The Carnot efficiency problem

[Tom Booth]

220
APPENDIX A.

(to be proved). Thus heat is produced by motion.If it is matter, it must be admitted that the matter is created by motion.

(2) When an air-pump is worked, and at the same time air is admitted into the receiver, the temperature remains constant in the receiver. It remains constant on the outside.

Consequently, the air compressed by the pumps must rise in temperature above the air outside, and it is expelled at a higher temperature. The air enters then at a temperature of 10, for instance, and leaves at another, 10 -f 90 or 100, for example.

Thus heat has been created by motion.

(3) If the air in a reservoir is compressed, and at the same time allowed to escape through a little opening, there is by the compression elevation of temperature, by the escape lowering of temperature (according to Gay-Lussac and Welter). The air then enters at one side at one temperature and escapes at the other side at a higher temperature, from which follows the same conclusion as in the preceding case.

(Experiment to be made : To fit to a high-pressure boiler a cock and a tube leading to it and emptying into the atmosphere; to open the cock a little way, and present a thermometer to the outlet of the steam; to see if it remains at 100 or more;

[Tom Booth]

APPENDIX A.

to see if steam is liquefied in the pipe; to see whether it comes out cloudy or transparent.)

(4) The elevation of temperature which takes place at the time of the entrance of the air into the vacuum, an elevation that cannot be attributed to the compression of the air remaining (air which may be replaced by steam), can therefore be attributed only to the friction of the air against the walls of the opening, or against the interior of the
receiver, or against itself.

(5) M. Gay-Lussac showed (it is said) that if
two receivers were put in communication with each other, the one a vacuum, the other full of air, the temperature would rise in one as much as it would fall in the other. If, then, both be compressed one half, the first would return to its previous temperature and the second to a much higher one. Mixing them, the whole mass would be heated.

When the air enters a vacuum, its passage through one small opening and the motion imparted to it in the interior appear to produce elevation of temperature.

We may be allowed to express here an hypothesis in regard to the nature of heat.

At present, light is generally regarded as the ...

[Tom Booth]

222 APPENDIX A.

result of a vibratory movement of the ethereal fluid. Light produces heat, or at least accompanies the radiating heat, and moves with the same velocity as heat.

Radiating heat is then a vibratory movement. It would be ridiculous to suppose that it is an emission of matter while the light which accompanies it could be only a movement.

Could a motion (that of radiating heat) produce matter (caloric) ?

No, undoubtedly; it can only produce a motion.

Heat is then the result of a motion.

Then it is plain that it could be produced by the consumption of motive power, and that it could produce this power.

All the other phenomena composition and de-composition of bodies, passage to the gaseous state, specific heat, equilibrium of heat, its more or less easy transmission, its constancy in experiments with the calorimeter could be explained by this hypothesis.

But it would be difficult to explain why, in the development of motive power by heat, a cold body is necessary ; why, in consuming the heat of a warm body, motion cannot be produced.

It appears very difficult to penetrate into the real essence of bodies. To avoid erroneous reasoning, it would be necessary to investigate carefully

[Tom Booth]

APPENDIX A. 223

the source of our knowledge in regard to the nature of bodies, their form, their forces; to see what the primitive notions are, to see from what impressions they are derived ; to see how one is raised successively to the different degrees of abstraction.

Is heat the result of a vibratory motion of molecules ?

If this is so, quantity of heat is simply quantity of motive power.

As long as motive power is employed to produce vibratory movements, the quantity of heat must be unchangeable; which seems to follow from experiments with the calorimeter; but when it passes into movements of sensible extent, the quantity of heat can no longer remain constant.

Can examples be found of the production of motive power with actual consumption of heat?

It seems that we may find production of heat with consumption of motive power (re-entrance of the air into a vacuum, for example).

What is the cause of the production of heat in combinations of substances? What is radiant
caloric ?

Liquefaction of bodies, solidification of liquids,...

[Tom Booth]

'224. APPENDIX A.

