driven.

Having no mechanical power output the Vuilleumier machine does not convert much if any heat to any other form of energy. It outputs HEAT exclusively.

A Stirling engine CONVERTS heat to mechanical power output at very high efficiency.

A combined Stirling/Vuilleumier machine could theoretically take in heat from both a hot and less hot source outputting the heat at a temperature higher than either, convert the high grade heat to mechanical power output. If there is "excess" "waste heat" this could be "rejected" to ambient, rather than to the colder heat source. At least I have difficulty tracing out the reason why that should be "impossible".

A quick sketch to illustrate:

 

Initially, of course, this would require expending energy for running a refrigerator/freezer to create a ∆T to operate the Vuilleumier heat pump.

Vuilleumier machines ordinarily operate with very high thermal input however, like 1000°F not ambient, drawing heat from ambient as a secondary heat source, then "rejecting" the combined high grade heat back to ambient. The high grade heat output however requires continuous cooling.

Such speculations however are not the issue at this juncture.

The issue is the "Carnot limit", which I don't necessarily thing is "wrong" exactly, but I think perhaps it has been misinterpreted somewhere along the way, historically, making it much more restrictive than it actually is.

[Tom Booth]

The Carnot limit equation and it's resultant "efficiency", is actually nothing but the temperature difference transmuted by mathematical trickery into a percentage of the absolute temperature scale.

In other words, starting out at ambient, (300°K) we elevate the temperature to,let's say 375°K (slightly superheated steam).

In the process we just elevated the temperature 20% on the absolute temperature scale.

Is it a coincidence that Carnot efficiency at this ∆T is also exactly 20% ?

We raised the temperature 20% on the Kelvin scale and brought the "Carnot efficiency" up exactly the same percentage.

This is true at any and all temperature differences. The "Carnot limit" is IS the temperature difference.

Is this a measure of efficiency?

The best we can do is utilize the heat we put in and in the process bring the heat back down to the 300° ambient baseline.

The only "available heat" for conversion to work is that heat used to create the temperature differential in the first place.

How can a percentage of a temperature scale have anything to do with the actual efficiency of the engine. (It's power to convert "available heat" into "work").

If we convert all the heat we supplied back into work we are just back where we began, at 300°K and "Carnot efficiency" falls to zero.

But we have not violated conservation of energy.

We have not taken out any more than we put in.

But, someone at some point in history misunderstood this basic principle and took the results of the equation to represent a percentage of OUR supplied heat. As if when we elevate the temperature 20% on the absolute scale we can only utilize 20% of the energy we just supplied. The other 80% of the heat captured, stollen, by the imagined "cold reservoir". This is insane.

Some professor teaching thermodynamics made a blunder, maybe 150 years ago and this nonsense has been perpetuated ever since.

Some numbskull who didn't understand that the equation only represented the actual temperature difference, the elevation of temperature on the absolute scale made a blunder.

Carnot "efficiency" is, if anything, just a measure of how far down the absolute temperature scale it is before you end up back where you started before adding heat to go up the absolute temperature scale.

If you went up 20% of the way (on the absolute temperature scale) you can only go back down that same 20% of the way (on the absolute temperature scale).

Use some common sense.

 

Edited January 30, 2023 by Tom Booth

[Ghideon]

38 minutes ago, Tom Booth said:

Some professor teaching thermodynamics made a blunder, maybe 150 years ago and this nonsense has been perpetuated ever since

If you wish to continue the discussion you may want to focus on the experiments instead.

4 hours ago, Tom Booth said:

I had theorized that if expansion work had a cooling effect on the working fluid. Perhaps the working fluid was getting colder than the "sink" itself (sink = ambient outside the engine) and insulating the sink could, perhaps, increase the ∆T by blocking heat infiltration by ambient heat. That is, if the engine could increase its own temperature differential as it ran, insulation might actually help it to do that BETTER!

If this is still something you want to test, adding heating to the cold side may help in this scenario? I get the impression that your idea* allows for two Stirling engines to be mounted cold plate to cold plate to increase the efficiency of both the engines? 

*) If correct that is...

Edited January 30, 2023 by Ghideon
added a question

[sethoflagos]

2 hours ago, Tom Booth said:

You don't seem to comprehend the actual aim of the experiment 

To completely eliminate all possibility of transfer of any heat from the engine into any sink or "cold reservoir" outside the engine.

Just to clarify, the intent is to make the following changes to the Stirling Cycle.

