DaveC426913
Valued Senior Member
No, just encourages them into more fruitful avenues.
Origin and verification of e=(Th-Tc)/Th
- Thread starter Tom Booth
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Tom Booth
Registered Senior Member
If you would like to make that case i.e. "Carnot cycle efficiency limit is a direct consequence of the Gas Laws."
Please do. We can pursue that road as well if you like.
Tom Booth
Registered Senior Member
Have we not just established that the second law, or one version of it anyway, informed and guided the mathematics from which the Carnot Limit equation sprang?
As such is it not also simply another version, restatement of the second law as applied to one specific area of concern: heat engines?
Tom Booth
Registered Senior Member
As a matter of fact, I believe I can show that the ideal gas law predicts the experimental outcomes I have observed, and incidentally, recorded on video posted to my YouTube channel.
At any rate, how can it be that "objective" observers can simply dismiss empirical evidence off hand? Not only dismiss offhand, but outright bar from any consideration?
At any rate, how can it be that "objective" observers can simply dismiss empirical evidence off hand? Not only dismiss offhand, but outright bar from any consideration?
exchemist
Valued Senior Member
Well yes but that’s not circular, surely? The Carnot cycle, i.e. the most efficient though impractical, engine it is possible to imagine, came first. That gave Clausius , Kelvin and others the idea from which the 2nd Law was formulated. And then, using the equation we have been talking about, the formula for the efficiency of the Carnot cycle was derived. That is linear development, not circular, surely?
exchemist
Valued Senior Member
The advantage of laws in physics is they predict outcomes of experiments. Outcomes that violate well established laws rightly demand special care to demonstrate the effect is real, as experience shows it is highly likely to be some artifact and not a real result.
In your case, perpetual motion cranks are two a penny on the internet. We are not morally obliged to stop and listen carefully to every nutter on a street corner, just in case he’s right and the end of the world really is nigh. So we are not obliged to waste a lot of time on whatever contraption you have knocked together in your garage. You have to do the work to get the attention of a justifiably sceptical science community. And you will struggle. But we’ve rehearsed these speeches many times now.
I’m always happy to delve into the history of thermodynamics with you, because I get something out of it. Just don’t demand that I listen to claims that you can beat Carnot efficiency with some home-made gizmo, when all the designers of engines and power plants in the world have strained for over a hundred years to get anywhere close. Because that is delusional.
exchemist
Valued Senior Member
For Tom Booth , further to this post I have just read the following in the Wiki entry on Sadi Carnot:
QUOTE
Carnot understood that his idealized engine would have the maximum possible thermal efficiency given the temperatures of the two reservoirs, but he did not calculate the value of that efficiency because of the ambiguities associated with the various temperature scales used by scientists at the time:
UNQUOTE
So the sequence was indeed as I outlined: Carnot cycle (qualitative) -> 2nd Law -> quantitative equation for Carnot cycle efficiency.
Tom Booth
Registered Senior Member
Moving on to "part B" of my question:
Do you agree with the above? Would you consider that a valid experimental approach or not?
Specifically: "This same result can be gained by measuring the waste heat of the engine".
Tom Booth
Registered Senior Member
The way I figure it, we cannot measure the output of a Carnot engine for comparison, as in reality there is no such thing .
The "efficiency limit formula" however, does provide us with the theoretical MINIMUM waste heat we should expect from any real engine. At least as much or more than what the formula predicts for the hypothetical Carnot engine.
Are you aware of any such experiment, or any comparable experi.ent having ever been performed so as to actually prove the validity of the formula?
The "efficiency limit formula" however, does provide us with the theoretical MINIMUM waste heat we should expect from any real engine. At least as much or more than what the formula predicts for the hypothetical Carnot engine.
Are you aware of any such experiment, or any comparable experi.ent having ever been performed so as to actually prove the validity of the formula?
exchemist
Valued Senior Member
Certainly.
