Isothermal Heat Transfer

[VincentG]

Only if some working fluid has been bled from the engine at working temperature near TDC. Otherwise, you're not going to get the partial vacuum at BDC needed for the ambient atmosphere to do any pushing on the return stroke.

Negative. We are seeing a strong return stoke with these engines while having the same mass of gas contained within. Thats really the subject of controversy regarding high efficiency.

[Tom Booth]

Only if some working fluid has been bled from the engine at working temperature near TDC. Otherwise, you're not going to get the partial vacuum at BDC needed for the ambient atmosphere to do any pushing on the return stroke.

Negative. We are seeing a strong return stoke with these engines while having the same mass of gas contained within. That's really the subject of controversy regarding high efficiency.

Theorizing now, as of course this is a departure from what has been the "established science" on heat engines for 200 years... Probably violates the Carnot limit and the Second law of thermodynamics, ushers in an age of perpetual motion, free energy and gets somebody the nobel prize yada yada yada...

1) heat is energy that can be converted.

2) on expansion heat is converted to work

3) some of that work is converted to velocity and momentum (mass x velocity).

Note: in a "free piston" type engine it is generally found that the piston must have a substantial mass or added weight for the engine to operate, and changing the mass or weight on the piston will change its behavior. With a heavier piston or one with more added weight the oscillations of the piston increase in amplitude.

4) when approaching BTC when the internal gas pressure and external atmospheric pressure reach equilibrium, a heavy piston still has momentum so piston travel continues.

Notes/observations: In a free piston engine running "no-load" the pressure equilibrium point appears to occur not at the end of the expansion stroke, but exactly midway between TDC and BDC so that the piston is oscillating from a central point of pressure equilibrium so that the working fluid pressure is below atmosphere towards BDC from center and above atmosphere towards TDC from center.

In a crank driven engine with a flywheel or other factors that control or limit piston movement the "central" balance point apparently may be considerably offset. This change or variation probably occurs also with varying loads on the engine. The available Live PV tracings (all crank engines afaik) do not agree with this observation putting the equilibrium point much closer to BDC and TDC but usually (afaik always) sometime prior to either. In any case, the pressure equilibrium point is almost always reached prior to BDC. (This does not apply to idealized PV diagrams)

5) when the piston travels beyond the point of pressure equilibrium, either due to its own momentum, or combined with the momentum of the flywheel, the working fluid continues to transfer energy to the piston, so that the gas continues doing work on the piston causing the internal energy and temperature of the working fluid to continue to decrease.

Why does #5 happen? This is difficult to understand.

The gas sealed within the engine only "sees" the piston from the inside. As far as the working fluid is concerned, it is still full of considerable kinetic energy, it is still "pushing" the piston from the inside and the piston is still moving as a result. Infact, although the piston may be carried beyond the equilibrium point by its own momentum and/or that of the flywheel, the internal gas pressure is still contributing, still doing work and still actually losing internal energy so still dropping in pressure and temperature due to work output.

This "extra" extended work output can apparently result in a more forceful return stroke. Once the stored momentum in the piston is used up in a free piston engine, the pressure balance, (or imbalance) has shifted so that the internal pressure is very low relative to the outside atmospheric pressure.

In a crank engine with a flywheel, of course, the stored momentum is not entirely "used up" but some momentum is carried through BDC.

Generally the engine will find some new steady state balance again after some change in heat input or load. But there are occasions when the return stroke may appear to be more forceful than the power stroke due to the above described "extended" expansion, giving outside atmospheric pressure the "upper hand" in terms of the relative internal/external pressure balance.

[Stroller]

the internal gas pressure is still contributing, still doing work and still actually losing internal energy so still dropping in pressure and temperature due to work output.

This is the part I'm having trouble with. The working fluid can only still be doing work while it's above ambient pressure, but you seem to have been saying it falls below ambient pressure sometime before BDC (due to increasing volume, work extraction and contact with the cold side). If that's the case it's going to be working against the momentum of the flywheel instead of contributing to it, isn't it?

[Tom Booth]

the internal gas pressure is still contributing, still doing work and still actually losing internal energy so still dropping in pressure and temperature due to work output.

