But per Carnot, maintaining a fixed temperature differential against a fixed thermal resistance is cheaper (requires less work) at a higher temperature (1/(1-(Tcold/Thot)) is the carnot-limited "coefficient of performance" for a heat pump).
So theoretically they should be able to maintain the design differential even at higher outdoor temperatures, causing indoor temperatures to raise from ~21°C to 26°C comparing the "still works at 35°C" and "40°C happens regular in $current_year".
Also, people often don't realize that the temperatures that matter thermodynamically are degrees Kelvin, not Celsius. 30 below 0 is 243K; 20 above (room temperature) is 293K. The coefficient of performance for a Carnot heat pump at those temperatures is 293 / (293 - 243) ~= 5.86; that means that one joule of work will transfer 5.86 joules of heat. This isn't great, but it's less of a difference than people would expect given our subjective experience of how cold -30C is. The coefficient of performance for a heat pump trying to heat 0C ambient temperatures up to room temperature (or alternatively, an air conditioner cooling 40C temperatures to room temperature) is 293 / (293 / 273) = 14.65, so your heat pump in Calgary will be maybe 2.5x less efficient than one in NYC. Drill below the frost line, like you suggest, and you'll get similar efficiencies regardless of where you are.
The Carnot limit of heat pump heating from -25C (-13F) to 20C (68F) is over 6.5. That's 650% efficient. There's a lot of heat in our 'cold' air. If you're going to try to claim 'thermal dynamics' [sic] you should at least do the math on it first:
The way modern heat pumps work, I can't answer your question yet. What's the outside temperature? Let's say that taking your room from 15C to 20C takes 1.0 energy unit. If it's 15C outside, then I can use a heat pump to gain a bunch of efficiency, say only using 0.2 units of electricity to heat up the inside by one unit. If it's 25C outside, I can do the same in reverse, but I do have to also cool the A/C. We'll say taking the room from 25C to 20C when it's 25C outside takes 0.25 units.
The problem happens when there is a big difference in outside temperature. All of the gains of heat pumps disappear. So cooling from 25C inside to 20C inside when it's 30C outside might take 0.5 units of energy, which is a pretty common case. Heaters generally have to deal with much bigger swings, though. It's not uncommon to heat from 15C inside to 20C inside while the outside is at -10C, which takes (asymptotically approaching) 1.0 energy unit.
So the inefficiency of the A/C producing heat does matter, but not as much as the difference between the desired temperature and the outside temperature. The rate of heat transfer of the house also depends on the difference in temperature. Keeping a house 10C cooler than ambient takes less energy than keeping a house 20C hotter than ambient.
Considering that temperatures on Earth vary from about -90C to 50C, and humans like to keep indoor temps around 20C, cooling is generally more efficient than heating.
if carnot diagram is drawn, it will show nothing cheap.
try to recall thermal dynamics taught many years ago.
heat pump works well when the exterior temp differ not much from interior temp.
Namely for places like Cal and Tex, still the winters need heating.
if it is freezing temperature, much energy will be spent on the mechanical part. Literally an electric heater but maybe less efficient than an interior heater by your knee. Not very logically coherent. Recall the professor's words.
thermal dynamics is a very chilling subject, basically demysterifying fundamnetally and establish a solid view of engineering. Its experiments were repeated by millions of engineering students, the rules derived still hold firmly on earth so far.
Heat pumps can heat in cold temperatures, but at decreasing efficiency or COP, which is how much heat you pump from the outside divided by how much heat it took to run the compressor. The theoretical COP is infinite if $\Delta T = 0$, and you can use Carnot to calculate the upper limit otherwise.
Now, the whole point of having a heat pump is to have a COP (much) greater than 1 (an excellent furnace has a COP just below 1). Once the difference in ambientT-outsideT becomes large, you approach COP = 1. The heat pumps manufacture will report the actual COP vs $\Delta T$; that is including losses, vs theoretical.
