∆T, Another Sacred Cow?

[Tom Booth]

We have probably all heard, read or repeated many times that:

"efficiency depends only on the temperature of the hot source and the cold sink." Or:

"The maximum efficiency, known as the Carnot efficiency ηmax, is dependent only on the temperatures of the hot source and the cold sink TH and TL, as shown in Figure 1, and is given by the equation below[3]

(1)

ηmax=1−TL/TH"

Random source: https://energyeducation.ca/encyclopedia ... efficiency

So, in theory, (more generally, accepted as actual fact), a Stirling engine should run just as well or even more efficiently when the temperature difference is greater, even though lower on the temperature scale.

In other words, the engine should, in theory, run just as well on COLD as it does on heat because efficiency depends "ONLY" on the temperature difference

Now I have done numerous experiments running Stirling engines on ice, (or more accurately, on ambient heat), and felt some satisfaction at my cleverness, however, I cannot say truthfully, that I have ever been particularly impressed by the performance of these engines running on COLD rather than on HEAT.

They always, inevitably, seemed rather slow and sluggish.

I tended to write this off as due to mechanical issues.

Probably the shrinkage of the power piston due to the unusual cold caused a loss in compression. I would think, with a furrowed brow. A tighter fitting piston should remedy the problem

Or, the lubricant used may be to blame. The graphite, oil or whatever simply does not perform well at low temperature. Some other method of lubrication should solve the problem.

Or there is not enough air circulation. Adding some small fan blades or paddles to the flywheel could move more air past the engine, so the engine gets more heat flow and runs better.

The idea that there might be something wrong with "established science", the theory behind thermal efficiency or the basic assumption of the efficiency formula, or the mathematics of the formula itself, tended always to escape blame.

Well thinking more deeply about it recently, I think that maybe a Stirling engine tends to run a little sluggish and slow "on ice", (even in spite of there being a greater temperature difference, in many cases), for another reason, which, now that I think about it, seems pretty obvious, and I'm not really sure why I did not realize this before

Cold gas molecules move more slowly and have less energy than hotter gas molecules.

So a quantity of gas working between, say 300 and 400 Kelvin does not impart the same energy to the engine as a working fluid operating between 200 and 300 K.

Or does it?

Well, logically, if heat is the transfer of "vibration" or motion between molecules, or the transfer of kinetic energy, then naturally a hotter gas contains more kinetic energy than a colder gas Right? Or does it?

Well, a colder gas is more dense so... maybe it averages out or something,...

Nevertheless, I have to admit that experimentally, it has not really appeared to me that a Stirling engine runs just as well on a ∆T lower on the temperature scale. It just doesn't. At least that has been my experience

Same as far as dozens of YouTube videos I've watched of Stirling engines running on ice, dry ice, liquid nitrogen or some other COLD source. The performance is generally not all that impressive.

Admittedly though, I have never done any carefully controlled experiments to address this specific question, but has anyone, ever?

Not that I'm aware of. Mostly it seems to just be taken as established fact. It is NOT heat that powers a Stirling engine, it is the temperature difference.

But is this really true?

Would a heat engine REALLY run better or more efficiently between 0 and 100 K where the gas molecules are nearly motionless, than between 1000 and 1099 K ?

What does the math say ?

0 to 100 = 100% efficiency

1000 to 1099 = 9% efficiency

Does the math really reflect reality?

[dlaliberte]

Maybe the efficiency, based on the heat difference, is a rate of transfer of energy from the hot side to the cold side, or to work. And with lower temperature on the hot side, there is less energy that can be transferred, so even if two engines have the same efficiency, the one running with less energy will run slower because there is less energy to transfer.

As a rate of transfer, this doesn't mean that only a percentage of the heat energy can be converted to work, but that we can only do the conversion at a certain rate. And maybe people got confused about this rate since a leaky engine will also lose energy at a similar rate.

[Tom Booth]

Maybe the efficiency, based on the heat difference, is a rate of transfer of energy from the hot side to the cold side, or to work. And with lower temperature on the hot side, there is less energy that can be transferred, so even if two engines have the same efficiency, the one running with less energy will run slower because there is less energy to transfer.

As a rate of transfer, this doesn't mean that only a percentage of the heat energy can be converted to work, but that we can only do the conversion at a certain rate. And maybe people got confused about this rate since a leaky engine will also lose energy at a similar rate.

I agree considering Carnot "efficiency" a percentage makes little, if any sense. How exactly do you get a percentage from the relative temperature of what is supposed to be an "inexhaustible reservoir"

Originally I don't think Carnot ever used the term "efficiency". He meant simply that you can get more power from a waterfall that falls further, he imagined the ∆T as a similar fall of the "caloric" fluid.

Trying to reinterpret that nonsense has just lead to additional more convoluted nonsense

IMO the whole proposition/theory should be tossed out altogether.

[dlaliberte]

I should have said that the current belief is the efficiency number is a fraction (or percentage) of the energy that is transferred into the hot side of the engine, not a fraction of all the energy that is available to be transferred through. And the belief is that only that fraction of the energy transferred through can be converted to work, so the rest must be exhausted to the cold side.

But your evidence is that the cold side does not have to warm up as much as would be required to account for the larger fraction of wasted heat. So if the efficiency formula is at all valid, it would have to be reinterpreted as a rate of transfer of the energy that is transferred through the engine, regardless how much energy might be available to be transferred through. And as a rate of transfer, then we could compute how long it would take for some amount of available energy to be transferred through.

But despite all this, I am not actually so concerned at this point in figuring out exactly what the standard belief is, and more interested in just showing that a much higher fraction of the energy transferred into the engine can be converted to work. Once that is firmly established, then we can deal with reinterpreting the standard efficiency formula or creating a new one.

[Tom Booth]

Who knows what Carnot or Clausius or whomever might have been driving at, what I see being actively taught as thermodynamics today is:

The % from absolute zero to Th represented by the ∆T dictates the maximum percentage of the heat actually supplied to the engine that can be converted to work.

Seems like saying if I have a water wheel that has one gallon buckets, if the wheel diameter only measures 20 feet and it is roughly 9.5 million feet to the center of the earth then only 1/475,000 part of each gallon of water can be usefully employed for producing work.

While it is true, the bigger the water wheel, the more energy can be derived, equating the ratio of the diameter of the earth to the diameter of the water wheel as a determinant of efficiency is at best unproven with no theoretical basis and at worst, just fanciful nonsense.

I think, likewise, relating engine efficiency with the ratio of the ∆T with the difference between T hot and zero Kelvin has no rational basis.