My main issue is with the dictum that:
the second law of thermodynamics has a third form:
A Carnot engine operating between two given temperatures has the greatest possible efficiency of any heat engine operating between these two temperatures
.
The quote is lifted from this page directly:
https://courses.lumenlearning.com/physi ... -restated/
But any one of thousands of other citations making the same claim will do.
This assertion, I would offer, has absolutely no empirical foundation whatsoever. First of all, a "Carnot engine" is a theoretical construct. It is not a real engine, so no actual experimental comparison is possible to conclusively demonstrate the claim.
Second of all, the so-called "efficiency" of this theoretical Carnot engine was based on the known fallacy that heat is an "indestructable fluid".
Further, the mathematics for calculating "Carnot efficiency" were originally derived using the same flawed theoretical foundation, namely; that a heat engine derives power from heat in the same way a mill wheel derives power from a fall of water. A mill wheel takes in a quantity of water, which results in the turning of the wheel to output useful work and ALL the water is let out at a lower level. Likewise a heat engine takes in heat and the heat engine turns and produces useful work and the heat is let out at a lower
temperature.
We shall ignore mill wheels that use the undershot method, as there the analogy breaks down.
https://youtu.be/-JXLPRVkW24
No water is "lowered down" in this case (though some is raised) The water remains horizontal. Somewhere the water had been lowered, so it can now impart kinetic energy to the wheel, but it is not lowered by, or through the wheel. Similarly the sun imparted some energy to the atmosphere. That is now kinetic energy, not a "fluid".
This "lowering" of heat was not considered an analogy, though, it was considered an exact correspondence.
Carnot believed, at first, that heat was actually a fluid and that it was actually "let down" and just like water ALL of it let out at the lower temperature.
The power output of a mill wheel depends on the distance the water travels in being lowered, so the reasoning goes, or went, so, likewise the "efficiency" of a heat engine:
"depends only on the temperature difference"
On the basis of that reasoning, we have the formula:
Efficiency = (Qh - Qc)/Qh
From what exactly is that formula derived?
A completely "ideal", or in other words IMAGINARY engine that operates on a fallacious theory of heat.
For a little toy Stirling engine running on a cup of hot water that works out to, at best, somewhere around 20% "Carnot efficiency". And we are informed again, Carnot efficiency represents the efficiency of a "perfect" Carnot engine and that this "perfect" Carnot engine:: "has the greatest possible efficiency of any heat engine"
In reality then, the toy Stirling cannot hope to approach anywhere near 20% efficiency.
So again, how was this formula derived?
Efficiency = (Qh - Qc)/Qh
Is that equation based on any experimental work? Was it calculated on the basis of actual measurements? Temperature readings from actual engines? How was it proven? How was it verified? How was this "LAW" actually established as FACT?
What does it mean anyway?
Well, the "h" in the equation is the hot temperature, the "c" is the cold temperature. So we take the hot temperature and subtract from that the cold temperature and we get the temperature difference.
Wait a minute. The temperature difference? You mean, Carnot's original fallacious theory about the distance the bucket of water is lowered down by a water wheel?
Well, actually yes.
The heat is lowered from Th down to Tc and supposedly Qc/Qh=Tc/Th for reasons that are never explained but anyway, if we want to rewrite this temperature difference as an efficiency it needs to be in the form of a percentage so we take the temperature difference and divide that by the high temperature (or "all the heat" on the absolute scale)
So, this supposed "efficiency" is just the same old "height of the fall" or temperature difference written as a percentage of the absolute temperature scale.
So, we have gone directly from a fallacious theory of heat as a fluid to an equation based on the same known fallacy with ZERO experimental evidence to back it up.
On what basis exactly is this accepted as a "LAW".
Well.
Historically, nobody has ever succeeded in building a perpetual motion machine, so,...
So what?
So, in spite of being wrong in every other respect, heat is not a fluid, he SOMEHOW got it right.
Looking at this, I can only shake my head in disbelief.
20% of "all the heat" down to absolute zero is not the same thing as 20% of the heat required to bring a cup of water to a boil. Is it?
How do we equate "efficiency" with the temperature difference anyway? The one has nothing whatsoever to do with the other.
But, for arguments sake, let's try a few simple experiments.
How much of the actual heat in the cup of hot water is traveling up and out through the top of the engine?
Where is this 80% (or theoretically much more as this is no "perfect" Carnot engine) of the heat put to the engine actually going?
According to the prevailing theory, nearly all the heat, 80% or more, should be "rejected" by the engine to the "sink" or "cold reservoir" as waste heat.
But, experimentally, the top of my toy engine running on scalding hot boiled water for an hour remains cold to the touch the entire time.
With all that heat "rejected" to the "sink", the top of the engine, shouldn't the top of the engine be getting noticeably warmer?
So let's add some insulation anyway, just for laughs. Subjective experience about how something "feels" to the touch, warm or cold is meaningless.
Insulation results in the engine running faster.
Explanation?
The insulation actually increased the surface area so heat is actually dissipated faster.
Again, I can only shake my head in disbelief at the abject absurdity of it all.
Needless to say, I do not find the explanation that insulation conducts heat to air faster than aluminum very convincing.
What about acrylic?