By itself, heat energy goes from an object with high temperature to an object with lower temperature.

Refrigerators have to pump heat backwards, from low temperature inside to higher temperature outside. They do this by exploiting a behavior that gases have, if you compress them they heat up, and if you let them expand they cool down.

So the refrigerator compressor compresses the gas to high pressure (and very hot), and then a fan is used to blow room-temperature air at the radiator containing this hot gas, to cool it down to room temperature. The room where you have the refrigerator gets hotter as a result.

Then inside the pipes in the refrigerator, the gas is allowed to decompress. The gas goes very cold as a result, and a fan inside the refrigerator blows air inside the refrigerator compartments over the very cold pipes, chilling the inside and warming up the pipes.

Then the gas is compressed again and the whole process is repeated.

Gasses heat up when they're compressed (squeezed) and cool down when they expand. If you push gas around in a loop, and you have half the loop set up so that it compresses the gas, and in the other half you expand it, you'll have a loop with a hot side and a cold side.

Refrigerators work by using a loop like the one I described above. They put the cold side in the box and the hot side outside the box. Because the cold side is colder than the food and air inside the box, it absorbs some heat. That heat moves with the gas to the hot side, and because the hot side is hotter than the surrounding air it expels some of the heat it's gathered, cooling the gasses again.

Continuously moving heat from inside the box to outside the box means it stays cold and keeps your food chilled.

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If you have a gas under pressure and you release the pressure, the gas cools down as it expands. So the refrigerator has a setup whereby it compresses a bunch of gas in a part of the system outside of the fridge, and depressurizes that gas in a part of the system inside the fridge. So, heat is released outside of the fridge and the inside of the fridge is allowed to get very cold. The fridge will have a thermostat that determines when to run or when to stay idle, so that things don't get too cold.

When you compress a gas - say, a volume the size size of a beachball and it squeeze it into a volume the size of a golf ball - also condenses all of the heat that was in the gas in the beachball into the golf ball size. This makes the compressed golf ball volume hotter than when it was the size of a beachball. If you cool the golf ball down to room temp using a fan, then release that gas back into the beachball, the beachball will be much colder than room temp.

That’s how refrigeration works, in principle. In practice, the gas is a special gas that works more efficiently than air, and the process of compression-cooling-decompression runs in a continuous loop (as long as the compressor is running).

Compress a gas and it heats up. If you dump that heat somewhere, then decompress the gas, it gets very cold. Run this cold gas through your fridge and it absorbs heat from the air and food inside. Recompress the gas, dump the heat and repeat the cycle.

Ever used a cooling spray, or sprayed yourself with liquid butane while filling a lighter? The evaporating liquid carries away a lot of heat, so it feels cold.

Refrigerators do the same thing essentially, but in a closed tube, and then they recompress the evaporated gas to squeeze the heat out (this happens in the warm tubes you'll find on the outside rear of the fridge), so that it can go around and work as a cooling spray again.