The Carnot efficiency problem

[Tom Booth]

...

Isothermal is an ideal mathematical construct that is used to show maximum conversion percentage.
....

Maybe you could provide some reference to support this.

Isothermal simply means constant temperature. You say it is to show "maximum conversion percentage".

Maximum conversion of what? Heat? Internal energy? Converted to what work?

It is possible, (theoretically that is, since isothermal process is not actually possible or practical in a real engine) to have an isothermal process with any amount of work output, including zero "useful" work. You could have 100% of the heat introduced escaping to a water jacket with 0% work or anything in between. " Isothermal" says nothing whatsoever regarding the percentage of heat converted to work. Ice melting to form a puddle is isothermal.

Other paths will convert heat to less work.

An adiabatic process is the lowest path and it's reversible. Zero heat is converted to work.

One quantity of internal energy is thermal energy....

Neither isothermal nor adiabatic says anything specific about work output.

All the heat (thermal energy) transfered into the working fluid becomes "internal energy" If the "internal energy" then goes out as work there is a drop in temperature.

Are you really trying to argue that no "heat" has been converted to work in the process ?

You can have 100% conversion of "heat" (internal thermal energy) into work in an adiabatic expansion, you just have to add the "heat" in an isochronic process or otherwise, such as in a previous adiabatic compression (conversion of work into heat). True there is not a direct conversion of heat into work.

And who says that expansion and compression have to follow the same adiabatic path?

You can have adiabatic expansion at a high temperature with work output lowering the temperature followed by adiabatic compression at a lower temperature with work input raising the temperature. Which appears to be what actually takes place in a real engine. Supplied heat (isochronic or prior adiabatic compression) effecting the expansion with work output and a drop in temperature, followed by contraction of the colder gas with some work supplied by atmospheric pressure effecting "compression".

That probably looks something like this:

viewtopic.php?f=1&t=5534

[Tom Booth]

Resize_20230522_031849_9086.jpg (175.66 KiB) Viewed 7597 times

What is most interesting is the continued drop in temperature during "compression".

I would hesitate to assume that this is due to heat "rejection" to the sink only.

It seems theoretically plausible to me that an elastic fluid could do "work" while contracting just like a rubber band or spring can do work after being stretched.

Not possible for an "ideal gas" but real gasses have actual molecular attraction. Water vapor condenses into droplets etc.

If, experimentally, heat "rejection" to the sink is eliminated or ruled out, what would be the explanation for a temperature drop during compression?

[Tom Booth]

Another problem, at least it is begining to appear to be a potential problem but I would have to study it in more depth.

Kelvin, in his work cited earlier, after asserting that he will be proceeding on the assumption that Caloric theory is correct, goes on to draw a PV diagram to illustrate an engine cycle.

This would tend to suggest, to my mind anyway, that these PV diagrams assume "work" output to be ONLY a kind of side effect of the expansion.

In other words, any potential CONVERSiON of heat into work, apparently, is not actually represented at all.

In other words, suppose my engine is running no-load. There is no resistance. It traces a certain path on a PV diagram but there is very little work output

Now, theoretically, I think, the same, or a similar engine under a very heavy load with a great deal of work output could trace the exact same path.

All a PV diagram shows is the pressure and volume at various points in the cycle but actually says nothing about how much heat input or work output went on to get from point A to point B.

To get from one pressure and volume to another, I could input a lot of heat while doing a lot of work or I could input a little heat while doing little work. The PV tracing for both of these operations could appear to be identical.

Is this true? Am I wrong?

At any rate, the apparent fact, that these diagrams were developed under the assumption that Caloric theory is correct makes them suspect IMO.

How can any conclusions be drawn regarding the conversion of heat into work based on a mathematics and diagrams that did not account for such a possibility?

Supposedly the " shaded area under the curve" represents the work.

Theoretically, starting at point A on a PV diagram, could I not add 200,000 joules of heat and simultaneously output 200,000 joules of work without actually moving off point A on the PV diagram, or moving so little as to be imperceptible?

It would matter not in the least if those figures were changed to 100 joules of heat in and simultaneous work out or 100,000,000 in and out.

A PV diagram does not actually indicate or take into account, conversion of heat into work at all. It only assumes work to be a side effect based on caloric theory.