1. The isothermal expansion stage at T_H stays as is outputting power W_E.

2. Isochoric cooling stage becomes a null event since it is adiabatic. Q_C = 0.

3. The isothermal compression at T_C stage becomes an adiabatic compression from T_H to T_A absorbing power W_c.

4. The isochoric heating stage from T_C to T_H becomes an isochoric cooling from T_A to T_H.

Are we all in agreement?

Edited January 30, 2023 by sethoflagos

[exchemist]

36 minutes ago, Tom Booth said:

The Carnot limit equation and it's resultant "efficiency", is actually nothing but the temperature difference transmuted by mathematical trickery into a percentage of the absolute temperature scale.

In other words, starting out at ambient, (300°K) we elevate the temperature to,let's say 375°K (slightly superheated steam).

In the process we just elevated the temperature 20% on the absolute temperature scale.

Is it a coincidence that Carnot efficiency at this ∆T is also exactly 20% ?

We raised the temperature 20% on the Kelvin scale and brought the "Carnot efficiency" up exactly the same percentage.

This is true at any and all temperature differences. The "Carnot limit" is IS the temperature difference.

Is this a measure of efficiency?

The best we can do is utilize the heat we put in and in the process bring the heat back down to the 300° ambient baseline.

The only "available heat" for conversion to work is that heat used to create the temperature differential in the first place.

How can a percentage of a temperature scale have anything to do with the actual efficiency of the engine. (It's power to convert "available heat" into "work").

If we convert all the heat we supplied back into work we are just back where we began, at 300°K and "Carnot efficiency" falls to zero.

But we have not violated conservation of energy.

We have not taken out any more than we put in.

But, someone at some point in history misunderstood this basic principle and took the results of the equation to represent a percentage of OUR supplied heat. As if when we elevate the temperature 20% on the absolute scale we can only utilize 20% of the energy we just supplied. The other 80% of the heat captured, stollen, by the imagined "cold reservoir". This is insane.

Some professor teaching thermodynamics made a blunder, maybe 150 years ago and this nonsense has been perpetuated ever since.

Some numbskull who didn't understand that the equation only represented the actual temperature difference, the elevation of temperature on the absolute scale made a blunder.

Carnot "efficiency" is, if anything, just a measure of how far down the absolute temperature scale it is before you end up back where you started before adding heat to go up the absolute temperature scale.

If you went up 20% of the way (on the absolute temperature scale) you can only go back down that same 20% of the way (on the absolute temperature scale).

Use some common sense.

 

And for 150 years, all engine designers have been failing to apply common sense, in your expert opinion, based on some half-arsed experiments you've done with a $200 toy Stirling engine?

Stroll on! 😁 

 

[studiot]

And a happy New Year to you too.

Edited January 30, 2023 by studiot

[Tom Booth]

 

 

2 hours ago, Ghideon said:

If you wish to continue the discussion you may want to focus on the experiments instead.

If this is still something you want to test, adding heating to the cold side may help in this scenario? I get the impression that your idea* allows for two Stirling engines to be mounted cold plate to cold plate to increase the efficiency of both the engines? 

*) If correct that is...

The theory I'm currently entertaining, after 15 years of research and observation (intermittently that is as time and resources permitted, since about 2007) is this:

A Stirling engine, rotating in the same direction in either case acts as either an engine OR a heat pump depending on if it is being driven by heat or by a motor, respectively. (Or both engine and heat pump  simultaneously)

The "ideal" of isothermal expansion and compression is, I think, a generally recognized impossibility. (I can cite numerous sources to thet effect if need be) generally. And,

Isochronic heating and cooling are also impossible, for a number of reasons, at the points of the cycle they are supposed to take place, in a Stirling engine of modern design specifically, for a number of reasons.

For the past 15 years I've been researching how Stirling engines work with the original intention of building one while staying on my land in a remote location beyond power lines or utility services generally.

I did eventually have an underground phone cable extended to the land but for power relied on a generator, wind or solar or "peddle power". None of these sources of electricity proved to be adequate, but I was cooking and heating with a wood stove continually so a heat engine seemed like an attractive alternative. No power producing Stirling engines, however we're available for purchase anywhere at any kind of reasonable price.

And so the necessity of learning how to build one myself was both a matter of circumstance as well as a matter of basic survival.

I don't have time at the moment to elaborate in detail on what I consider how a Stirling engine ACTUALLY operates, but maybe I'll have more time later this evening.

To answer your immediate question though, placing two engines together with their cold sides adjacent one another is an interesting idea. However, many people have a habit of blasting a Stirling engine with more heat than it can handle or easily convert to work output. On top of that, the engines are generally given no actual shaft work to perform, so the engine becomes flooded with heat.

