Talk:Coefficient of performance

Derivation Section - Fixes needed?

I would appreciate someone expanding on the section called "Derivation" and fix what appears to be some misleading info.

1) Should section be renamed? This section seems aimed at showing COP in terms of Th and Tc for an ideal engine. OK, but I wonder if "Derivation" is the right name of the section.

2) Equation subscript error? The section substitutes W=Qh-Qc into the starting definition COP.heating=Q.h/W, to find COP.heating = Qh/(Qh-Qc). Then for the perfect engine (Carnot) the section says COP.heating = Th/(Th-Tc). If I have the concept right, the equation subscript should add .ideal to show COP.heating.ideal, to avoid confusing it with COP.heating in the previous section.

3) Can section be updated to show a real world compressor efficiency factor variable? The equations for COP.heating using Th and TC would give me a more complete understanding if it were expanded upon to show an equation for the non-ideal world that shows an efficiency factor of a real world compressor. I think I am looking for an equation along the lines of: COP.heating.nonideal = (equation to be determined by editor using variables Th, Tc, and some sort of efficiency factor).

4) The COP.cooling equation seems wrong. The equation says COP.cooling = Qc/(Qh-Qc) = Tc/(Th-Tc) If I have the concept right, the last equivalency [Qc/(Qh-Qc) = Tc/(Th-Tc)] is only true for the perfect engine and left me confused on the definition of COP. — Preceding unsigned comment added by 2601:283:4204:d6d0:98f5:bd89:44a8:dd53 (talk) 17:23, 7 June 2020 (UTC)[reply]

The equation is correct. Coefficient of performance is only applicable to refrigerators and heat pumps; it is never applicable to a heat engine. The figure of merit for a heat engine is its thermal efficiency. COP is greater than unity (one) for every refrigerator and heat pump; and thermal efficiency is less than unity for every heat engine.

You may not have the concept right. Nothing in this article is applicable to heat engines. Read the article again, very carefully. If you still have a question about it, post your question here again. Dolphin (t) 23:01, 8 June 2020 (UTC)[reply]

The equations that are based on Q and W; and those based on Qh and Qc, are applicable to all refrigerators and heat pumps - ideal and non-ideal. The equations based on Th and Tc are only applicable to Carnot devices. All Carnot cycles comprise two isothermal processes and two isentropic processes so, for Carnot cycles:

Qh/Qc = Th/Tc and Qh — Qc = Th — Tc. Dolphin (t) 23:20, 8 June 2020 (UTC)[reply]

Coefficient of performance

AN ERROR, I THINK: I don't have time to fix this right now, but the article's statement about Qc/Tc = Qh/Th is NOT generally true (actually never true I think) for real-world devices. I believe (though I'd need to review the algebra a little bit) that this proportionality is, rather, a statement that applies to the thermodynamically ideal, best-theoretically-possible performance of an idealized device, i.e. the best the performance could get before it actually violated the Second Law of Thermodynamics -- that is, I think it's a corollary of Carnot's theorem about the efficiency of heat engines (heat pumps just being heat engines driven backward, so following the same physical laws).

To see why this proportionality doesn't apply to real machines, consider that any real machine is going to have mechanical losses in it that convert mechanical work directly into heat. In addition, it will have its heat transfers occurring across substantial temperature differences (as opposed to heat passing reversibly across infinitesimal differences, as required by Carnot's theorem -- which shows how idealized a thought experiment Carnot's theorem is, because that process would take infinite time). How much of these non-idealities occur will vary with each particular machine. So you could consider a number of sample machines, all running between the same pair of cold and warm reservoirs, and all drawing heat from the cold one at the same rate. The MINIMUM amount of shaft work they require will be given by the Carnot Theorem, whose result is expressed in terms of the hot and cold (absolute) temperatures. But then suppose that these machines have varying amounts of mechanical losses and thermal irreversibilities in them. These will all add to the shaft work required, and will also add to the heat getting expelled at the hot side. So when these losses are added to the picture, the proportionality of heat flow to temperature breaks down; and in general (because of all sorts of these losses inside real machines) the COPs of actual machines you can buy are far below the ideal number given by the ratio of temperatures.

crispin_miller@mindspring.com

The above poster is correct, but I don't know how to prove the exact mathematical reasoning for it. Would it be sufficient to state in the article something along the lines of: "For a Carnot refrigerator, Qhot/Thot=Qccold/Tcold..."? I'll go ahead and make the change, but someone with more knowledge, feel free to go in and add more detail.

