The Reversible engine

[Tom Booth]

A really efficient engine is a "reversible" engine.

I was reading recently, something about reversible steam engines on trains. This is actually just a valve system that allows a steam engine to operate in reverse, so as to back up a train when necessary.

It got me to wondering if in the early days of the formation of thermodynamics if this "reversibility" of certain steam engines had any influence, by way of a misunderstanding or something in the development of the concept of a "reversible" heat engine.

Kelvin or somebody reading an engineering manual about reversible steam engines had an "aha!" moment.

Anyway, here is the first description I came across for a thermodynamically "reversible" engine:

Carnot assumed that an ideal engine, converting the maximum amount of thermal energy into ordered energy, would be a frictionless engine.

It would also be a reversible engine.

By itself, heat always flows from an object of higher temperature to an object with lower temperature. A reversible engine is an engine in which the heat transfer can change direction, if the temperature of one of the objects is changed by a tiny (infinitesimal) amount.

When a reversible engine causes heat to flow into a system, it flows as the result of infinitesimally small temperature differences, or because there is an infinitesimal amount of work done on the system.

If such a process could be actually realized, it would be characterized by a continuous state of equilibrium (i.e. no pressure or temperature differentials) and would occur at a rate so slow as to require an infinite time

http://labman.phys.utk.edu/phys221core/ ... d_law.html

My first question is; is this really something that actually originated with Carnot himself?

The old fathers of thermodynamics seems to have had a habit of attributing things, like the "efficiency limit" to Carnot, though it is based on the Kelvin temperature scale which wasn't around in Carnot's day, but he somehow has to take the blame.

As a simple mechanic wanting to build the best Stirling/hot air engine possible, do I really need to know about or understand this "reversibility"?

How exactly can a heat engine, or any engine for that matter be "efficient" when quite obviously it has no chance whatsoever of operating at all with no temperature or pressure differential?

[Fool]

A reversible engine is, by definition, a perfectly efficient engine. Meaning if reversed 100% of the heat can be put back onto the hot mass/source using 100% of the work that came out. There are two perfectly reversible processes that I know, adiabatic and isothermal. There may be others.

I think Carnot calls his "thought" engine reversible, and mentions how it is so. I have no clue if he'd heard that before or coined it himself. I don't think it came from the steam locomotives. They were in their infancy right around 1801. The modern reverser gears came out as early as 1841. After Carnot had passed. Carnot may have not have studied a locomotive. I don't know but think it was those that came after Carnot, Clausius for one, that are responsible for those definitions. Forward and reverse concepts were invented long before those dates.

As a mechanic, and as my brother used to say, "What does 'need' have to do with anything?" If we are ignorant, what we could have learned will in no way be used to help. You probably can go on happily building Stirling Engines with zero thermodynamic knowledge. Happiness doesn't depend on success. Phillips engineers used impressive engineering talent and schooling to build impressive engines, that to this day, few have equaled. Copying them and using their theories would, IMHO, be a good starting point. Wright Brothers method, learn what others have done, do very careful, extensive, and, rigorous scientific research, build, test. Random guessing will probably take a longer and more expensive route.

The quote isn't indicating a total of zero temperature or pressure change. It is adding more and more up as the pie is cut into smaller slices, you still get a whole pie.

Adding infinite infinitesimals (limit to zero size and infinite slices) is the definition of calculus. It needs to be explained in a proper mathematics lecture. It leads to "derivatives" d/dx and "integrals" area under a curve and opposite of a derivative. It starts by adding up small amounts and as the slice size is halfed, the number added up is doubled. (1/100)•100=1 up to (1/infinity)•infinity=1. Students laughed at the math teacher when something similar was put on the board. Kind of a "duh, so what?" Moment. To which the instructor said something like "It probably seemed very trivial, at their time too, when the mathematicians looking at Egyptian Pyramids were inventing the field of calculus.". Calculus is a very useful tool in engineering.

I hope this helps in understanding that learning is difficult and painful, but what we are forced to learn is, at times, very useful. Often it is forgotten before a use is realized.

I just relate back to why do we need to learn phonics? I now use it often. My all-time most used child game skills come from the ludicrously simple game Pickup Sticks. I live on a farm with a great deal of winter yard and forest litter, which gets piled up, moved to new piles, and eventually a bon fire. To bad I didn't burn that game when I was younger, it would have provided great realism, LOL. I don't need to know thermodynamics or chemistry to eliminate yard debris in a bon fire, but it helps. At the very least I'm able to ponder incredible thoughts including Stirling Engine design. Learning is painful, but using that knowledge to think is fun. As Feynman said, it's additive beauty.

