It’s like mopping up water with a sponge, and wringing it out into a bucket.

Gas molecules bounce around in the space they’re in - and the more heat energy they have, the faster they go.

The more you compress the gas, the more often they hit the walls - like shrinking the room down on a bunch of angry bees: you’re going to be hearing a bunch more thudding noises per second.

And that rate-of-collisions is what we call temperature.

When you bring two things into contact, it’s the temperature difference, not the heat difference, that determines which way the energy difference evens out.

So if you squeeze a gas, its temperature rises, and the heat energy leaks out through the sides of the container it’s in, until the temperature drops down to match the surroundings. The molecules get slower and slower, until the rate of collision on the inside matches the rate on the outside.

Lots of slow bees in a small room, smaller number of fast bees outside, the rate of thudding noises on either side of the wall will be the same.

If you now decompress that gas, let it out into the original-sized space it was in before - the now slow-moving molecules collide with the walls a whole lot less often than they did before; their temperature is a lot lower.

That low-temperature gas is now really eager to soak up any heat energy that’s going.

Pump the gas over here, squeeze it down, heat gets dumped out of it.

Pump the gas over there, un-squeeze it, suck heat back up into it.

Rinse and repeat. Sponge and bucket.

It’s more efficient than a heater, for the same reason a bicycle courier can bring you a gigantic feast in 23 minutes: they didn’t have to make it, they just carried it. The heat energy isn’t coming from the power lines, it’s coming from the atmosphere. All the electricity is doing is moving it.