[Fool]

It was always my understanding that the adiabatic lines were only changeable by adding or subtracting heat. If you have a method or machine that can switch adiabatic paths without adding or rejecting heat, please let us know.

I also understand that the points on a PV diagram are 'states', meaning a single temperature can be calculated for any single point. Adding heat or work would move from that point, on a specific path, to a new point determinable by the amount of heat or work being applied. The path is determined by heat and or work.

Calculating work from a PV diagram is the same as for a Force Distance diagram. ∆V=∆d•A, A=area, ∆d=distance, and P=F/A. Standard Newtonian Mechanics.

F•∆d=work
∆V•P=work

The same is true for a TS diagram.
∆S•T=work

I would assume that the: pressure drop and temperature drop, followed by a pressure rise with more temperature drop, during the compression stroke, in the indicator (PV) diagram provided; is caused by a cold sink being at a significantly lower temperature than the working gas. The bigger that temperature difference the faster the gas will cool. It's limit would be the cold sink, if the stroke were to stop for an extended long period.

[Tom Booth]

It was always my understanding that the adiabatic lines were only changeable by adding or subtracting heat. If you have a method or machine that can switch adiabatic paths without adding or rejecting heat, please let us know.

I also understand that the points on a PV diagram are 'states', meaning a single temperature can be calculated for any single point. Adding heat or work would move from that point, on a specific path, to a new point determinable by the amount of heat or work being applied. The path is determined by heat and or work.

...

Well, to keep things simple (LOL, maybe not so simple, but anyway)

"The path is determined by heat and or work".

The effect of each is the same though right?

Let's try to keep this on a single adiabatic path.

Say we have a "perfect" frictionless piston and cylinder and the piston is oscillating between two air springs.

Any work of compression or expansion at either end cancels out. We can examine each air spring "chamber" separately to keep things simple, but they are both basically identical, equal but opposite.

This oscillation, since it is adiabatic and there is no heat loss can theoretically continue indefinitely. We can though have work out and at each end we can have isochoric (constant volume) heat addition via an infrared flash heater.

Work output is by the piston being magnetic and the cylinder surrounded by a coil of wire. Work output. Or load on the engine, is increased or decreased by a series of LED's each with a switch.

The setup would look something like this:

Resize_20230729_003057_7765.jpg (170.58 KiB) Viewed 7568 times

Without switching on the heaters or the LED's the oscillation continues normally back and forth along the (whatever) adiabatic path.

After a time the infrared heating element is activated so as to introduce one joule (or 0.5 joules alternately at each end) of heat only at the instant an air spring is fully compressed, when the piston is stationary, changing direction and the volume of each chamber is constant.

The flash, infrared heating would increase the pressure slightly but simultaneously one LED is switched on while the piston resumes movement, reversing course thus causing the magnetic piston to do one extra joule of work as it traverses the cylinder, this extracts one joule of "internal energy", which lowers the temperature and pressure, or rather keeps the pressure and temperature at the same levels.

One joule in as heat and one joule out as work.

This is technically not an unusual arrangement. It pretty much describes an electronically controlled NASA type Stirling with linear generator and load balancing.

The net effect of the isochoric addition of one joule of heat along with the performance of one joule of work along the path to light an LED results in no change in the PV diagram. Or in what way would it change?

The potential increase or change in pressure or volume is exactly compensated for by an equal amount of work output

This can continue. By increasing the radiant heat input another Joule while simultaneously switching on another LED.

Whatever value in Joules we add as heat there is an equivalent simultaneous compensating adjustment in work output.

Eventually we have 100 joules of heat added for each 100 joules of work powering 100 1 joule LEDs, 1,000, 10,000 whatever.

Like I said, having simultaneous heat input along with work output is not unusual in a Stirling engine it is the ordinary, standard way that these engines work

Such a conversion of heat into actual useful work output, joule for joule however, is apparently off the radar.

Again, the above description is not some impossible scenario, it is basically how a modern high-tech Stirling engine actually operates with a linear generator bouncing between air springs.

Or how would this be modeled using a PV diagram?

Would the diagram look any different at the various power levels? 1 watt, 10, 100, 1,000 10.000 etc. ?

