Trying my best to give an ELI5 answer:
If you push your palm down on your leg, you feel heat where your palm is pressing. It’s similar with gasses—if you put a gas in a cylinder and you have a device that can compress the gas, you will increase the pressure and the temperature of that gas. Now if you have a little tube connected to the cylinder, that hot pressurized gas will shoot out of the cylinder through the tube. If you make the tube really long, bunch it up, attach some metal that conducts heat really well to the tube, put that bunched up coil of hot tubes in your house, and blow air over it with a fan, the air will get hot! But all you did there was “move” the heat from the hot pressurized gas to the air that you blew over it through the metal that made up that tube because the tube was hotter than the air that blew over it and hot always moves to cold. The only “energy” that you’ve actually added so far was the electricity to compress that gas and to run the fan.
But what happened to the hot pressurized gas inside the tubes when you blew the cooler air over it and made it colder? Well it lost a lot of heat energy (moved it into the air) and it actually condensed into a liquid because gas needs a lot of energy to stay a gas. Just like when moisture in the air condenses on a cold soda can. So now it’s a lower temperature liquid in the tube but it’s still a high pressure. And since you don’t want that colder liquid inside anymore, you keep it moving outside. Because you want a net gain of heat inside the house and you want to be able to keep this cycle going and going.
Now outside in the tube we have a high pressure lower temperature liquid and we need to get it back to a gas. And how do you get a liquid to become a gas? You boil it! If you take that high pressure lower temperature liquid and smash it through a little hole/choke point in the tube, you’ll have a lot of pressure on one side of the choke point and a really really low pressure on the other side of the choke point. Once the liquid gets smashed through the hole it will get broken apart just like when it comes out of a spray bottle. This is the part that seems like magic—what was high pressure and lower temperature (but still pretty hot) on one side is now a really low temperature and really low pressure on the other side. So low that if you blow outside air over the same type of tubes surrounded by conductive metal as you had inside the house and with a similar fan, heat will actually move from the outside air into the tube and boil that low temperature/low pressure liquid immediately! And the outside air actually has enough heat energy in it to eventually boil it all so that it all turns back into a gas! And the cycle can continue!
I know it’s weird to think about cold outside air “boiling” a liquid, but that’s the magic/science of refrigerants and gasses. They can boil at crazy low temperatures and they can get to crazy high temperatures when they’re compressed.
The energy that you’re adding to that system is the electricity to compress the gas, to run the inside fan, to run the outside fan, and any other little components. So you’re only “consuming” enough electricity to help that heat move around. It’s kind of like how a bicycle helps a human move really far while not expending nearly as much energy as running.
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