...crystallization are they not forms of combinations of integrant molecules ?

Supposing heat due to a vibratory movement, how can the passage from the solid or the liquid to the gaseous state be explained?

When motive power is produced by the passage of heat from the body A to the body B, is the quantity of this heat which arrives at B (if
it is not the same as that which has been taken from A, if a portion has really been consumed to produce motive power) the same whatever may be the substance employed to realize the motive power?

Is there any way of using more heat in the pro-
duction of motive power, and of causing less to reach the body B ? Could we even utilize it entirely, allowing none to go to the body B ? If
this were possible, motive power could be created without consumption of combustible, and by mere destruction of the heat of bodies.

(...)

Carnot continues, in this textual monologue... But this passage covers many of the questions being addressed here.

Unfortunately Carnot died at a young age and these notations remained in the hands of his family for some 50 years or so.

Carnot no doubt considered these matters of the utmost importance.

[Tom Booth]

@Fool
" I would like to point out that PV/T=mR/M are state points on a PV diagram. Heat and Work aren't in that equation."
Just to point out :

p : Pascal
V : M3 (cubic meter)
T: Kelvin
m: kilogram
R : 8314 Joule/Kelvin*kilomol (gas-constant)
M : Molar weight in kilogram/kilomol (for air its app. 29 gram/mol)

So heat surely are in this equation. All it actually tell you is, that p*V/T is a constant for a specific gas.

A Stirling engine is a closed system with a fixed amount of gas inside, so m is constant, R is constant and M is constant.

So here pressure, volume and temperature always relates to each other on a fixed set of rules.
But it it very hard to tell which is where and when in a sterling engine, as it depends on cam-angles and stroke-lengths.
If with a magnetic connected displacer, it gets even worse to figure out, as seen in Tom´s slomo video.

So it will be hard to calculate these values and plot them in a pV diagram. You will have to measure them in realtime.

Hmm, but where to put the probes ?
If we put a thermocoupler probe inside the middle of a thick base copper or aluminium plate. I have Just drilled a ø4mm hole from the side of a 8mm thick plate.

So I know the temperatur of "heat in". Of cause it´s also nice to know the amount of kilojoules going in . . .

But it can be really messy to point out the exact p, V and T in a running Stirling engine

Have a nice weekend !

There are a few things to consider that I don't see.

Momentum/velocity motion/work things that have to do with mechanical work input and output.

Velocity of a piston in motion for example.

The piston was set in motion by the expansion of a gas that was expanded by the addition of heat.

You could, I believe say that when the piston is forced to move by the pressure of the expanding gas, the conversion of heat into "work" has already reached completion so that there is a temperature fall a subsequent reduction in pressure and a return to the initial state, however the piston has been set in motion and continues traveling until it meets resistance. The gas undergoes additional expansion and loss or conversion of internal energy.

The "system" has been left off balance as a Stirling engine is a sealed chamber working in conjunction with external atmospheric pressure.

Internal temperature and pressure have fallen as a result of conversion of the heat (or internal energy) to velocity/momentum/work, but internal volume has increased. The piston is moving outward.

No heat has to be lost to bring the piston back to the starting position, the heat has already been converted to velocity/"work".

The pressure differential between internal working fluid and external atmosphere results in an internal "vacuum". This imbalance grows as the piston continues moving outward.

The pressure balance cannot be restored until the piston stops, reverses course and is pushed ALL the way back in by atmospheric pressure.

There is no argument, I don't think, that the heat can be converted 100% into work on the expansion stroke.

If that is so, then it follows that the piston will be driven back without any further "heat rejection" being necessary.

It is already necessary for the piston to return to the starting position to restore a balance of pressure after the heat has been converted.

On the return stroke however, the force exerted by atmospheric pressure is again converted to velocity so that the piston is in motion and will not stop until it meets resistance. That is, the internal working gas pressure builds up higher than the external atmospheric pressure.

Once the internal pressure builds the piston is forced out again.

The piston will then continue to oscillate between the two pressure extremes.

