While going through the course I had one question. How does the refrigerator get significantly colder than the room if during the cycle the air is compressed, then the radiator brings the gas's temperature to equilibrium with the room and then the gas is expanded. Doesn't that mean that the expansion valve can only ever expand the gas to some degree above room temperature?
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Great question! The compressed refrigerant loses enough heat in the radiator that when it's expanded, its temperature is quite a bit lower than air temperature in the room.
It sounds like what may be confusing to you is why we compress the refrigerant in the first place. Why make it hot just to expand it and make it cold again? The primary reason for this is the inner workings of a refrigerator are cyclic. The refrigerant needs to end up in the same state that it was in initially.
In theory, you could cool a refrigerator by simply sending refrigerant through an expansion valve, the without doing any more to it, but then you'd end up with tons of expanded refrigerant that you'd just have to throw away. By compressing it, you can reuse it, as long as you let the excess heat go somewhere before you put it through the expansion value again.