With such an arrangement some careful load balancing would likely be a necessity. But that is also true generally, but with an "infinite" ambient sink, generally not fatal.

 

2 hours ago, exchemist said:

And for 150 years, all engine designers have been failing to apply common sense, in your expert opinion, based on some half-arsed experiments you've done with a $200 toy Stirling engine?

Stroll on! 😁 

 

More like $20

Edited January 30, 2023 by Tom Booth

[Ghideon]

40 minutes ago, Tom Booth said:

To answer your immediate question though, placing two engines together with their cold sides adjacent one another is an interesting idea.

A quick followup; let's assume the engines cold sides are adjacent (in contact) and that they are insulated (for instance using the materials you proposed early in the thread) so cold side is not disturbed by room temperature. What is your opinion* about the overall efficiency of the combination of two engines versus the sum of the two engines running separated from one another? Do your ideas allow for some additional gain since the two adjacent cold sides "help each other", if I understand you correctly.

 

*) According to your ideas

Edited January 30, 2023 by Ghideon
clarification

[Tom Booth]

4 minutes ago, Ghideon said:

A quick followup; let's assume the engines cold sides are adjacent (in contact) and that they are insulated (for instance using the materials you proposed early in the thread) so cold side is not disturbed by room temperature. What is your opinion* about the overall efficiency of the combination of two engines versus the sum of the two engines running separated from one another? Do your ideas allow for some additional gain since the two adjacent cold sides "help each other", if I understand you correctly.

 

*) According to your ideas

Perhaps. Certainly worth experimenting with, IMO.

There is obviously some heat loss to ambient due to the piston (in an open atmosphere, rather than hermetically sealed engine) doing work on the outside air during expansion to displace the atmosphere occupying the cylinder. The "work" to push atmosphere out of the cylinder is transfered to the air outside the engine, but the heat is returned when the atmosphere reclaims that cylinder driving the piston back to it's starting position.

Taking a look at the arrangement of the engine, this work/heat does not influence the cold plate heat exchanger. Not directly anyway, it is "exhausted", above the cold plate.

To have the cold side of both engines adjoined, the power cylinders would need to be relocated, probably to the side, such an arrangement (with the piston off to the side) is not unusual. (Or perhaps rotation could be reversed and the bottom plates adjoined, thinking briefly on that, it might be the best way to go if there isn't some catch).

Thinking about it a bit more, your idea is quite brilliant. My problem running a Stirling engine on ice has been how to isolate the ice from ambient heat. Using a second engine as "insulation" is a brilliant idea. Maybe a CUBE of 6 engines would achieve complete isolation of the "cold hole" (Tesla's term for a heat engines self-generated "sink".)

It solves an additional issue I've grappled with. How to insulate the engine while keeping the power piston exposed to atmosphere.

There may be some minor issue with displacer action due to gravitational pull. A Ringbom displacer arrangement should resolve that easily though.

(Ringbom engines use the engines internal pressure changes to actuate the displacer.)

[sethoflagos]

3 hours ago, sethoflagos said:

6 hours ago, Tom Booth said:

You don't seem to comprehend the actual aim of the experiment 

To completely eliminate all possibility of transfer of any heat from the engine into any sink or "cold reservoir" outside the engine.

Just to clarify, the intent is to make the following changes to the Stirling Cycle.

1. The isothermal expansion stage at T_H stays as is outputting power W_E.

2. Isochoric cooling stage becomes a null event since it is adiabatic. Q_C = 0.

3. The isothermal compression at T_C stage becomes an adiabatic compression from T_H to T_A absorbing power W_c.

4. The isochoric heating stage from T_C to T_H becomes an isochoric cooling from T_A to T_H.

Are we all in agreement?

I do know that you've read this, so I'll take your failure to respond as concurrence. 

[Tom Booth]

21 minutes ago, sethoflagos said:

I do know that you've read this, so I'll take your failure to respond as concurrence. 

If you read my last post, I stated, among other things that isothermal processes are generally recognized as impossible, so no I do not concur, not at all. Sorry.

I'm extremely busy today, but have a moment to say that much. I'll explain in more detail if I have time later this evening, as I've already stated.

I do have I think a graph of the general cycle as I see it. I may get a chance to post or link to before then.

[sethoflagos]

35 minutes ago, Tom Booth said:

If you read my last post, I stated, among other things that isothermal processes are generally recognized as impossible, so no I do not concur, not at all. Sorry.

