Heat pumps: a critique

The British public have been remarkably reluctant to adopt heat pumps as a means of home heating. Some take this as a sign of British arrogance — they think everyone should take the experts’ word for it. But I think the widespread scepticism is a reassuring reflection of British scientific common sense.

I too am sceptical about heat pumps. (I’m a mitigated sceptic, like Hume, not a conspiracy theorist — conspiracy theorists aren’t sceptical enough, particularly about conspiracies).

If you’d prefer not to read the words of someone who disagrees with the experts, please take this as nothing more than a humble admission of being mistaken, and of the woeful lack of understanding that has led me — silly me! — into error. Please accept this instead as a sincere plea for an explanation: How can a heat pump conceivably heat a home more efficiently than a standard electrical heater?

My scepticism is inspired by the thought that a “miraculous” claim is being made about heat pumps. In effect, the claim is that heat pumps somehow manage to circumvent the Second Law of Thermodynamics.

The Second Law of Thermodynamics says that heat flows from warmer places/bodies to cooler places/bodies as a matter of statistical inevitability. This is the result of the dissipation of motion among molecules. To make heat do the reverse, i.e. to get it to flow from a cooler place (like outdoors) to a warmer place (like the interior of a house), energy has to be added to the system. (Because its entropy is decreasing, it can’t be a closed system.)

That’s why a fridge costs money to run: it creates more heat overall than it can extract from its interior. We usually don’t notice heat emanating from vanes tucked away at the back of the fridge, but having a fridge in a house actually warms the house up overall as it carries out its business of making one small part of the house cooler.

It’s often said that “a heat pump works like a fridge in reverse”. Perhaps to those who aren’t aware of a fridge’s overall heating effect, who suppose that a fridge “absorbs energy and cools things down”, the suggestion here is that its opposite must “release energy and heat things up”.

Alas, that’s the “miraculous” way of looking at things. A heat pump does work like a fridge in reverse, but the “reverse” aspect of it is that the warm vanes that were formerly at the back of the fridge have now become the radiators inside the house, and the heat source that was formerly the interior of the fridge has now moved outside the house altogether, preferably somewhere where it can absorb as much heat as possible from the ambient outdoor surroundings. Alas, like a fridge, a fridge-in-reverse still costs money to run.

Now most readers will protest that they never supposed for a moment that a heat pump releases energy by being “the opposite of a fridge, which absorbs energy”. These more sophisticated people might instead appeal to the way a fridge heats a house overall — and add that a heat pump must do it even better by having the “cold bit” (i.e. the heat source) completely outside the house.

So far so good. No one is saying that a heat pump can’t heat a house at all. But how efficiently can it do it? We find a clue in Wikipedia’s entry on “Coefficient of Performance”:

The coefficient of performance or COP (sometimes CP or CoP) of a heat pump, refrigerator or air conditioning system is a ratio of useful heating or cooling provided to work (energy) required[…] Higher COPs equate to higher efficiency, lower energy (power) consumption and thus lower operating costs.

The COP usually exceeds 1, especially in heat pumps, because, instead of just converting work to heat (which, if 100% efficient, would be a COP of 1), it pumps additional heat from a heat source to where the heat is required. Most air conditioners have a COP of 2.3 to 3.5. Less work is required to move heat than for conversion into heat, and because of this, heat pumps, air conditioners and refrigeration systems can have a coefficient of performance greater than one.

Sounds impressive! — Except, the coefficient of performance is a measure of efficiency of refrigeration, of efficiency in the creation of differences in temperature, not efficiency of heating, and heating is what we’re interested in. It’s the only thing we’re interested in: heating is what a heat pump is for.

Wikipedia tells us that a heat pump has a CoP of greater than 1 because “instead of just converting work to heat” it does something even better. But as far as I’m aware, no real-life refrigeration system has a CoP of less than 1, and no real-life heater converts work to heat. Heat engines convert heat to work, but the only thing I can think of that does the reverse are brakes, which heat up as they make a vehicle (or whatever) slow down. (Brakes would make pretty bad heaters, though, because they release other kinds of energy as well as heat, such as sound.)

Heaters convert various forms of energy (chemical, electrical, whatever) into heat. Some kinds of heater are pretty inefficient: for example, coal fires never burn their fuel completely and much of the heat goes up the chimney. But the form of energy they convert to heat is so cheap, they are economically worthwhile. Other kinds of heater are more efficient, but the form of energy they convert to heat is so expensive that they are not economically worthwhile.

For most of the brief period electrical energy has been available to us, it has been too expensive to be used as the main source of heat in houses. But if you are already in possession of electrical energy, there could hardly be a more efficient means of heating, because practically all of it gets converted to heat.