However, calorimetry is notoriously difficult to do accurately. It is generally a lot easier to measure the work output, e.g. via a dynamo, than the waste heat. This is especially true of engines in which waste heat is carried away by more than one route, e.g. exhaust heat, radiator cooling etc.
exchemist
Valued Senior Member
Yes, but an amateur is highly likely to fail to capture all the waste heat emitted. He may then fool himself into thinking his machine is more efficient than it really is. It is probably prudent to measure the work output as well, to mitigate errors of this kind.
exchemist
Valued Senior Member
I see you have added a final line. I will not reply to that, as I did so at length when you asked the same thing on the other forum. So you know the answer. I will just observe that no experiment can ever prove a theory. So proof is the wrong word.
Tom Booth
Registered Senior Member
Can you provide a link to your definitive response about some such past experiments because I don't recall, and frankly don't believe you ever provided any.
At any rate, proving that a Carnot engine is "the most efficient engine" via comparative work output is an impossibility.
I could say Santa at the North Pole showed me the backup engine for his sleigh for when the Reindeer get pooped out and it certainly exceeded the Carnot engine in efficiency.
Proving or simply approximating any claim regarding the mythological Carnot engine is unfalsifiable, just like the backup engine in Santa's sleigh.
Until someone actually does some better experiments, the ones I've performed so far measuring waste heat output are the standard of excellence. The best that has been attempted so far and the results stand. No "waste heat" output whatsoever from your typical off the shelf model Stirling engine. Not through the working fluid.
Measuring heat that has been converted to "other forms of energy" (other than "waste heat") is an impossibly complicated proposition. You have vibration, clattering nose, radiation back out the hot end, friction at various points, bearings connecting rods, air resistance on a spinning flywheel, etc. etc.
I've done nearly all I can possibly do with my limited resources.
So far every test, every experiment has failed to come anywhere near to validating the Carnot Limit predictions. Which in most cases would be 5 times more "waste heat" emanating from the sink than being utilized to power the engine.
What do we find? Nothing at all!
Zero "waste heat".
Infact, my instrument readings have, at times indicated a degree or two of cooling, below the ambient surroundings.
Thermal imaging camera readings, recorded on video.
What seems delusional to me is the unwillingness to make critical observation of the reality that's right in front of your face.
Of course, you are under no obligation to pay any mind whatsoever to whatever I may be doing. Frankly I've reported your posts, as you know as off topic.
Who can keep you away?
You have no time for reasoned consideration of actual empirical evidence, but all the free time in the world, apparently, to sit in judgement and throw darts and ridicule for another's efforts while you do what exactly?
Anyway, thanks again for the references. I've learned a few things, but since you've reverted back to your original name calling tactics, and there is no getting you to just go away, I don't see much chance of making any further progress here.
exchemist
Valued Senior Member
At least I have made the effort to engage with your reasonable questions and have done some digging to help find where these formulae originated, so you are further on than you were. Nobody else here has commented at all.
I can't help but notice it is when I point out a likely source of error in your experimental approach that, instead of addressing the point, you snap back into a pose of victimhood and try to deploy the Galileo Gambit. All part of keeping your dream alive, I suppose.
You can wait and see if anyone else offers a comment, of course.
If you come back with any more questions on the history of thermodynamics I'll be happy to try to help out, as I have in the past.
See you in a few years, then. Maybe.
Tom Booth
Registered Senior Member
Again thanks.
I'm still not satisfied with the "history" behind the origin of the Carnot Limit equation which. Seems merky at best.
At face value, of course, it is a simple ratio, based squarely on Caloric theory and Carnot's heat as a waterfall supposition represented mathematically.
In reality, I have no issue with the mathematics. It's more the origin of the current academic interpretation and the rationale behind it.
OK, so, the "distance" on the absolute temperature scale between T(cold) and T(hot) is 20% of the distance between T(hot) and absolute zero. So what?
What physical control could that possibly have so as to influencing how the joules of heat supplied to an engine above T(cold) are actually utilized by tbe engine? Why should that in any way limit, say, 10,000 joules of available heat to just 2,000 able to be convertible to work and 8,000 minimum joules that must be tossed out as "waste heat".
A more sensible interpretation is that 20% of "all the heat" is what has been supplied, above and beyond the "background energy" or "heat" present all around in the ambient surroundings as well as the given internal energy of the working fluid prior to any additional heat being supplied.
The 20% then would represent ALL 10,000 joules actually supplied above T(cold) or the given ambient.
You can only get back what you put in, in perfect accord with conservation of energy.