Fish are pretty isothermal. As is a bucket of iced water. Why are you running scared of the isothermal assumption, Tom? If anything it works to your favour by maximising the efficiency of your machine.

I'm perfectly happy with 'nearly isothermal', or 'not even nearly isothermal' or even 'adiabatic' if you want the lowest possible efficiency. Your choice. But I do insist that you make a choice.

2 hours ago, Tom Booth said:

Isochronic heating and cooling are also impossible, for a number of reasons, at the points of the cycle they are supposed to take place, in a Stirling engine of modern design specifically, for a number of reasons.

It's spelt 'isochoric' and means 'conducted at a constant volume'. I'll only accept 'very nearly isochronic' since it's pretty easy to ensure machinery isn't too elastic. But again, the theoretical ideal works to your advantage. Your choice. But I do insist that you make a choice.

'Isochronic' is something entirely different. 

 

[Tom Booth]

1 hour ago, sethoflagos said:

Fish are pretty isothermal. As is a bucket of iced water. Why are you running scared of the isothermal assumption, Tom? If anything it works to your favour by maximising the efficiency of your machine.

I'm perfectly happy with 'nearly isothermal', or 'not even nearly isothermal' or even 'adiabatic' if you want the lowest possible efficiency. Your choice. But I do insist that you make a choice.

It's spelt 'isochoric' and means 'conducted at a constant volume'. I'll only accept 'very nearly isochronic' since it's pretty easy to ensure machinery isn't too elastic. But again, the theoretical ideal works to your advantage. Your choice. But I do insist that you make a choice.

'Isochronic' is something entirely different. 

 

That was the unfortunate choice of words selected by my phone's over confident and overzealous and lacking in programming for thermodynamic terminogy auto-spell that I'm constantly having to fight with. Isochronic Isochronic I just wrote Isochoric those two times and it changed it each time. If I catch it and change it back it will usually leave it alone but I failed to catch it this time as I was in a hurry, sorry. As I said I'm VERY busy.

[sethoflagos]

12 minutes ago, Tom Booth said:

 As I said I'm VERY busy.

Then I suggest you don't waste your valuable time in composing one of your usual 500+ word rambles.

I summarised your proposed cycle in about 50 words. Your alternative proposed wording should be similarly concise.

Don't link to external sources. Just plain simple wording for all to see.

[Tom Booth]

8 hours ago, sethoflagos said:

Fish are pretty isothermal. As is a bucket of iced water. Why are you running scared of the isothermal assumption, Tom? If anything it works to your favour by maximising the efficiency of your machine.

I'm perfectly happy with 'nearly isothermal', or 'not even nearly isothermal' or even 'adiabatic' if you want the lowest possible efficiency. Your choice. But I do insist that you make a choice.

I'm not "running scared of the isothermal assumption". The term is simply inadequate for describing the processes involved in a real Stirling heat engine operating at speed.

A functioning heat engine is not a "bucket of ice water" or a fish which are certainly appropriate examples of isothermal systems.

By "impossible", I think it should be obvious I mean; as applied to any REAL heat engine. It can of course be applied to a Carnot engine just as it can be applied to the Flintstone mobile.

I'd like to remind you of the topic: "Is Carnot efficiency valid"

My experiment, insulating the cold sink of a Stirling engine, that introduced the thread was not intended to prove the Tom Booth theory, It was intended to prove or demonstrate the Carnot Limit or at least one of the assumptions that  follow from it.

The generally accepted interpretation, apparently universally taught and assumed true of the Carnot Limit equation as that a 20% efficient engine must in the strictest legal sense of an absolute requirement, "reject" at a minimum, the other 80% "waste heat" to the "cold reservoir".

The expected result of the experiment, which was to eliminate or reduce to a minimum, the possibility of such waste heat rejection, was that the waste heat would build up behind the insulation destroying the ∆T, and the engine would be unable to complete a cycle or at least soon cease operating, if able to run at all under such circumstances.

The expected result was not observed.

As flattered as I may be that you are interested in hearing my personal musings regarding possible alternative theories to explain the observed results, I'd like to return to the actual topic of the thread.

How can the Carnot Limit actually be demonstrated or tested experimentally? My simple methodology of insulating the "sink" to prevent heat "rejection" to the "cold reservoir" apparently did not produce conclusive results.

Some suggestions, I think, for improving procedure have been made, so I think the focus should really be on future followup experiments. My own theories are really off topic and irrelevant.