My point being, a PV diagram only shows Caloric theory type work output. The actual conversion of heat into work is not recognized.

That's my impression anyway.

[Tom Booth]

In Caloric theory no heat is converted.

Work is accomplished by transporting heat through the engine from source to sink without loss. Heat being an indestructible fluid, heat is conserved. That is Caloric theory and for the most part, this appears to be what modern thermodynamics, as it relates to heat engines generally still, like Kelvin wrote; "I shall refer to Carnot's fundamental principle, in all that follows, as if its truth were thoroughly established". Models the heat engine using Caloric theory as the fundamental assumption completely ignoring heat conversion into work output.

In reality, a heat engine that only "transports" heat from source to sink would have zero work output. It would not be able to function.

Work output is not accomplished by transporting heat through the engine to the sink, it is accomplished by NOT transporting heat but by converting heat to work so that it does not get transported through to the sink at all.

Again Kelvin wrote regarding heat engines and Caloric theory:

if it has absorbed any heat during one part of the operations, it must have given out again exactly the same amount during the remainder of the cycle. The truth of this principle is considered as axiomatic by Carnot, who admits it as the foundation of his theory; and expresses himself in the following terms regarding it, in a note on one of the passages of his treatise:

"In our demonstrations we tacitly assume ... that the quantities of heat lost by the body under one set of operations are precisely compensated by those which are absorbed in the others. This fact has never been doubted; it has at first been admitted without reflection, and afterwards verified, in many cases, by calorimetrical experiments. To deny it would be to overturn the whole theory of heat, in which it is the fundamental principle."

(...) I shall refer to Carnot's fundamental principle, in all that follows, as if its truth were thoroughly established.

[Tom Booth]

Contrasted with this picture, Nickola Tesla wrote:

... I read some statements from Carnot and Lord Kelvin (then Sir William Thomson)

...These statements interested me intensely.

...Heat, like water, can perform work in flowing down, ...But can we produce cold in a given portion of the space and cause the heat to flow in continually? ...

... let us reflect a moment. Heat, though following certain general laws of mechanics, like a fluid, is not such; it is energy which may be converted into other forms of energy as it passes from a high to a low level. ...

...If the process of heat transformation were absolutely perfect, no heat at all would arrive at the low level, since all of it would be converted into other forms of energy....

We can set aside speculations regarding "perpetual motion". The question is, what is the actual, fundamental nature of heat?

Is heat like a fluid that is simply transported through a heat engine from source to sink like water through a water wheel from a high to a low level, or is it just another form of energy that can be (or is) converted so that it does not pass through the engine and out to the sink as heat at all, but instead goes out as "work".

In numerous experiments, so far, it looks as if Tesla was probably mostly right and Carnot and Kelvin were mostly wrong.

If there is a heat flow out of these engines, I'm unable to block it with insulation and I'm also unable to measure it using ordinary instruments, at least not in the quantities predicted by thermodynamics. (I e. the Carnot limit formula)

[Tom Booth]

I'm not interested in "perpetual motion" or "free energy" particularly

I'm interested in engine design.

So to me, this is an important question. What are we actually trying to do?

Are we trying to get heat into and out of the engine, or get heat THROUGH the engine to the sink as quickly as possible or

Are we trying to retain as much heat as possible, prevent the heat from passing through so that it can be CONVERTED.

These two theories of heat engine operation and function are not reconcilable, they are at complete odds.

You can't have "magic" heat that is a form of energy that is converted to work and goes out from the engine as work but ALSO flows through to the sink, going out from the engine as heat.

[Tom Booth]

I think Tesla's mistake was to accept without question or examination the basic premise that heat, in some way "seeks out" cold and that some force or other exists which "compels" heat to "flow" towards or into cold in the same way water flows downhill seeking it's own level.

At this point I don't believe any such compelling force exists.

Heat doesn't seem to "flow through" a Stirling type heat engine at all. Rather, the piston oscillates between two more or less static and isolated energy sources. Or "bounces" between two gas springs.

Heat goes in on one side causing expansion, and the heat is converted to work output which leaves the gas on that side cold enough and at a low enough pressure that the pressure of the other energy source can then drive the piston back.

The whole premise, that heat flows from hot to cold just like water flows downhill is a fallacy.