This is the part I'm having trouble with. The working fluid can only still be doing work while it's above ambient pressure, but you seem to have been saying it falls below ambient pressure sometime before BDC (due to increasing volume, work extraction and contact with the cold side). If that's the case it's going to be working against the momentum of the flywheel instead of contributing to it, isn't it?

Well, as "fool" always insists, air pressure inside the engine is never "negative".

So:

momentum + internal pressure > external pressure

past the point where

internal pressure(alone) = external pressure

The more momentum, the further this can be carried.

It could be said that the momentum of the piston is mechanically expanding the gas, "stretching" it out like a rubber band, but apparently that is not exactly right.

How "mechanical expansion" results in the gas loosing energy and cooling is explained in this video:

https://youtu.be/PMKPZuCj9a0?si=rz-sRRStMW3mHKSg

In the video the instructor is using his muscles to pull the plunger so the gas can expand. So it seems as though he is doing all the work.

In reality though, the plunger is moving due to muscle + internal pressure > external pressure.

In other words, in spite of appearances, the gas is contributing to the work of moving the piston, "pushing" from the inside while he pulls the plunger from the outside.

[VincentG]

the internal gas pressure is still contributing, still doing work and still actually losing internal energy so still dropping in pressure and temperature due to work output.

This is the part I'm having trouble with. The working fluid can only still be doing work while it's above ambient pressure, but you seem to have been saying it falls below ambient pressure sometime before BDC (due to increasing volume, work extraction and contact with the cold side). If that's the case it's going to be working against the momentum of the flywheel instead of contributing to it, isn't it?

Enter the theory of relativity lol. If at this point the buffer pressure was a total vacuum, it would be easy to see that the internal gas is still doing work on the piston. But since internal pressure is falling below buffer pressure, it doesn't seem this way.

So I guess you could look at it either way, the piston doing work on the gas or the gas continuing to do work on the piston. In any event, I don't think the gas cares

That being said, I would imagine the biggest reduction in temperature would be from expanding gas into a vacuum where the gas is able to use all it's kinetic energy to expand unrestricted.

[Tom Booth]

..., I would imagine the biggest reduction in temperature would be from expanding gas into a vacuum where the gas is able to use all it's kinetic energy to expand unrestricted.

Actually it's just the opposite.

When expanding into a vacuum the gas has nothing to do work against so doesn't loose energy, the internal energy remains constant and the temperature stays the same.

That is, for an "ideal gas" anyway.

In reality the gas temperature could go down or, non-intuitively up, depending on the gas and it's "inversion temperature", or maybe that is only at atmospheric pressure, if NOT expanding into a vacuum.

I need to brush up, anyway:

https://en.m.wikipedia.org/wiki/Inversion_temperature

[Fool]

But by doing work and loosing energy and getting cold, the gas contracts.

By contracting, this allows outside atmospheric pressure to do the work of returning the piston to TDC.

The gas by pushing to expand, by pushing, the volume increases, because it was heated to a higher temperature, using that temperature and pressure to push outwards against atmosphere suddenly looses all its energy to work, cools off enough so that it gets compressed back down to its original volume, even though all that was done was the addition of heat. No heat removal.

Oh wait, it isn't compressed, it "contracts" suddenly to the starting volume leaving a void for the piston to be pushed back inwards. Or wait... It pulls the piston in with it. And ends up at the starting point with 15 psi, ready to be heated again. Thus avoiding the temperature increase associated with volume decrease/compression.

Hmmm. Don't you think that the maximum expansion from heat added would end up leaving the volume expanded at the same atmospheric pressure and elevated temperature? I do. That is how PV = NRT was measured and derived 200 years ago, and still works today. VincentG has been doing that with his experiments.

[VincentG]

I can't seem to find how they measured pv=nrt.

[Tom Booth]

From that article I thought this was interesting. Something I haven't seen before:

So for 𝑇 > 𝑇inv, an expansion at constant enthalpy increases temperature as the work done by the repulsive interactions of the gas is dominant, and so the change in kinetic energy is positive.

But for 𝑇 < 𝑇inv, expansion causes temperature to decrease because the work of attractive intermolecular forces dominates, giving a negative change in average molecular speed, and therefore kinetic energy.

