Let me start by saying: In this household, we obey the Laws of Thermodynamics.
So I got into a nerd-fight in the comments section (on a video of a Stirling Engine in operation) of YouTube.
Someone posted (words to the effect) “Refrigerators are something like 300% efficient - so if you used the Stirling engine to power a heat pump, you could run the Stirling engine off the hot output of the heat pump and get free power!”
I (perhaps foolishly) replied to the effect: “nuh-uh - you can’t extract more work out of the temperature difference created by a heat pump than was expended in creating that temperature difference” - and I’m pretty sure I’m right.
The other guy continues to bang on about heat being all around us, and that fridges are 300% efficient. I really should just walk away, but I can’t.
So what is the deal with the energy-efficiency of heat pumps - I believe is is true that (for example) a 1kW heat pump can output the equivalent heating of a 3kW heater - but it can’t be doing more work.
So is it just that moving heat around requires less work than generating it from scratch? (and if so, there is less work available to be exploited in the finished configuration)
Stirling Engines are limited (theoretically) by Carnot Efficiency - where efficiency gets better as the hot/cold sinks have a bigger difference in temperature.
On the other hand, the Coefficient of Performance (COP) of a heat pump gets worse as the hot/cold sides have a bigger difference in temperature.
Combining the two together results as you’d expect- no free energy.
I think they’re both actually Carnot cycle devices - a heat pump is almost the exact reverse of a Stirling engine, both mechanically, and in terms of what they attempt to do.
Question is though: the Coefficient Of Performance is not the same thing as ‘efficiency’ in a thermodynamic sense, is it?
Either he’s trolling for nerds, or he’s too dumb to notice that nobody has actually done this yet. If there were free power to be had in that scenario, we would not be resorting to coal/wind/solar/nuclear/hydro for electrical power generation; we’d just have giant, pollution-free Stirling engine/heat-pump power plants dotting the country side.
I think he’s probably doing exactly that, in fact he pretty much dismissed my attempt to argue they’re not the same.
Also, looking at some of the other videos he’s commented on, they’re mostly the ‘free overunity magnet motor working!’ bullshit that’s all over YouTube.
Yes, the efficiency of a heat pump can be and often is greater than one. The thermodynamic limit for a heat pump acting as a heater (as opposed to a refrigerator) is 1/(1-TC/TH) where TC is the cold temperature (the input) and TH is the hot temperature (the output), and efficiency is the ratio of the heat output to the mechanical work. Heat pumps are very efficient when you’re only trying to heat a little bit, so TH and TC are close to each other.
An engine driven by heat (aka a heat engine) is just the opposite. The efficiency of a heat engines is always less than one and it is most efficient when there is a large difference in temperature. The thermodynamic limit is the reciprocal of the limit for a heat pump, i.e. (1-TC/TH).
So, like all schemes for perpetual motion, if you achieved the theoretical limit for the heat engine and the heat pump, and you didn’t lose any heat, you would be able to pump heat around forever, but you could not generate any energy. With the inevitable inefficiencies and losses, your perpetual motion machine will quickly gring to a halt.
You could make fridges more efficient by attaching a sterling engine to the back but the gain in efficiency wouldn’t be worth the cost of the engine. You could never make it over 100% efficient.
If you have a hot plate and cold plate touching, there will be an automatic heat transfer proportional to the difference in temperature. No energy input is required. This is somewhat obvious and no one thinks you can get perpetual motion out of it.
As the temperature difference goes to zero, so does the transfer rate. But it’s easy to imagine that you could move heat from one side to the other with very little effort–and in fact you can. You can move an arbitrarily high amount of heat across that plane with arbitrarily low energy. It just requires a gentle nudge–after all, it would go by itself if there was even the slightest difference in temperature.
Of course, this gets more difficult as the temperature difference goes the other way. It drops from “infinitely” efficient down to 1.0 or worse. And this is what makes perpetual motion impossible; if you’re going to run a heat engine on your reservoirs later on, you need a temperature differential. And to create that differential you had to run your heat pump in a low-efficiency regime. You left the high-efficiency regime as soon as you pumped enough heat to create a temperature difference.
Wouldn’t it just make it less efficient, period? A fridge is doing work to try to separate hot and cold; a Stirling engine is trying to equalise hot and cold, and outputting a bit of work. Both are lossy in their operation - so whatever extra work the Stirling engine contributed to the fridge motor would be more than outweighed by the additional heat it put back into the cold side.
A heat pump is like pumping water uphill. It simply pumps energy “uphill”. a stirling engine is like a hydro generator, extracting energy from water flowing downhill.
The analogy is not bad. A really efficient heat pump can pump a lot of heat/water a short distance uphill, so you get high volume (heat quantity) but not height(temperature). Same analogous efficiency.
Similarly, a Stirling engine like a generator, can get a bigger output from a small a small amount of water / heat dropping a long distance (big height/temperature difference) or a lot of water/heat energy a short distance.
Quite a good analogy. Furthermore - a whole heap of water, on its own, can do nothing. What you need is somewhere the water can flow to. Similarly, heat on its own can’t do work - its the flow of heat to a colder sink that does work.
That (as well as the conflation of COP/efficiency) is what’s confounding my debate opponent - he’s under the impression that a Stirling engine takes in heat and outputs ‘cold’. When actually, it equalises a temperature difference, and outputs work.
That’ll be a different definition/meaning of the word ‘efficient’ though - and not one appropriate to be compared against the Carnot efficiency of a Stirling engine (that would be like saying Tom Cruise nearly three times as tall - at 172cm, as Ron Perlman, who is only 72 inches in height)