That a heat engine derives it's power by intercepting this imagined "flow" is a fallacy.

We have wind, not because heat is flowing from a hot air mass to a cold air mass, but because hot air rises and some other cooler air moves in to take its place. The two air masses remain isolated, you don't see the heat "flowing" out of a hot air mass towards or into a cold air mass, they don't blend together but form a "front".

The examples where heat DOES NOT "flow" towards or into cold could be multiplied.

Warm water accumulates on the surface of a pond, colder denser layers remain below that. You don't see the heat rushing down from the surface to warm up the lower cold layers.

Yes heat does, quite often, tend to disperse, and eventually make a general migration outward in all directions so as to mostly warm a cold area more than an area that is already warm,but that is not always the case and is something very different from a "compelling force" causing heat to make a direct beeline for cold in such a way that energy could be extracted from the "flow".

There is no "FLOW".

[Fool]

Work and heat are not the same on a PV diagram. They take different paths. Work takes the adiabatic path. Heat diverges from that path towards a higher or lower adiabatic path.

If your double cylinder takes in one Joule on one side it will increase the temperature and pressure of the gas. That pressure will move the piston towards the second side producing work, which can be removed with magnets and coils and you will get out one Joule electrical power.

The piston will stop at the point where pressure is the same on both sides. There will be zero residual mV because the energy was removed by the generator. The gas temperature will be lower than before the expansion, and higher than the gas in the second side. The gas in the second side will have a higher pressure than before the compression, and lower than the first side. Pressure will be the same as side one.

There now becomes two ways to reset the first side.

1: By cooling. Removing less heat than put in, because the temperature is cooler than when added. Positive work out. Constrained by Carnot.

2: By firing the second side. The piston will move back to the center and stop. Pressure and temperature will be equal on both sides. Temperature will now be equivalent to the heater max temperature. It will take a one Joule heat input on the second side, equivalent to the work the first side put out, to reset the first side. Now all that can be done to reset both sides is waiting for them to cool by irreversibly wasting heat into the atmosphere. Net work out for this technique: Zero, zilch, notta. Also constrained by Carnot.

[matt brown]

Well, to keep things simple (LOL, maybe not so simple, but anyway)

"The path is determined by heat and or work".

The effect of each is the same though right?

Let's try to keep this on a single adiabatic path.

Say we have a "perfect" frictionless piston and cylinder and the piston is oscillating between two air springs.

Any work of compression or expansion at either end cancels out. We can examine each air spring "chamber" separately to keep things simple, but they are both basically identical, equal but opposite.

This oscillation, since it is adiabatic and there is no heat loss can theoretically continue indefinitely. We can though have work out and at each end we can have isochoric (constant volume) heat addition via an infrared flash heater.

Work output is by the piston being magnetic and the cylinder surrounded by a coil of wire. Work output. Or load on the engine, is increased or decreased by a series of LED's each with a switch.

The setup would look something like this:

Resize_20230729_003057_7765.jpg

Without switching on the heaters or the LED's the oscillation continues normally back and forth along the (whatever) adiabatic path.

After a time the infrared heating element is activated so as to introduce one joule (or 0.5 joules alternately at each end) of heat only at the instant an air spring is fully compressed, when the piston is stationary, changing direction and the volume of each chamber is constant.

The flash, infrared heating would increase the pressure slightly but simultaneously one LED is switched on while the piston resumes movement, reversing course thus causing the magnetic piston to do one extra joule of work as it traverses the cylinder, this extracts one joule of "internal energy", which lowers the temperature and pressure, or rather keeps the pressure and temperature at the same levels.

One joule in as heat and one joule out as work.

This is technically not an unusual arrangement. It pretty much describes an electronically controlled NASA type Stirling with linear generator and load balancing.

The net effect of the isochoric addition of one joule of heat along with the performance of one joule of work along the path to light an LED results in no change in the PV diagram. Or in what way would it change?

The potential increase or change in pressure or volume is exactly compensated for by an equal amount of work output

This can continue. By increasing the radiant heat input another Joule while simultaneously switching on another LED.

Whatever value in Joules we add as heat there is an equivalent simultaneous compensating adjustment in work output.

Eventually we have 100 joules of heat added for each 100 joules of work powering 100 1 joule LEDs, 1,000, 10,000 whatever.