Identical math, just interpreted with some ordinary common sense.
Of course you can't get back more than the 10,000 joules you actually supplied above the ambient "background".
That also harmonizes with my experimental results. Stirling engines are known to be theoretically equivalent in efficiency with the Carnot engine. That then would be complete utilization of the supplied heat. No contradiction there.
What justifies this slash and burn of 80% of the supplied heat?
A mathematical ratio is just a mathematical ratio. It either represents 20% (all the heat supplied above T(cold) on a scale from T(hot) down to absolute zero or 20% (20% of the heat supplied above T(cold).)
I see no theoretical basis for or empirical justification for the latter interpretation.
Who first decided the 20% should represent only 20% of the heat supplied and not what it actually is; 20% of the thermometer reading between T(hot) and absolute zero.
Even the rhetoric indicates the correct interpretation is the later
"for 100% efficiency, you would need the sink to be at absolute zero".
That only makes sense if the 20% "efficiency" represents 20% of ALL the "heat" or all the internal energy of the working fluid all the way down to absolute zero NOT 20% of the 20% of the heat actually supplied above T(cold).
20% of 20% is applying the ratio twice. First taking 20% of "all the heat" down to absolute zero, then carving that up into 20% heat we can convert and throwing out the other 80%
IMO someone at sometime just fudged the interpretation of the math because they didn't like the implications if applied to running a heat engine on ice.
In that case, an engine with an efficiency equivalent to the Carnot engine could, (running on ice), theoretically have available to it all the heat in the ambient surroundings above T(cold). The temperature of the ice, and no "waste heat" would be left over to accelerate the degradation of the thermal sink.
Exactly Nikola Tesla's proposition: Unlimited "free energy" from the surrounding ambient environment.
So far my experiments have not been able to prove Tesla wrong. On the contrary, the indications are he was right.
Tom Booth
Registered Senior Member
BTW, if it isn't obvious, the above is based on a situation where T(hot) = 300°K and T(cold) = 375°K
Or experimental conditions where ambient is 300°K and the heat source is at a temperature of approximately 375°K
That is, a model Stirling engine, for example, running over boiling water as the heat source.
Carnot efficiency in that circumstance is calculated to be 20%
From 375°K moving downward to 300°K the temperature difference is 20% of the temperature scale, 80% is the remaining distance if we continue downward until we reach absolute zero.
Another question that crosses my mind, if Clausius and Kelvin were, as you say, still working with the Celsius scale and the Kelvin scale was yet on the horizon, then the Clausius inequality would still be prior to the current "Carnot Limit" formula using the Kelvin scale.
Or experimental conditions where ambient is 300°K and the heat source is at a temperature of approximately 375°K
That is, a model Stirling engine, for example, running over boiling water as the heat source.
Carnot efficiency in that circumstance is calculated to be 20%
From 375°K moving downward to 300°K the temperature difference is 20% of the temperature scale, 80% is the remaining distance if we continue downward until we reach absolute zero.
Another question that crosses my mind, if Clausius and Kelvin were, as you say, still working with the Celsius scale and the Kelvin scale was yet on the horizon, then the Clausius inequality would still be prior to the current "Carnot Limit" formula using the Kelvin scale.
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Tom Booth
Registered Senior Member
BTW,
What is your take on this discussion:
physics.stackexchange.com
Do you agree with these statements by one of the contributors there?:
"A reversible isothermal expansion process can be 100% efficient. That does not violate the second law. It’s the efficiency of a cycle that can’t be 100%.
"So, yes, if you had a one cylinder car performing a reversible isothermal expansion you could theoretically continue converting heat to work as long as the cylinder (and car containing it) keep expanding forever (they become infinitely large).
"But even more importantly, since PV=PV= constant, as the volume increases the pressure, and thus the force exerted by gas, decreases."
What is your take on this discussion:
Does isothermal expansion not beat the efficiency of Carnot Heat Engine?
Ques: If I just take the 1st step of a Carnot Heat Engine (CHE) than it turns out to be more efficient than the CHE itself. Explanation: The 1st step of a CHE is the pure isothermal expansion of (i...
physics.stackexchange.com
Do you agree with these statements by one of the contributors there?:
"A reversible isothermal expansion process can be 100% efficient. That does not violate the second law. It’s the efficiency of a cycle that can’t be 100%.