Without an external load the only additional heat required to maintain the oscillation is make up heat to compensate for loses.

With an external load, to maintain the oscillation, additional heat is required to compensate for the external work load.

Conspicuously absent in this scenario is any necessity to transfer any heat to a "sink".

[Fool]

I take Carnot's comment to mean, if an engine expels zero heat to a cool sink, a perpetual motion machine can be built. There will be no need to feed a hot source from burning fuel. Carnot seemed to comment that the cold sink is evey bit as important as the hot source.

My thoughts for an upsidedown test:

1: Putting ice on the flat side will allow the piston side to be warmer, so less condensation will be observed.

You observed that the engine runs better when cooled above heated below. Upsidedown will allow that, without cooling the piston and displacer rod. Maybe causing less condensation on them. Anything below the dew point for the room will cause condensation.

2: If heated from below, insulated on top, and piston side is up, there is a chance that the insulated "leaky" piston and displacer gland will pull in cool room air and push out warm engine air.

Running it upsidedown allows the piston bottom side to be heated and the flat top side to be cooled. Now the leaks will pull in heated air and push out heated air.

Some building of a heat container around the hot side would be necessary. It would eliminate the possibility for cooling, by mass flow in and out, to be happening.

From what I've seen here, we all seem to agree that an LTD pumps heat. If driven, one side gets hot and the second gets cold. If reversed one side gets cold and the second get hot. It switches. There is a Phillips video demonstrating some of this.

If run as an engine heat enters the hot side. It seems hard to believe that it doesn't operate as a heat pump and also come out the bottom side since the machine is identical and run at the same speed. Tom's experiment appears to refute that.

So, either 200 years of science is wrong, or we are missing some explanation in Tom's experiment. I'm betting on an explanation.

Running it upside down will allow insulation to be easily added and removed. It will allow any thickness to be used. How it behaves with several different thickness and diameters is just good science. Try preheating and cooling the insulation too. If you have the time, curiosity, interest, and desire.

May those studies go well. My thought is that the graphs and charts presented here seem to support 200 year-old heat pump theory, despite Tom's description. Sorry. Even if Tom is correct he and I and other followers will find it impossible to convince main stream science. Tom asked for someone to disprove him, if they could. I don't know if I can without working those experiments in the same lab with him. Or prove him right. I need to see if I can, either way, before throwing out conventional science. Numbers rule, so watch out.

[Tom Booth]

I believe you could remove the displacer, install an electric heating element inside the engine and place a pressure switch in (or over) the hole formerly occupied by the displacer connecting rod.

Adjust the pressure switch to "fire" the heating element as the piston nears TDC.

Give the engine a spin.

You could probably do something similar with one of these Ruchardt tubes.

I've been meaning to try this sometime but haven't got around to it.

Put a heating element in the bottle and have it fire briefly when the piston approaches the bottom of the tube. That should allow the oscillation to continue indefinitely

https://youtu.be/vT6n7VVBvqw

[Tom Booth]

I take Carnot's comment to mean, if an engine expels zero heat to a cool sink, a perpetual motion machine can be built. There will be no need to feed a hot source from burning fuel. Carnot seemed to comment that the cold sink is evey bit as important as the hot source.
(...)

This seems rather remarkable.

Did you actually bother to read the quoted passages?

Your comments appear to relate to his published book where he most definitely stated that a cold sink is just as necessary as a hot source.

In these later writings it is perfectly clear that due to new scientific findings he changed his mind, discarded Caloric theory, was now leaning towards Kinetic theory which he thought, if true did not support his former conclusions regarding the necessity of a "cold body"

He also spectates that heat might be used in its entirety to produce "motive power" so that none at all would arrive at "body B".

If you did read it, it's interesting how two people can read the same passages and come away with two entirely different ideas about what was put down in pretty plain language in black and white.

[Tom Booth]

(...)

My thoughts for an upsidedown test:

1: Putting ice on the flat side will allow the piston side to be warmer, so less condensation will be observed.