Now, a heat pump runs (almost certainly) on main power, and the alternative (usually) on natural gas.
It's a simple matter, therefore, to calculate the CO2 and financial cross over point for a heat pump vs. a furnace. I did that calculation when I had one installed in my house (for ductless AC; heating is an added bonus). It's somewhere between about -5 or -10 C, if I recall correctly.
Sure, a heat pump can work at -25C but it'll cost more and emit more CO2. This is because, dumb Joule for dumb Joule, natural gas piped to my home is cheaper and cleaner than the same natural gas piped and burned in a thermal power station [1]
In my small corner of the world this means that the heat pump is usually better to run than my furnace. But I keep my furnace on anyway, basically set on idle because there is no way that a heat pump can compete with a furnace on reliability. I don't want burst water pipes.
In Europe, heat pumps make 100% sense. Even though Europe is significantly north of the US, the winters are mild with few stretches below 0. In contrast, in some parts of the midwest long stretches of -20 C are not impossible. A week at -20 is not unheard of. In this situation Id be loath to have to rely exclusively on heat pumps.
[1] actually coal in my case so I fudged it in favor of the HP. Coal is also the case for many of you as well because coal is typically used as marginal power during the winter since it's easy to store and gas pipelines' pressure drop in the winter due to home demand.
Just guessing but maybe heat pumps have a lower max power rating, so that you'd need better insulation to reach a desired temperature during colder days.
Modern heat pumps are still highly efficient at 40F (4C) the coefficient of performance is 4+ at this temperature. We switched from an hybrid set to a full-electric setup (also PV and solar thermal) and are super happy with (live in Amsterdam, so regularly goes below 40F/4C). There's probably something wrong with your neighbors setup.
I'd say practical limits of current models are probably around -20C (-4F)
If you're interested here is an example datasheet[1] of an air to water heat pump (2018) (using Celsius here):
Mitsubishi PUHZ-SHW112YAA Guaranteed operating range (outdoor): Heating: -28 to +21 Domestic hot water: -28 to +35
On page 108 you can find the actual co-efficient of performance (COP) for different outside temperatures and inside water heating temperatures. As an example: at -10 and an water temperature for heating at 25 you still get a COP of 3+. That means that 100% electricity moves 300% of heat into your house.
I think he's a bit mixed up. That rule of thumb is for when you're pumping from cold area to warm area, which is what you usually do. For instance from outside (10 degrees C air) to inside (21 degrees C air). Then you can see how the performance would drop as the differential changes.
A heat pump should perform really well when the place it's pumping from is high temperature like this. Pumping from 19 degrees C to a house that's 21 degrees C is going to be great.
Obviously things will be much less efficient if the heat pump were being used to warm the Underground from outside air (5 degrees C) but no one's going to do that! The Underground air is going to go into the home (which is at 21 degrees C). The street air isn't in the picture at all.
A heat pump is much more effective if you only have a small temperature difference [0]. If your house is well insulated and you have underfloor heating, you can heat your house with 40°C (sorry for European units) water to keep it warm inside. If you have poor insulation and small heating elements, you need much hotter water (>60°C).
A heat pump can have a carnot efficiency (theoretically achievable efficiency) of >10 to warm water from 20 to 40 degrees, but only ~5 if you have to heat it from 20 to 60 degrees (not sure about the numbers, but you get the idea).
Yeah, depending on your climate, a heat pump can have a Coefficient of Performance [1] of like 3.5. If you don’t take this into account and just take “natural gas in therms => kWh” it often seems like a heat pump would be a large increase. Divide by 3 and it’s suddenly much better :).
Heat pump efficiency drops as the difference between the indoor and outdoor temperature grows. No one specifically cares about the freezing point of water for this, but it’s a good proxy for “big temperature difference”.
Heat pumps become less efficient as the temperature differential across them increases, around 2% less efficient for every 1°C increase. If it's 5°C at street level and 19°C in the tunnels, that's a 14°C difference or around 28%.
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