Coefficient of performance for different refrigerants, etc.

Can somebody please provide details of variation of coefficient of Performance for different refrigerants, for different evaporator and condenser temperatures."

Usage of COP

Can someone explain how a COP is used in industry/science? Is it just simply a unit for comparing two or more devices? —Preceding unsigned comment added by 206.174.82.201 (talk) 19:56, 19 August 2008 (UTC)[reply]

"the COP is the ratio of the heat removed from the cold reservoir plus the heat added to the hot reservoir by the input work to input work" - as far as i understand, it means

COP_{heating}={\frac {Q_{hot}-Q_{cold}+W}{W}}\quad (Q_{c}=Q_{hot}-Q_{cold})

For ideal machine

W=Q_{hot}-Q_{cold}

, so

COP_{heating}={\frac {Q_{hot}-Q_{cold}+W}{W}}={\frac {W+W}{W}}=2

, hence the Derivation section of the article looks like a bullshit. 193.110.114.207 (talk) 17:08, 7 February 2011 (UTC)[reply]

Well -- I agree that the sentence you're trying to make sense of was not completely clear, even in its current version that moves "to the input work" toward the beginning (to avoid ending with "by the input work to input work") -- it now reads "the COP is the ratio to input work of the heat removed from the cold reservoir plus the heat added to the hot reservoir by the input work" -- but the bookkeeping it's trying to describe is different from the equation you've written for it. "Plus the heat added to the hot reservoir by the input work" is not meant to name an amount of energy Qhot PLUS W, it's meant to name W alone -- perhaps it might be better phrased as something like "plus the heat added to the process by the input work itself." Also while the sign conventions do get confusing when one flow is defined as heat coming out of the cold reservoir and one is defined as heat going into the hot reservoir, what the definition is concerned with is the absolute amounts, so unless you mean for the value of Qcold to have a negative sign (and then mean to make the value positive by subtracting a negative), you don't want to be indicating a subtraction.

All that this is saying is that when heating is the result desired, the Q that applies is bigger than the Q that applies when cooling is the result desired, i. e., Qhot > Qcold, because Qhot = Qcold + W. So the equation meant by the sentence you quote is just

COP_{heating}={\frac {Q_{cold}+W}{W}}

whereas in comparison

COP_{cooling}={\frac {Q_{cold}}{W}}

Crispin Miller — Preceding unsigned comment added by 96.237.236.153 (talk) 21:04, 22 July 2012 (UTC)[reply]

Sudden/Massive change in content

Can someone please explain why the massive change in content, as seen here: http://en.wikipedia.org/w/index.php?title=Coefficient_of_performance&diff=551658073&oldid=541953253 is warranted?

The replacement is poorly formatted, and is riddled with bad English and awkward phrasing, and a shit-ton of material has just been mass-deleted. 124.148.225.248 (talk) 12:18, 7 May 2013 (UTC)[reply]

The current content is strange at least. The guy says :

"The equation is: COP > Q/W"

A scientist (or engineer) would have never said that. The above thing is maybe relation or law or axiom, or whatever you want, but its not an equation.

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Impossible?

Re "Double and triple effect chillers are significantly more efficient than single effect, and can surpass a COP of 1."

Doesn't the second law of thermodynamics prevent that?

--Mortense (talk) 12:45, 26 September 2020 (UTC)[reply]