The questions you ask were also asked about a year ago on the Stirling engine forum and my answers are there "for all to see".

Is there something to prevent anyone here from following a link?

Anyway your "choice" of either isothermal or adiabatic is, I think, inadequate. Like asking a Native American to choose between White or Hispanic to describe his nationality.

If you are really interested in my analysis of how a Stirling engine works, does the forum support private messaging? Or perhaps in another thread.

I'd really like to end the derail and get back on topic if you don't mind.

[sethoflagos]

3 hours ago, Tom Booth said:

I'd really like to end the derail and get back on topic if you don't mind.

I remind members of the opening few paragraphs of the OP

On 1/24/2023 at 8:21 PM, Tom Booth said:

I've done nearly everything possible I can think of to block the "flow" of heat out of a Stirling engine, with the idea that if the "heat rejection" could be blocked, the engine would quickly overheat and stop running, or be unable to start running in the first place.

To that end, I recently sent away for a silica Aerogel blanket, which is supposed to be very good at blocking heat. I was able to apply a propane torch to one side and not feel heat through the blanket with my hand on the other side.

I also used a glass globe from a Coleman lantern to block drafts.

As in previous experiments just using styrofoam or house insulation, the engine started and continued running.

This result seems contrary to the "efficiency formula" or "Carnot limit" which, would calculate that some 80% or more of the heat supplied to or entering into the engine would need to be rejected to the sink or cold side back to atmosphere for the engine to continue operating.

Exactly how much of this are we supposed to accept without question?

Given the extraordinary nature of the claims in this OP, I think it quite right and proper that we take a very close look at exactly what it is the OP is trying to do. I note the OP's reluctance for us to do so, and that in itself tells a story.

So what exactly should we expect to happen when we fully decouple a Stirling engine from its cold sink.

Despite the OP's earnest protestations, I'm going to start with the idealised model because that's how it's done. And let's put some numbers in:

Stage 1: Isothermal expansion @ T_H

The power available from isothermal expansion of an ideal gas from compressed volume V_C to expanded volume V_E can be expressed as

                                   W_E = nRT_Hln(V_E/V_C)

where n & R have their normal IGE meanings. To keep matters simple we can assign it the value of 1 kJ over a certain number of cycles. The source of this energy comes entirely from heat input from the hot source hence

                                 Q_E = W_E = 1 kJ

Stage 2: Isochoric cooling

Adiabatic null process by design. See Stage 4.

Stage 3: Adiabatic compression from V_E to V_C

Here we must introduce the ratio of specific heats k (1.40 for air), and can derive:

                           W_C = knRT_H/(k-1).((V_E/V_C)^(k-1) -1) >= knRT_Hln(V_E/V_C) >= kW_E >= 1.4 kJ

The approximation tends to equality as V_E/V_C tends to unity. Since I've introduced inequalities, I'll use absolute values for Q & W to avoid confusion.

Stage 4: Isochoric cooling from T_A to T_H

The balance of energy, heat of compression, is returned non-reversibly to the heat sink at T_H which is now functioning as a cold sink.

                            Q_C = W_C >= 1.4 kJ

Non-ideal behaviour

OP is of course correct in asserting that idealised processes can rarely if ever be fully realised in practice. However, that does not make them intractable. Stage 1 may be allowed to have a reasonable adiabatic element by allocating a k value of say 1.04 rather than the implied default of k=1 for ideal isothermal behaviour. This will have the effect of allowing some expansion cooling below T_H and slightly increase power output on the expansion stroke. Similarly reducing the k value for Stage 3 from 1.4 to say 1.36 will introduce some isothermal behaviour, reducing T_A and slightly reducing the power absorbed by the compression stroke. 

Which leads us to consider whether the machine is truly decoupled from its cold sink, since if it isn't this will reintroduce Stage 2 cooling and drastically reduce the adiabatic nature of Stage 3.  We will return to this.  

Summary

1) While the Stage 3 compression phase is more adiabatic in nature than the Stage 1 expansion phase, the machine would require a significant work input to continue running for more than a couple of cycles. To this extent the OP prelinary assumption is true. 

2) In response to the semi-rhetorical question posed by the OP

On 1/24/2023 at 8:21 PM, Tom Booth said:

So why does the engine not stop from overheating when the cold side is insulated, blocking the flow of heat out of the engine to the "cold reservoir" ?

 It is clear that

On 1/25/2023 at 2:30 AM, sethoflagos said:

You are not reducing the cold side overall heat transfer coefficient as much as you think you are. 