It sounds like the molecular repulsive force gives the expansion a little extra kick, so kinetic energy increases. Like springs being set loose?

But attractive molecular forces slow the molecules down as they are trying to expand, so the kinetic energy is pulled back, kind of like trying to stretch rubber bands, they contract and cool... After expanding maybe?

Anyway, this is basically what causes the air leaving that guys tank to get so cold as to make snow. But that is MINOR. The gas is only doing a bit of internal flexing, working with or against its own attraction to itself. Not doing any substantial REAL work.

Joule-Thomson throttling, as in ordinary refrigeration isn't even recognized by the ideal gas law or kinetic theory. It is pretty minor.

Expanding gas through an expansion engine, on the other hand... The gas is being forced to do some real heavy lifting like pushing an actual piston in a cylinder. Now your talking some serious cold.

[Fool]

Except that in a heat engine it is expanding because it is hotter from heat being added. The best it can do is to be expanded to the same pressure on either side of the piston. At that point any work developed during that previous expansion must be utilized, or an input of outside energy, to pull, expand and temperature-drop further.

In a cooling cycle, work is added to compress, heat is rejected to the hot plate to cool the gas, then an expansive process with outgoing work, temperature-drop is performed. The compressive work-in is more than the work-out, because it is done at a higher temperature and pressure.

That can be confirmed on a PV or indicator diagram. And simple integration.

[Fool]

VincentG, I'd need to do research to learn what their instrumentation was. I'm guessing volume was measured with a measuring stick. Temperature was measured with a glass bulb thermometer. N number of moles was measured by mass, a balance. I don't know when moles were invented. R was calculated from the others. And pressure probably was measured using a weight and cylinder, perhaps a torsion ballance. Units were probably all different too. No SI standard yet.

Just guessing.

[Tom Booth]

But by doing work and loosing energy and getting cold, the gas contracts.

By contracting, this allows outside atmospheric pressure to do the work of returning the piston to TDC.

The gas by pushing to expand, by pushing, the volume increases, because it was heated to a higher temperature, using that temperature and pressure to push outwards against atmosphere suddenly looses all its energy to work, cools off enough so that it gets compressed back down to its original volume, even though all that was done was the addition of heat. No heat removal.

Now you're getting the idea

Oh wait, it isn't compressed, it "contracts" suddenly to the starting volume leaving a void for the piston to be pushed back inwards. Or wait... It pulls the piston in with it. And ends up at the starting point with 15 psi, ready to be heated again. Thus avoiding the temperature increase associated with volume decrease/compression.

Hmmm. Don't you think that the maximum expansion from heat added would end up leaving the volume expanded at the same atmospheric pressure and elevated temperature? I do....

I certainly did, something like ten years ago.

My "theories" about why the piston returns, or what is actually going on at a molecular level is just that. Theorizing. I think it is perfectly fine to entertain conflicting theories in an effort to explain some perplexing or mysterious observation.

Here is another theory or analogy.

Air contains water vapor.

The sun heats up humid air near the ground. As a result the air rises. As it rises it expands, as it expands "adiabatically" it cools. As it cools it eventually reaches the dew point where water droplets condense. Clouds form and rain falls back down to the ground.

This is a description of our atmospheric, planetary "heat engine". A complete cycle driven by heat input. Not exactly the same process as our little terrestrial heat engines. Call it an analogy.

If you get deeper into molecular attraction and repulsion and the actual(????) reasons why things happen at the Quantum(????) level, God help you, because when, well, let me find something:

Compress_20240426_035556_6101.jpg (84.27 KiB) Viewed 138 times

Compress_20240426_040510_0232.jpg (72.42 KiB) Viewed 138 times

https://www.quora.com/Why-intermolecula ... -increases

Why is rubber "elastic"?

If you stretch a rubber band further and further you are "storing" more and more "potential energy" in the rubber band, at least up until the point where the rubber band breaks.

Part of the theory of gases I run into from time to time says that gases are "infinitely elastic".

Now, who can really believe or trust anything about gas behavior?

"Ideal gases" do this that and the other thing and have, or don't have such and such properties, but oh, by the way, there are no "Ideal Gases" in reality.

