Talk:Coefficient of performance
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[edit] 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.
Can somebody please provide details of variation of coefficient of Performance for different refrigerants, for different evaporator and condenser temperatures."