Remains by far the most credible explanation. The OP neglected to respond to this specific comment.

What was the goal of the experiment?

We need look no further than here

On 1/25/2023 at 2:34 PM, 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.

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

Likewise. Insulating the cold side of the engine mimics the condition of having the cold side at a lower temperature. Heat exchange on the cold side is reduced, the same result that would be achieved by reducing the cold side temperature.

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

Throughout this thread, the OP has treated the following statements as logical consequences of each other:

• A 100% efficient heat engine transmits no heat to its 0K cold reservoir.
• A heat engine connected to a 0K cold reservoir is 100% efficient.
• A heat engine transmitting no heat to a cold reservoir is 100% efficient.

By disproving any one of these propositions he imagines he disproves them all. 

[Tom Booth]

You've written a lot there.

As I see it, the formula under question is laughably simplistic and straightforward. A high T a low T.

Supposedly the macrocosmic ∆T reduplicated and applied to the microcosmic temperature difference determines the limit of efficiency.

Example:

When confronted with such apparent mysticism, perhaps I can be forgiven for being a little skeptical.

As far as I know, the above portrayal is not contested. Is that not an accurate representation of how the Carnot limit is arrived at ?

The Macrocosmic ratio on the absolute scale reapplied to the ∆T dividing the temperature difference proportionately ?

Please, if that's not how it's done I'd like to know.

 

As far as your quote following "we look no further than here", I've already explained, that was a Joke. You fell for it way too heavily, hook line and sinker.

By adopting the "Carnot theorem" POV I attempted to show the irrational consequences. How can the seemingly contradictory consequences of having all the heat flow into a 0°K "cold reservoir" at 100% Carnot efficiency be reconciled? It appears to contradict conservation of energy. 100% conversion to work AND 100% "waste heat".

[studiot]

1 hour ago, sethoflagos said:

So what exactly should we expect to happen when we fully decouple a Stirling engine from its cold sink.

I'm quite sure you are quite well aware of the consequences of this decoupling being possible.

It would lead to one of the standard derivations of the second law via a 'self acting machine'

i.e. one that can function as part of a machine with a single bath that acts as both source and sink, whilst at the same time magically outputting work.

This is commonly known as a perpetual motion machine of the second kind.

[sethoflagos]

36 minutes ago, studiot said:

I'm quite sure you are quite well aware of the consequences of this decoupling being possible.

It would lead to one of the standard derivations of the second law via a 'self acting machine'

i.e. one that can function as part of a machine with a single bath that acts as both source and sink, whilst at the same time magically outputting work.

This is commonly known as a perpetual motion machine of the second kind.

I could do with one of those. We've not had mains supply for 48 hours.

Edited January 31, 2023 by sethoflagos
sp

[exchemist]

2 hours ago, Tom Booth said:

You've written a lot there.

As I see it, the formula under question is laughably simplistic and straightforward. A high T a low T.

Supposedly the macrocosmic ∆T reduplicated and applied to the microcosmic temperature difference determines the limit of efficiency.

Example:

When confronted with such apparent mysticism, perhaps I can be forgiven for being a little skeptical.

As far as I know, the above portrayal is not contested. Is that not an accurate representation of how the Carnot limit is arrived at ?

The Macrocosmic ratio on the absolute scale reapplied to the ∆T dividing the temperature difference proportionately ?

Please, if that's not how it's done I'd like to know.

 

As far as your quote following "we look no further than here", I've already explained, that was a Joke. You fell for it way too heavily, hook line and sinker.

By adopting the "Carnot theorem" POV I attempted to show the irrational consequences. How can the seemingly contradictory consequences of having all the heat flow into a 0°K "cold reservoir" at 100% Carnot efficiency be reconciled? It appears to contradict conservation of energy. 100% conversion to work AND 100% "waste heat".

Yes you are quite right. Your diagram represents the Carnot cycle efficiency formula in the the form η=(T_H - T_L) / T_H .  The length of the line from absolute zero to T_H is 100% and, using the temperatures you have chosen, the length of it to T_L is 80%.  That's all it is. 

However what I think some other posters have been trying to do is explain how that very simple formula for the maximum possible efficiency is derived.

That too is fairly simple, but it does require you to understand the gas laws and what an isothermal and an adiabatic process are. The Carnot cycle simply applies these to a fixed amount of gas doing work by expanding against a piston and then being cooled so that it can repeat the cycle and do more work.

So if the gas laws are true, the Carnot efficiency formula is true.

More detail here: 

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/carnot.html

Edited January 31, 2023 by exchemist