You ever heard about how it takes as much energy to turn 100 C water into 100 C steam as it takes to heat 0 C water to 80 C water? That’s important, and called the enthalpy (or latent heat) of ~~fusion~~ vaporization. Phase changes consume (or release) a massive amount of heat energy. Have you ever used a can of air duster or a CO2 cartridge in food prep and it got super cold? That’s why. This is also how thunderstorms feed themselves, by the way. Also remember that compression and decompression will heat and cool fluids thanks to the ideal gas laws even without phase changes.
You can take advantage of this in a heat pump. One one side, you have a compressor, a pump that crushes some gaseous refrigerant (they can operate in wider temperatures than water) and heats it up in the process. Since it’s now hotter than its surroundings, it is run through a condenser – essentially a long conductive pipe that lets it radiate that heat until it’s the same temperature as outside. In this process, because it’s already under pressure, it condenses into a liquid, further releasing more heat.
Now it gets run into an evaporator where the opposite happens. The liquid gets dumped into a low pressure chamber, where it evaporates immediately. Remember the latent heat of ~~fusion~~ vaporization above? It absorbs an enormous amount of heat from its surroundings when it does so, just like your can of air duster. The now ambient temperature gas gets sent back to the compressor, where it starts over again.
Why is it more energy efficient? In a resistive heating element like your toaster, you can only ever get 100% of the heat you put in as electricity out again as heat. In a heat pump, you’re only moving heat, not generating it (compressor motor excepted). A motor converting electricity into fluid motion will move much, much more fluid and therefore more heat than the same amount of power heating a thick wire.
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