[Tom Booth]

A reversible engine is, by definition, a perfectly efficient engine. Meaning if reversed 100% of the heat can be put back onto the hot mass/source using 100% of the work that came out. There are two perfectly reversible processes that I know, adiabatic and isothermal. There may be others.

An adiabatic expansion or contraction CAN be, or COULD sometimes be "reversible" but "reversible" is not part of the definition of adiabatic. It's a subset.

If you have heat going in and actual external shaft work going out that is not "reversible" but can still be mostly adiabatic if the heat input is isochoric (at or near TDC in and engine).

The general term adiabatic is not restricted to adiabatic-isentropic that is a narrow subset of adiabatic.

[Tom Booth]

(...)

The quote isn't indicating a total of zero temperature or pressure change. It is adding more and more up as the pie is cut into smaller slices, you still get a whole pie.

Not really. I'll explain why.

Adding infinite infinitesimals (limit to zero size and infinite slices) is the definition of calculus. It needs to be explained in a proper mathematics lecture. It leads to "derivatives" d/dx and "integrals" area under a curve and opposite of a derivative. It starts by adding up small amounts and as the slice size is halfed, the number added up is doubled. (1/100)•100=1 up to (1/infinity)•infinity=1.
(...)

The problem with this type of slicing up into "infinite" segments is it is easy to ignore or neglect some very real phenomena that actually exist in the real world, between the slices so to speak.

When you cut up a gradient or continuous curved line into "infinite" flat segments to simplify your calculations something fundamental and real has been discarded. The actual slope.

To illustrate.

Suppose I'm pushing a car that has stalled up a slope.

If I divide that slope into perfectly flat segments what happens?

I'm now pushing the car without effort.

What is "in between" the segments is a step.

The more the slope is segmented the smaller each step until at infinity (mathematically) the slop vanishes, but this is not reality.

In the real world slopes, gradients exist and represent real physical forces.

Calculus can sometimes erase or neglect to take into consideration what is "between" each segment and therefore paints a false picture of reality.

This is how and why many of these "ideal" mathematical models are flawed. The calculus has vanished some of the actual forces involved by ironing out the slope

[Tom Booth]

This has an impact when trying to analyze real engine operation on the basis of "ideal" "quasi-static" processes.

Take this series of video tutorials for example:

https://youtu.be/obeGVTOZyfE

https://youtu.be/M5uOIy-JTmo

Now, in the video, the narrator does not entirely neglect to mention that there is actually a difference between this "quasi-static" expansion and real expansion, like there will be a decrease in pressure when the gas does work to push the piston up after a "pebble is removed"...

He dismissed this or brushes the fact aside as inconsequential as if the issue can be resolved by using smaller and smaller slices. But there are several very real forces and phenomenon being completely neglected or overlooked when using this mathematical "quasi-static" trick.

How does this differ from real expansion work in a real engine.

First of all a real engine does not have someone to remove pebbles.

The engine has to actually lift all the pebbles all by itself all the way up.

Also, what do the pebbles actually represent?

Atmospheric pressure.

You can't incrementally remove atmospheric pressure so the actual work the engine is performing is not just being grossly underestimated, actual external work is being ignored completely.

The consequence of all this is that the actual temperature and pressure drop due to work output for each incremental change is being discounted because it is "between the slices".

In reality, after each incremental change, the gas doing work, expands and the pressure drops and the gas temperature drops and in reality, the pebbles that were never actually removed (atmospheric pressure) would weight the piston right back down again.

If you add up all these incremental changes, neglecting to take into consideration the actual dynamics involved ACTUAL work output, actual pressure drop actual temperature drop your PV diagram fails to actually represent reality.

You end up with the piston at BDC out on the right hand side of the graph and imagine it is going to require additional work to push it back to TDC.

In reality at TDC heat is converted to pressure to momentum/velocity to work and there is, as a result of this EXPLOSIVE expansion REAL mechanical work output that results in real very sudden cooling and pressure drop that leaves a vacuum and the piston is returned as a result.

In reality nobody is "removing rocks" doing the actual work of lifting the rocks, the engine must do that work.

In reality atmospheric pressure and internal engine pressure are not equal as assumed in a "quasi-static" process.

If we equate atmospheric pressure with gravity as the "opposing force" rather than "pebbles", taking my example of pushing a stalled car up a hill.

On a flat plane (quasi-static) after I push my car a certain distance it stops and I have to push it back to return it to the starting point.

