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Why the efficiency of a refrigerator can be greater than 1

Answer: The efficiency of a heat engine and a refrigerator is not the same. Let me talk about the conceptual difference first. The efficiency of a heat engine refers to W/Q, which is the work W done by the heat engine to the outside world in the thermodynamic cycle, divided by the heat Q absorbed by the heat engine at the heat source. This value cannot be greater than 1 is the limit of the law of conservation of energy. The efficiency of the refrigerator refers to Q/W, Q is the heat absorbed from the cold source, and W is the work done by the outside to the heat engine in the thermodynamic cycle.

Why the efficiency of a refrigerator can be greater than 1

To use an analogy, a heat engine is like a river (the flow of heat flowing from a high-temperature heat source to a low-temperature cold source) that is intercepted and converted into mechanical energy. No matter how powerful the heat engine is, it can't directly cut off all the water in the river and then produce water out of thin air.

Correspondingly, the refrigerator is a porter responsible for transporting heat from a low-temperature cold source to a high-temperature heat source. What it does is not to intercept the flow but to transport it. We have to pay him the "price", that is, give it energy to make it do work, and then he can carry the heat. As long as the mechanical energy absorbed by the refrigerator (that is, the work done by the outside world on the refrigerator) and the thermal energy absorbed from the cold source are equal to the heat energy delivered to the high-temperature heat source, the law of conservation of energy will not be violated. Obviously, there is no restriction that "you cannot directly intercept the river and then produce water out of thin air", so the efficiency of the refrigerant can be greater than 1.