Most electric heaters work by passing a current through an element, which heats up because of its electrical resistance. As long as the element doesn’t glow brightly (releasing electromagnetic radiation other than infrared) and it doesn’t work as a radio transmitter, and doesn’t make much noise, or jump around the place excitedly, or anything wasteful of energy like that, practically all of the energy it uses is converted to heat. That is extremely efficient.

In fact it is so efficient, that I think it has to be be more efficient that a heat pump. How do I claim to know this? — In addition to heating the interior of a house, a heat pump creates a cold place outside the house. It’s cold because it’s the “heat source”, as far as the “pumping” of heat is concerned — it has heat drawn out of it, so that it falls to a lower temperature than its surroundings.

Because it’s at a lower temperature than its surroundings, there’s a temperature difference — and that could be exploited to run a heat engine. It might be a very weak sort of engine, perhaps nothing more powerful than one of those toy drinking birds. Nonetheless, it shows that energy went into creating it.

Suppose your next-door neighbour installs a heat pump. You have access to its cold “heat source”, and you run a heat engine off the difference in temperature between it and the warmer ambient surroundings. You could conceivably generate a tiny amount of electricity from it. But unlike stealing your neighbour’s home heating oil, you’d be doing him a favour, because you’d be adding heat to his heat source!

A heat pump does more than a simple electrical heater, which simply uses electrical energy to heat the indoors. The heat pump heats the indoors and in addition “refrigerates the outdoors”. It seems to me that the electrical energy needed to both heat the indoors and refrigerate the outdoors must exceed the electrical energy needed to simply heat the indoors and leave the outdoors alone, at the temperature it had in the first place. The colder outdoors is a wholly unwanted by-product of the heat pump’s work.

The extra energy that goes into creating it is what powers your heat engine. Where does the extra energy come from? — As far as I can tell, the only viable source is the electricity grid (in the UK, anyway).

So there you have it. A heat pump simply can’t be as efficient as an ordinary electric heater. Now, please tell me where I’ve gone wrong!

While I’m waiting for that, I think it’s worth noting that there are some interesting philosophical issues here. Thermodynamics is intimately connected with distinctly “deep” questions concerning the arrow of time, information, order, and probability. Where there are deep questions like these, there is the potential for profound error, even — perhaps especially — among experts. I know a world-renowned expert in probability theory who insisted that there was no advantage in “switching” while playing the Monty Hall Game. I know a world-renowned physicist who claimed that shuffled and unshuffled decks of cards have different weights. Of course, these two are no less experts in their fields for making mistakes — making mistakes is even more a part of what experts do than what non-experts do (because expert opinion is more abstract, more risky, more theoretical, etc., than common sense). Just think of the many experts of the past who put their energies into trying to square the circle or create perpetual motion machines.

What other lessons can we learn here?

The first and most obvious lesson is that there’s always the possibility — nay, likelihood — that I’m an idiot.

The second lesson is that the very term ‘heat pump’ is metaphorical, and it may be quite misleading. Heat can’t literally be pumped around like water, because energy can’t be re-identified as “the same”, the way bits of matter can. It makes sense to say that some of the water molecules in my current cup of coffee were once in Albert Einstein’s cup of coffee. But it doesn’t make sense to say that the heat energy that was once in my garden is now in my house. Energy constanty changes form — in a simple pendulum, kinetic energy turns into potential energy, and back again, over and over, as in a ticking clock. You can’t point to exactly where the energy is, or goes to, because it belongs to the entire system. I think people are taken in by the vague idea that after the heat pump has done its work shifting heat out of the garden and into the house, there is less energy in the garden. In fact (or so I claim) there is more energy overall in the garden, because its potential energy has increased to a greater extent than its heat energy has decreased. It contains less heat than before, but it’s like the thermal equivalent of a taut elastic band because of its increased potential energy. That’s why it can be used to run a heat engine, and why a heat pump inevitably costs more than simply heating the house.

A third lesson is that we tend to be more gullible when we are in the midst of things we don’t understand, guided only by the apparent authority of science and the apparent commanding power of morality.

The more esoteric concepts of thermodynamics — entropy, information, order, probability, etc. — weave a spell. They’re “hard to understand, but it’s science!” To many, this combination suspends disbelief, setting the stage for magic of the sort we’ve grown accustomed to in quantum physics, from entanglement to computing.

Where a moral issue is at stake — and currently one of the hot topics is the burning of fossil fuels — we clamber to be on the right side of it. When celebrities describe looking for oil in the North Sea as “an act of war against life on earth”, moral fervour runs high and critical reflection runs low. I suggest that some people see heat pumps as the green alternative to fossil fuels, authorized by the magic of science, and endorsed by the moral rectitude of environmentalism.






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