You observed that the engine runs better when cooled above heated below. Upsidedown will allow that, without cooling the piston and displacer rod. Maybe causing less condensation on them. Anything below the dew point for the room will cause condensation.

2: If heated from below, insulated on top, and piston side is up, there is a chance that the insulated "leaky" piston and displacer gland will pull in cool room air and push out warm engine air.

Running it upsidedown allows the piston bottom side to be heated and the flat top side to be cooled. Now the leaks will pull in heated air and push out heated air.

Some building of a heat container around the hot side would be necessary. It would eliminate the possibility for cooling, by mass flow in and out, to be happening.

From what I've seen here, we all seem to agree that an LTD pumps heat. If driven, one side gets hot and the second gets cold. If reversed one side gets cold and the second get hot. It switches. There is a Phillips video demonstrating some of this.

If run as an engine heat enters the hot side. It seems hard to believe that it doesn't operate as a heat pump and also come out the bottom side since the machine is identical and run at the same speed. Tom's experiment appears to refute that.

So, either 200 years of science is wrong, or we are missing some explanation in Tom's experiment. I'm betting on an explanation.

Running it upside down will allow insulation to be easily added and removed. It will allow any thickness to be used. How it behaves with several different thickness and diameters is just good science. Try preheating and cooling the insulation too. If you have the time, curiosity, interest, and desire.

May those studies go well. My thought is that the graphs and charts presented here seem to support 200 year-old heat pump theory, despite Tom's description. Sorry. Even if Tom is correct he and I and other followers will find it impossible to convince main stream science. Tom asked for someone to disprove him, if they could. I don't know if I can without working those experiments in the same lab with him. Or prove him right. I need to see if I can, either way, before throwing out conventional science. Numbers rule, so watch out.

Some of your suggestions are worth considering.

I think the idea that any significant cooling by "mass flow in and out" is rather ludicrous since a Stirling engine running at all depend upon there not being any air leaks.

Out of curiosity, I have also tested for this previously.

This experiment for example.

https://youtu.be/iOs3BADFeKI


The piston cylinder is completely sealed with a latex "balloon", actually a finger from a rubber glove, secured tight with rubber bands.

I did this to see if there was any "leakage" of hot air past the piston, or any other expansion or contraction of air past the piston while the engine was running.

The pressures involved in this high temperature engine are surely much greater than in an LTD, but, no leaks past the piston.

The balloon did not inflate or deflate.

I think you may be mistaken about the Phillips video, but I don't think enough information is provided to actually keep track of the direction of rotation and direction of heat flow, when the engine is acting as heat pump, or "refrigerator" or hot or cold running engine. What exactly is meant by " forward" or reverse, or "same" or opposite direction? Since it is impossible to see inside that type of engine, I gave up trying to figure it out and just went back to direct observation of actual engines in my possession.

https://youtu.be/GFfMruoRMGo

[Fool]

Goofy,

"R : 8314 Joule/Kelvin*kilomol (gas-constant)"

The Joule, in the gas constant R, is for the internal energy associated with the PVT point, not work, or heat. It was very difficult for me to separate the three energies. My understanding has improved since realizing those differences.

Internal energy is U.
Enthalpy is U+PV
Work is P∆V or F∆x
Heat is Q
Heat transfer (the real heat) is ∆Q nobody says that.

And Entropy is S =∆Q/T or more correctly dS=dQ/T

It gets confusing when one considers that adding heat Q can increase internal energy U, but not always.

Tom, a thought on insulation: If I enter a cold bed and wrap myself in a blanket, I am cold for quite some time. Humans put out 100 Watts. LTD's pull in milliwatts, and output???

If during the night the bedroom gets colder cold enough, I get cold and need to put on more blankets. More than 100 Watts were going out before it added blankets. An LTD is milliwatts.

My question would be, at one watt, how long would it take to heat up the insulation to any readable amount. And, insulation how thick, does one Watts dissipation need to be, to measure a temperature rise. How about for 20 milliwatts?

