A simple heater (furnace) that burns fuel and delivers some fraction of the released chemical energy as useful thermal energy while discarding the remaining fraction as warm exhaust does have an efficiency associated with it, and that efficiency is necessarily less than one. Furnaces do not have a coefficient of performance.
A furnace is very different from a heat pump, which uses mechanical energy to move thermal energy from a cold place to a hot place.
Yes. Just saying it’s not wrong all the time. In fact, that’s the definition more people would recognise.
In my experience, physicists use the terms “efficiency,” “Carnot efficiency”, or “thermodynamic efficiency,” to refer to the same thing as “coefficient of performance.” The terminology is unimportant, the physics is the same. Whatever you call it, the efficiency of an ideal heat engine is the reciprocal of the efficiency of an ideal heat pump. It is the same thermodynamic cycle run in reverse.
Stirling Google are restricted (theoretically) by Carnot Performance - where efficiency gets better as the hot/cold basins have a larger distinction in warm range.
On the other hand, the Coefficient of Performance (COP) of a electric gets more intense as the hot/cold factors have a larger distinction in warm range.
Combining the two together outcomes as you’d expect- no free energy.
I don’t think that can be right - they can’t be interchangeable terms for the same thing, because the values and scales are different.
The Coefficient Of Performance for a heat pump may be 3, when the Carnot efficiency of that device may be something like 0.6
They’re not quite the same. Coefficeint of Performance is |Qc|/W, i.e. the amount of heat energy you expend per unit of work done. Efficiency is W/Qh, i.e. the amount of work produced per unit of heat you take into the system.
It’s precisely this conflict of terms that caused the argument; the other guy’s position comprises (paraphrased):
“A heat pump has a COP of 3 - that means for every kW of work used to run it, you get 3kW of heat out - it’s 300% efficient! - thus, a Stirling engine only needs to be 50% efficient and you can join the two together for a net surplus of work”
I think he’d be right if it wasn’t for one detail.
If you have a refrigerator, that takes in work W1 and expels heat Qc=3W1 into an engine as Qh, and that engine outputs work W2=.5Qh, then you’re generating energy from nowhere. It’s absolutely true, math-wise. There’s one teensy little problem, the heat engine also expels heat as exhaust, Qc2, which means the net heat of the system will rise. It takes more work to cool a system the farther apart the hot and cold reservoir’s temperatures are, so overall the the system is unsustainable because Qc1 is always decreasing, meaning Qh, the input to the heat engine, is always decreasing.
ETA: Wait, I got that a little wrong. Since it’s only expelling .5Qh as exhaust, the temperature of the refrigerator’s cold reservoir is lowering, and the temperature of the hot reservoir is rising, and then it will degrade like I said (since it takes more work to cool a reservoir the bigger the temperature difference between it and its output reservoir). This process does, indeed, increase entropy like it should.
I’m just confusing myself now, Qc is the INPUT to the fridge, not the output. It’s 4AM and I drew a picture, it is, indeed, unsustainable but my scanner is broken and I can’t put it into words.
I disagree. While mixing up COP with efficiency can cause some confusion, I think it’s mostly being nitpicky, they’re both basically referring to similar things at a system level (energy that I’m putting into the device divided by desired energy that I’m getting out)
The other guy’s primary fault is assuming that the “efficiency” for a heatpump or a stirling engine is static, whereas in actuality, if you had a (theoretical) 300% “efficient” heat pump, the absolute best efficiency you could get out of your theoretical stirling engine is 33.3%.
I think I can get the problem in a bite sized form - it is much the same as the pumping water explanation.
The flaw in the argument is “the Stirling engine only needs to be 50% efficient”. The answer here is that if you have a 300% efficient heat pump it cannot create a temperature difference that allows even a perfect Stirling engine to attain 50% efficiency.
The efficiency of the Stirling engine is bounded by the temperature difference between the hot and cold sides. This efficiency is bounded by 1 - T[sub]H[/sub]/T[sub]C[/sub]. It cannot get any better than this.
The heat pump might be 300% efficient at moving heat, but it can only do this for a limited temperature differential. The COP for a heat engine heating is:
COP = T[sub]H[/sub]/(T[sub]H[/sub] - T[sub]C[/sub])
As has been noted above - as the temperature difference for the heat pump decreases the COP rises, but as the difference decreases, the maximum efficiency of the Stirling engine falls.
A 300% COP heat pump is 3 = T[sub]H[/sub]/(T[sub]H[/sub] - T[sub]C[/sub])
So 3T[sub]H[/sub] - 3T[sub]C[/sub]) = T[sub]H[/sub] thus
2T[sub]H[/sub] = 3T[sub]C[/sub]
The best possible efficiency a Stirling engine with this temperature difference is thus:
1 - 2/3 = 33.3%
And guess what? - this isn’t the 50% the protagonist requires.
It doesn’t matter what the COP of the heat engine is - it can never create a temperature difference larger than is needed to make a Stirling engine efficient enough to power it (except in a perfect friction free universe, where it makes exactly the power needed, and exactly no excess.)
I think the confusion is over what that “300% efficiency” means. From what I understand, heat pumps are able to generate more heat from electricity than simply running the current through resistors by using work to move energy against the normal direction of heat flow. That is, they take heat from somewhere cold and but it somewhere hot. The amount of energy that is transferred is greater than the amount of energy it takes to effect the transfer, so the idea of pumping heat uphill is more energy efficient than just turning the energy into heat directly.
That doesn’t mean that you get a free source of energy though. You’re putting energy into that system in order for the heat current to be running the wrong way consistently. The amount of work it takes to move that amount of energy is greater than the amount of work that would be able to be extracted by a heat engine running on the difference in the temperature between the hot and cold sinks. That’s simply due to the basic laws of thermodynamics. All the extra energy that you moved uphill came from the cold sink, and made it colder (and if that’s what you wanted in the first place, you’d be calling it an air conditioner). If you could extract all the energy that was moved in the form of work (which you can’t anyway), you’d be left with your sinks at a lower temperature than you started with, which is not indefinitely sustainable. In reality, from what I understand, it’s not actually possible to extract energy such that the cold sink gets colder and you have a positive amount of work. You can only move heat, which is the most entropic form of energy, and trying to get it to do useful work will require taking a loss in efficiency greater than any efficiency in a system that moved the heat.
Oops, the eagle eyed will note a typo here - H and C are reversed. :mad: The rest of my earlier post should be OK. (The post won’t make sense unless H and C are put back correctly.)