Like I said, having simultaneous heat input along with work output is not unusual in a Stirling engine it is the ordinary, standard way that these engines work

Such a conversion of heat into actual useful work output, joule for joule however, is apparently off the radar.

Again, the above description is not some impossible scenario, it is basically how a modern high-tech Stirling engine actually operates with a linear generator bouncing between air springs.

Or how would this be modeled using a PV diagram?

Would the diagram look any different at the various power levels? 1 watt, 10, 100, 1,000 10.000 etc. ?

My point being, a PV diagram only shows Caloric theory type work output. The actual conversion of heat into work is not recognized.

That's my impression anyway.

Tom, according to this, an adiabatic expansion would have a lower temperature after expansion when driving a load vs no load. Picking a fight with Carnot on isotherm processes/cycles got you nowhere, so now you moved on to adiabatic processes/cycles.

To put Carnot in his original waterfall analogy, energy into system raises water to a given height, so dragging water from ground level (zero) can only return as much energy as allowed to fall. What you're thinking is that a 100 ft waterfall produces the same output regardless where it falls, and somehow ignoring that (a) 200 ft to 100 ft is not the same as (b) 100 ft to zero. In (a) the water did not magically appear at 100 ft to start where you only had to drag it another 100 ft to 200 ft. In thermo buzz, this is the distinction between the system and the surroundings, and you're trying to ignore the surroundings. In Star Trek like thinking, this is similar to creating another dimension (the system) within this dimension (the surroundings) which FIRST requires fighting off THIS dimension.

No doubt, many here are wondering what Tom's smoking or whether he's checked the date code on his barrel of Infinite Wisdom that he's chugging. However, what I find more amusing is that many of his observations and conclusions parallel the caloric theory...

[matt brown]

We have wind, not because heat is flowing from a hot air mass to a cold air mass, but because hot air rises and some other cooler air moves in to take its place. The two air masses remain isolated, you don't see the heat "flowing" out of a hot air mass towards or into a cold air mass, they don't blend together but form a "front".

Tom, we have wind because the earth rotates, dragging the atmosphere with it. The air on the dark side is cooler and denser than the light side due to solar heating. As the earth rotates, the previous cold air becomes heated, thereby displacing some air (aka wind).

[matt brown]

You can't have "magic" heat that is a form of energy that is converted to work and goes out from the engine as work but ALSO flows through to the sink, going out from the engine as heat.

This is the crux of all your confusion where you use "heat" as a word of convenience. Just try ignoring that word and describing stuff as only temperature or energy. Another confusion revolves around something that is a coincidence vs a consequence, a subtlety that slips by many, but can make a world of difference. As fool says, an adiabatic expansion does not loose "heat", it looses internal energy which we observe (keyword) as a decline in both temperature and pressure.

Heat engines generally increase temperature to increase internal energy and lower internal energy to produce work. Stirling engines are unusual in that (ideally) no change in internal energy occurs during either expansion or compression. Indeed unusual, but so is the beta/gamma scheme where output is on the Tmin side of cycle.

The wiki entry on internal energy is poorly written. Ignore the first paragraph and scroll down to the second paragraph where internal energy is solely the kinetic energy of the gas, aka the kinetic theory.

[matt brown]

It was always my understanding that the adiabatic lines were only changeable by adding or subtracting heat. If you have a method or machine that can switch adiabatic paths without adding or rejecting heat, please let us know.

...

Let's try to keep this on a single adiabatic path.

Fool nailed it with jumping off an adiabat is a one way trip without adding or subtracting heat (oops, thermal energy).

Adding heat while on an adiabat is fine and dandy, but further adiabatic expansion will continue on a new adiabat that NEVER terminates with original adiabat, no matter how many baby steps or how few giant steps you take.

[Tom Booth]

It was always my understanding that the adiabatic lines were only changeable by adding or subtracting heat. If you have a method or machine that can switch adiabatic paths without adding or rejecting heat, please let us know.

...

Perhaps you could explain why, in your understanding, if the "internal energy" of the working fluid can be increased or reduced by adding or subtracting "heat" and the internal energy can also be increased or reduced by adding or subtracting "work" what exactly is the difference as far as the working fluid is concerned?