There has to be some measure of R-Value, heat capacity, thermal mass, power output to a load, and temperature to determine what is happening on a PV diagram. All before challenging Carnot Theory.

A simple dynamometer would be a stick with a friction, rubber band or magnetic brake on it and a spring scale or calibrated rubber band, to measure torque, and an rpm meter. All this takes time, interest, and dedication, so I understand if it doesn't pan out right away. Just some thoughts.

[Fool]

"Is there any way of using more heat in the pro-
duction of motive power, and of causing less to reach the body B ? Could we even utilize it entirely, allowing none to go to the body B ? If
this were possible, motive power could be created without consumption of combustible, and by mere destruction of the heat of bodies."

That appears to be his conclusion and appears as I've decribed.

[Tom Booth]

(...)
From what I've seen here, we all seem to agree that an LTD pumps heat. If driven, one side gets hot and the second gets cold. If reversed one side gets cold and the second get hot. It switches. There is a Phillips video demonstrating some of this.

If run as an engine heat enters the hot side. It seems hard to believe that it doesn't operate as a heat pump and also come out the bottom side since the machine is identical and run at the same speed. Tom's experiment appears to refute that.

So, either 200 years of science is wrong, or we are missing some explanation in Tom's experiment. I'm betting on an explanation.

(...)

In the Phillips video, the engine is run as an engine by heating the heater head on top.

Later in the video when the engine is operated as Quote a "heat pump" the heater head itself becomes glowing red hot.

Your conclusion: "either 200 years of science is wrong, or we are missing some explanation in Tom's experiment" does not necessarily follow from that rather ambiguous video.

The video does not ever show the actual rotation of the crankshaft so we have to rely on the discretion which is ambiguous "we are going to call this the forward direction" etc. Who can know what that actually means?

[Tom Booth]

"Is there any way of using more heat in the pro-
duction of motive power, and of causing less to reach the body B ? Could we even utilize it entirely, allowing none to go to the body B ? If
this were possible, motive power could be created without consumption of combustible, and by mere destruction of the heat of bodies."

That appears to be his conclusion and appears as I've decribed.

I think you are making an inference, and assuming he is speaking rhetorically, implying the opposite of what he says.

I think he is advocating something he considers a genuine possibility, if his new theory regarding the nature of heat can be believed.

In fact, can it not be truthfully stated that a Stirling engine can run: "without consumption of combustible, and by mere destruction of the heat of bodies."

A LTD running on the heat of a hand for example.

I interpret his words as a positive statement of something he considered a real possibility. You have apparently taken the opposite view thinking he is using reductio ad absurdum. I can find no evidence of that from the general context.

[Tom Booth]

His new theory to replace the Caloric theory is that heat is a "vibratory motion". And therefore:

Heat is then the result of a motion.

Then it is plain that it could be produced by the consumption of motive power, and that it could produce this power.

He goes on to clarify this later in the text:

Heat is simply motive power, or rather motion
which has changed form. It is a movement among the particles of bodies.

Wherever there is destruction of motive power there is, at the same time, production of heat in quantity exactly proportional to the quantity of motive power destroyed. Reciprocally, wherever there is destruction of heat, there is production of motive power.

Together with what I quoted earlier:

Is heat the result of a vibratory motion of molecules ?

If this is so, quantity of heat is simply quantity of motive power.

As long as motive power is employed to produce vibratory movements, the quantity of heat must be unchangeable; which seems to follow from experiments with the calorimeter; but when it passes into movements of sensible extent, the quantity of heat can no longer remain constant.

Can examples be found of the production of motive power with actual consumption of heat?

The part I've highlighted in bold is telling.

What does he mean by "sensible extent" where "the quantity of heat can no longer remain constant".

He is clearly proposing that heat is not conserved when transformed into "work". Motions we can actually see.

Granted, he is gripping for answers to questions that perplexed him. Way ahead of his time in considering heat as a form of molecular motion invisible to our eyes, but that could be transformed into other forms of motion that are visible to us.