On a real slope, when I stop pushing the car up the hill it will roll back down "all by itself" because the opposing force was never actually removed.

The car rolls back down due to gravity. The piston returns in a real engine due to atmospheric pressure. The opposing force is always present. In the real world nobody removes pebbles to expand the gas in an engine then has to put the pebbles back to compress the gas.

[Tom Booth]

A reversible engine is, by definition, a perfectly efficient engine. Meaning if reversed 100% of the heat can be put back onto the hot mass/source using 100% of the work that came out.

(...)

Well, I guess this is actually true!

Zero work out.

Zero is 100% of zero that's for sure.

[Tom Booth]

I've been doing some research to answer the question; is 100% of zero really 100% opinions differ, but I found this which I thought was numerous.

This percentage can be represented on a pie chart for visualization. Let us suppose that the whole pie chart represents the 0 value. Now, we find 100 percent of 0, which is 0. The area occupied by the 0 value will represent the 100 percent of the total 0 value. The remaining region of the pie chart will represent 0 percent of the total 0 value. The 100% of 0 will cover the whole pie chart as 0 is the total value.


https://www.storyofmathematics.com/perc ... cent-of-0/

[Tom Booth]

I meant humorous LOL.

[Tom Booth]

I kind of thought that this post where I'm trying to pretty much demolish calculus as it is currently being applied to engine cycles something of a masterpiece, but was really expecting some kind of comeback or rebuttal of some sort.

viewtopic.php?f=1&t=5554&p=19990#p19960

Surely, the calculus used for the past century or more to analyze engine cycles cannot be wrong or so easily refuted by this mathematically challenged, uneducated, likely insane grease monkey.

I'm disappointed.

Can't anyone here find the flaw in my reasoning? Tell me that I'm overlooking something and that somewhere in the math the cooling and pressure drop from expansion work has actually been accounted for in some way.

And if not, If my analysis IS correct, what happens when this missing expansion cooling is added into the equation?

My calculus isn't a little rusty or anything, just mostly non-existent, so maybe someone who is up on this kind of mathematical analysis could comment.

Have you all given up on me?

Certainly my comment is not iron clad and irrefutable.

I know learning a lesson hurts real bad, but I don't mind, I can take it. I've been wrong before.

Anybody? Or should we consider this case closed.

[matt brown]

My calculus isn't a little rusty or anything, just mostly non-existent, so maybe someone who is up on this kind of mathematical analysis could comment.

Have you all given up on me?

Certainly my comment is not iron clad and irrefutable.

I know learning a lesson hurts real bad, but I don't mind, I can take it. I've been wrong before.

Anybody? Or should we consider this case closed.

The narrator in that video is Khan himself. Overall, I'd rate it as C+ which is OK for beginners, but poses problems. The work area under the "curve" should be accurate, but there's other ways to verify this area. He's just using a PV plot akin xy plot per common schooling (as he points out). I have a "work" plot buried somewhere on my computer where I reduce work to equal squares (T vs V) which is amusing, but haven't been able to locate this bugger.

The main problem with this presentation is that Khan is pitching isobaric work segments without explaining any means of arriving at each pressure. I only watched the second video, so I need to watch the first video.

The simplest manual way to verify the work area of any PV is with this toy

https://www.youtube.com/watch?v=jMvEOmpy8Kw

And I still have mine from my sailboat design days when this was a standard tool, but the legacy designers (think British Admiralty and such) relied on "Simpson's Rule" which used subdivision. Thermodynamics is so loaded with proportions that there's various ways to verify any of these common areas.

[Tom Booth]

Interesting device, but it does not account for simultaneous heat input and work output.

If we run a planimeter around the rim of an overflowing bathtub it can give you the fixed area but knows nothing about the real input and output.

[Tom Booth]

You see the problem is thermodynamics was confessedly (see Kelvin's admission previously cited) based on Caloric theory.

Let's start with a water wheel with buckets that are hanging upright.

The wheel would not complete a revolution because the buckets would still be full on the way back up. Some primitive water weeks have a stop of some sort to tip the bucket and let the water out (analogy of a "cold sink" letting out heat).

With the water tipped out you can then calculate the potential work output by measuring the diameter, distance of travel, height of the fall.

This does not account for water 'evaporating" into thin air on the way down. ( Analogy for Heat converted into work).

If the water wheel were big enough and the ambient air hot and dry enough there would be no need to tip out any water, it would all evaporate.

In a real engine heat "evaporates".