Real gases actually behave this that and the other way so forget all the "LAWS" we just told you, now you need to learn how to make adjustments and corrections using these "constants".

And everything you read contradicts something you can find somewhere else that says the opposite.

But maybe gas can "stretch" like a rubber band. IDK.

Do I know what I'm talking about?

No. I'm just groping in the dark.

But I can see that the piston in a Stirling engine does infact return. Without a flywheel. Without a displacer. With no apparent "sink" or viable heat outlet. I've done the experiments myself, so I can't really just dismiss what I see happening.

Maybe I'm fooling myself?

OK, I guess that's possible.

So what do I do?

I went to the science/physics forums. What did I say in my first introductory post there?

If possible I would like to see others perform the experiment to see if they get similar results.

Reference: https://www.physicsforums.com/threads/s ... ne.991714/

Maybe when the gas expands too far the "photon mediated" "virtual particles" appear out of the quantum flux field or "foam" or ether or WTF ever and yank the piston back to TDC then vanish back into the thin air.

Maybe Carnot was right all along and heat really is a fluid. I don't know.

Maybe heat is energy and/or a fluid and/or a particle, depending on what you do with it or how you look at it, or DON'T look at it.

Efficiency = 1 - Tc/Th

Really?

I wish it were that simple.

[Stroller]

VincentG, I'd need to do research to learn what their instrumentation was. I'm guessing volume was measured with a measuring stick. Temperature was measured with a glass bulb thermometer. N number of moles was measured by mass, a balance. I don't know when moles were invented. R was calculated from the others. And pressure probably was measured using a weight and cylinder, perhaps a torsion ballance. Units were probably all different too. No SI standard yet.

Emil Claperyon is credited with having formulated the ideal gas law in 1834. The giants whose shoulders he stood on include organic chemists such as Gerhard, who was a student of Leibig and Laurent, who was a student of Dumas; and physicists such as Avagadro who first hypothesised moles.

An example of the kind of apparatus used to determine molecular weights would be those employed by the Viktor Meyer method, a mid C19th refinement of the sort of experiments conducted by Gerhard and Laurent.
https://en.wikipedia.org/wiki/Victor_Meyer_apparatus

[Stroller]

But maybe gas can "stretch" like a rubber band. IDK.

But I can see that the piston in a Stirling engine does infact return. Without a flywheel. Without a displacer. With no apparent "sink" or viable heat outlet. I've done the experiments myself, so I can't really just dismiss what I see happening.

The piston is leaky, air expanded by heat inside the stirling engine will leak past it while it is pushing it to BDC. As it starts to cool and contract due to work extraction, increase in volume (due to the piston's continued motion towards BDC), and also due to the fact that the displacer is 90 degrees ahead and already starting to move working fluid to the cold side, the piston and flywheel's momentum does indeed "stretch the gas like a rubber band". i.e. they are preventing the contraction that would otherwise be starting to take place by this part of the cycle. Just past BDC, the working fluid's gas pressure is now below atmospheric, due to the earlier piston blow-by and the ongoing cooling induced by displacer motion forcing more of it to the cold side.

Hence the 'forceful return stroke' as ambient atmospheric pressure shoves the piston downwards during the first half of its motion towards TDC, and before the displacer starts to transfer working fluid back to the hot side. Because the piston is leaky, and the flywheel and piston have inertia as well as momentum, some ambient air will be entering the engine, this will restore the full-cycle average pressure at running equilibrium.

[VincentG]

Hence the 'forceful return stroke' as ambient atmospheric pressure shoves the piston downwards during the first half of its motion towards TDC, and before the displacer starts to transfer working fluid back to the hot side. Because the piston is leaky, and the flywheel and piston have inertia as well as momentum, some ambient air will be entering the engine, this will restore the full-cycle average pressure at running equilibrium.

While undoubtedly the pistons leak and alter the true nature of a stirling cycle while at speed, this is also undoubtedly not the cause of the power return stroke.

It is caused by the gas temperature being lowered after the high temperature gas has pushed the piston to a point where internal pressure is at or below ambient while still hot.

At this point, cooling the gas causes a strong vacuum and the subsequent return power stroke. This is a fact.

It is easy to demonstrate at slow speed with a cold sink.