Tom Booth wrote: ↑Wed Oct 02, 2024 10:28 am
Fool wrote: ↑Wed Oct 02, 2024 7:49 am
Tom Booth wrote:As said before, "efficiency" is a term with various different applications, meanings and definitions. I've never gotten a clear answer about what "efficiency" the so-called Carnot Limit equation uses, or is supposed to represent, which comes in handy for you 2nd Law advocates who can then change the definition willy nilly to suit your argument at any given time
Because Tom Booth can't follow simple definitions of efficiency, the rest of us aren't allowed to use it in any equations... Many people understand it. It's easy to follow. Definitions are given. Your inabilities have been demonstrated often here. Proves nothing. Zero cohesive mathematics from you. Take some college level math courses, or even highschool level math courses. Get good instruction.
OK, please answer this:
Does "Carnot efficiency" include friction as part of the "rejected" so-called "waste heat" or not?
If you can find an authoritative reference I'd be very grateful.
Likely though, I could find you as many that say the opposite.
Supposedly the Carnot engine discounts friction, so logically so does the "Carnot limit" though many references include it as part of the heat "rejected".
If so, how can "friction" be precisely calculated by the ∆T?
Please resolve this, if you can, as I've seen as many references say one opinion as the other, and I think you have flip flopped on the subject as well.
Argument from authority is a logical fallacy.
https://en.m.wikipedia.org/wiki/Argument_from_authority
I hope you will notice the contradicting points in that web page. It's a logical fallacy but, "likely to be correct if the authority is a real and pertinent intellectual authority". When authorities appear to clash using them is definitely a fallacy. Even though we are not going to put forth any data about clashing authorities or if they even are an authority, let us not use them for this discussion.
We are going to have to come to a conclusion on this using mathematics, logic and definitions.
Definition: The Carnot limit is defined as n=(Th -Tc)/Th. For ideal cycles, real cycles, cycles drawn on a PV diagram, even measured indicator.diagrams, and measured heat in and work output, to be the perfect maximum efficiency that could ever be expected from a perfect heat engine running in a cycle, with temperature limits Th and Tc. It must have a cycle that starts at a specific pressure, and volume, which also is a specific temperature, and it must also have a set cyclic working specific gas mass open or closed system. In other words the path drawn on a PV diagram must start and end at the same point and enclose a smooth area with zero breaks.
Yes it is my description in my own words as to what the definition of a Carnot limit is limited to. Right or wrong it gives a footing for our discussion. We can discuss any differences we may have on this definition. We may discuss any apparent deviations from this definition that might crop up in the following discourse.
Use the following for a 'more' authoritative description:
https://en.m.wikipedia.org/wiki/Carnot% ... odynamics)
It boils down to the same equation for 'n' efficiency.
Mathematics: From the above definition the only mathematics for the Carnot limit is: n=(Th -Tc)/Th. That's it. Case closed. Even though there can be tons of mathematical calculations leading up to that equation, the end result is that simple equation.
Logic: That equation has only efficiency as the dependent variable and temperatures as the independent variable. It doesn't have friction in it. In fact it doesn't have either of the two thermodynamic variables pressure or volume in it. It is devoid of size, windage, pumping losses, pressure, heat, heat in, heat out, internal energy, displacer shape pancake or sausage, direction of rotation, North or South, up stream, down stream, kinematics, computers, PV path shape, you get the point. Friction is not a variable.
The Carnot efficiency is only dependent on temperature and the binding definition. Definition? Whoa, slow down. Yes the definition limits it to systems that cycle.
At this point I'd like to compare it to the maximum sized house that can be built from a single sheet of plywood. In the ideal realm the sphere is the shape with maximum volume to minimum material or surface area. So we equate the surface area of plywood 4'x8', to the surface area of a sphere 4πr^2, to get the radius, then calculate volume of the sphere, 4/3πr^3. Of course it is recognized that, it is impossible to build a perfect sphere from plywood. So we use it as a target. Cut the plywood into pieces. Assemble it into a sphere like box, see how it compares to a sphere. Then we modify it to be more convenient. Longer to be able to sleep in it taller to get in and out easier.
Derivation: Yes, equations are only as good as the mathematics use to derive them the Carnot formula can be derived several ways using mathematics. It has been derived from as simple as the first law: Qh=Qc-W. That is as simple as the first law gets. A whole lot more can be added to it, like Qf heat loss from friction, but it wasn't added. Adding it would not end in the maximum Carnot formula, so fiction is left out.
It also needs the ideal gas formula and heat capacity. PV=MRT and Q=CvMT. None of which has friction loss in them. Heat energy, work energy, temperature, gas property, and constant mass, yes. Friction no.
Usage: Here is were people, authorities, and even me, get confused, slip up, goof, become the fool. The Carnot limit is used for comparison to all real heat engines and heat pumps. It is the spherical-plywood-house gold standard. Unfortunately when measuring real engines all the extra inefficiencies get in the way. People sometimes try to circumvent that somewhat by comparing an indicator diagram to a Carnot or Stirling engine diagram, but even that has limitations. No one compares temperatures of the hot and cold plates to Carnot. All it would do, is tell a person what the Carnot limit is. It would tell nothing about heat flow, power, work, energy, friction, cycle path. Just temperature. When you insulate the cold plate and no change is noted, all that signifies is that the energy is flowing out in some or another way, or your attempted insulation is in error.
If work is measured, before and after insulation, any change in performance is of greater value. Dropping to almost zero means heat needs to get out. Significant increase in work output, an anomaly and unexpected, could just mean the heat is getting out faster, some way or another.
Does the perfect sphere include saw kerf when cutting up the plywood? No, but you will lose to that when trying to beat the volume of your plywood house even when comparing it to a perfect sphere.
Given all the losses a heat engine will have, it still won't beat the Carnot limit. A real engine with all its losses must have a measured overall efficiency, n=W/fuel, that is higher than the Carnot limit, before anyone will understand it. Measuring Th and Tc with insulation is inconclusive. Measure the work output, and the heat developed, becoming the heat to be supplied, to become an even smaller Qh also known as Qin. See how close it is to Carnot.
I'm find it challenging to answer your simple questions when it requires deeper in depth answers that you typically dismiss, deny, fail to address, and misunderstand. The above is still a mere simplification.
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