[Fool]

We've pretty much given up on you. Wink. I have an evil gene in me that gets triggered when someone says something so counter to what I've learned that I figure there is no answer capable of them understanding. When that happens I stop communicating. Do not confuse lack of response with correctness of one's own position.

Example: A friend countered one of my discussions with the statement "How do you use less soap." The context was such that he was claiming impossibility if said point.

The endless ways I can think of to use less hand soap, came to mind when I realized the poor understanding of his viewpoint suddenly lead me to think there was no way of reaching him. He would fail to understand any of those easy methods. So I went silent. I think his mindset was such that he could only use the perfect amount of hand soap and it was the same amount everytime he washed his hands. Go figure!

He gloated saying, " Hah. I finally got you.". I remained silent. I never did tell him his mistake. I regret that but, realize it probably was the only solution to the situation.

Here I can be silent for quite a while as I try to fathom another posters views an motivations

Calculus can be thought of as two techniques. One part is the derivative. A second is the integral. They are opposites, similar to multiplication and division. Take the derivative of an equation, you get a second equation. Take the integral of the second equation an you end up back with the first equation.

Integrals tend to make the hills smoother. Derivatives tend to make them larger. Both of them are perfect representations of the original equation, bumps and all. Nothing gets lost.

A derivative is the slope of the equation at any point, all bumps acknowledged. The integral is a summation of the area under the path and all waves are perfectly added. The path is most important.

It is possible to do either numerically on measured data. Your denunciation of calculus is, at best, humorous as it is completely opposite to what calculus can provide. At worst it is a sad plea to argue for the sake of arguing.

Remember a Fool never argues, he just explains why she or he is correct, no matter how much it hurts.

I hope I haven't hurt anybody, especially you Tom. I hope it is entertaining and knowledgeable. I hope I'm not fooling myself into the idea you might learn and understand this stuff and not just being a devils avocate. I don't mind defending my points if the other person is sincere.

[matt brown]

Surely, the calculus used for the past century or more to analyze engine cycles cannot be wrong or so easily refuted by this mathematically challenged, uneducated, likely insane grease monkey.

If you're mathematically challenged then thermodynamics is a poor choice of hobbies. Many engineers admit that this was the hardest part of their studies (and many admit that they still don't "get it").

My calculus isn't a little rusty or anything, just mostly non-existent, so maybe someone who is up on this kind of mathematical analysis could comment.

Learning thermo doesn't require calculus, but it helps. It's mainly only good for some calculations, but there's usually other ways to get around this. However, learning thermo does require a weird mathematical mindset where the ability to creatively "count" is paramount (the Kelvin scale is an xlnt example).

[Tom Booth]

The basic, fundamental issue is, or has, I think, been narrowed down to this:

How does the piston return to TDC after an expansion stroke so as to complete a cycle?

The theory and the math for the past 200 years has been assumed to show that completion of a cycle is "impossible" without heat "rejection" to a "cold reservoir".

If a piston could return, all the way back to TDC without heat being rejected to the sink during the return stroke of the cycle, this would be contrary to the Carnot limit and the Second Law of thermodynamics, or so I've been repeatedly told, and so it says in thermodynamics textbooks, online tutorials and lectures etc.

Historically there are actually a number of scientists who contested these conclusions, and there arguments make a lot of sense, Tesla being one.

The ramifications are potentially enormous.

There are several observations that indicate the "accepted theories" are false.

Perhaps first and foremost the return stroke is, or can be extremely rapid. No significant heat transfers in or out of the engine are possible within such an extremely brief timeframe.

If you heat up a cold Stirling engine it often takes several minutes to heat up. Often the piston can be seen gradually moving in the cylinder as the gas inside slowly heats up and expands. Say it takes 30 seconds for the gas to expand and push the piston out. That is the speed at which heat can be conducted into or out of the engine.

Logically conducting heat back out of the engine to a "sink" should take just as long. No engine actually operates by an extremely slow isothermal (involving conduction through the engine to an external sink) expansion and contraction. This is a widely recognized fact.

Add to these basic facts my own experiments and observations, insulating the sink and so forth and the supposedly "established science" looks to be on pretty shaky ground.

Add to that the fact, as far as I've been able to discover, that there has NEVER been any rigorous experimental proof of the Carnot limit.

A scientific principle is established by experiment not decree, and as far as I can see the second law is nothing more than that. A decree or assertion with zero proof.

It can't be disproven, because there is no such thing as a Carnot engine. How could anyone ever prove experimentally that a Carnot engine is the most efficient engine possible? A "reversible" engine?

There's no such thing.