"So, yes, if you had a one cylinder car performing a reversible isothermal expansion you could theoretically continue converting heat to work as long as the cylinder (and car containing it) keep expanding forever (they become infinitely large).
"But even more importantly, since PV=PV= constant, as the volume increases the pressure, and thus the force exerted by gas, decreases."
exchemist
Valued Senior Member
What's the point of this crap, Tom?BTW,
What is your take on this discussion:
Does isothermal expansion not beat the efficiency of Carnot Heat Engine?
Ques: If I just take the 1st step of a Carnot Heat Engine (CHE) than it turns out to be more efficient than the CHE itself. Explanation: The 1st step of a CHE is the pure isothermal expansion of (i...
Do you agree with these statements by one of the contributors there?:
"A reversible isothermal expansion process can be 100% efficient. That does not violate the second law. It’s the efficiency of a cycle that can’t be 100%.
"So, yes, if you had a one cylinder car performing a reversible isothermal expansion you could theoretically continue converting heat to work as long as the cylinder (and car containing it) keep expanding forever (they become infinitely large).
"But even more importantly, since PV=PV= constant, as the volume increases the pressure, and thus the force exerted by gas, decreases."
Yeah, if you have a quasi-static (i.e. infinitely slow), one-way isothermal expansion, you can go on extracting work until the gas pressure asymptotically approaches zero.
But it is not a cycle, so it tells you nothing about any heat engine. The Carnot cycle involves such an isothermal expansion in its first stage, followed by an adiabatic expansion after disconnection from the heat source. That's the good news. The bad news is that you then need to cool the gas again, so that the process can be repeated, which is where a heat sink is required.
If you can't repeat the process you don't have an engine, obviously.
exchemist
Valued Senior Member
How are you measuring the heat input and the work output to calculate the efficiency?
Tom Booth
Registered Senior Member
The point is, the "Law" only applies to cycles, though it is recognized that heat can indeed be converted into work 100% in a "process", such as expanding gas in a cylinder to drive a piston.
The further out the piston is driven the more the pressure drops, as you point out: "until the gas pressure asymptotically approaches zero."
A Stirling engine operates by heating and expanding a gas which raises the internal pressure relative to the external (atmospheric) pressure. The engine ( in the real world) is not operating in a vacuum.
So what happens when the gas does work drives out the piston to let's say double the volume.
Before adding heat to the working fluid the internal and external pressure were in equilibrium. As the gas expands and the heat is converted to work (100%) the internal pressure falls.
According to the ideal gas law, at double the volume, the pressure will be halved (in an isothermal process) so we end up with 0.5 atmosphere internal pressure as the engines piston approaches "bottom dead center" or the full extent of it's expansion stroke.
But at about 3/4 into the expansion, in a Stirling engine the heat input is cut off so the final portion of the stroke is completed without heat input. Momentum carries the piston the final distance. What happens to the pressure and temperature as the gas continues to expand and do additional work adiabatically?
The pressure already dropped down to 0.5 atmospheres.
Additional expansion and adiabatic cooling aside, what volume do we have to return the gas to in order to restore the internal pressure so that it is balanced by the external pressure of 1 atmosphere?
According to the ideal gas law, the volume would need to be reduced to 1/2.
At some point during expansion the external atmospheric pressure is going to overwhelm the falling internal pressure, and with the heat input having been cut off what will happen when the piston reaches bottom dead center?
Atmospheric pressure will drive the piston back, will it not?
In an internal combustion engine we need a flywheel to carry the engine through the compression stroke, but in a Stirling engine this is not necessary. The piston returns by atmospheric pressure.
So, if all the heat has already been utilized during the expansion stroke with 100% efficiency, and the cycle completes by external atmospheric pressure, returning the system to equilibrium or its starting condition, then how is it possible for the "Carnot Limit" to be valid which says the conversion efficiency is limited to say 25 maybe 30% or whatever.
The heat was already fully utilized 100% during the expansion stroke and from there the cycle is competed by atmospheric pressure.
How do we retroactively deduct 75% of the heat input reserved for the "cold reservoir" when it is already gone?
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