Refrigerators and heat pumps

The refrigerator or air conditioner is a machine designed to remove heat from the low temperature side and pump it to the high temperature side by doing some work on it. So the coefficient of performance, the efficiency is ouput divided by input. Here the input is the work provided, and the output is the extracted heat QL. Here is an example. We have a freezer at temperature of -20 degree celcius and the outside is 30 degree celcius. Heat is extracted from the low temperature side. We can schematically represent the freezer like this. When we take the machine as our system as before, the relationship between QH, QL and W is the same as before for the heat engine.

So the coefficient of performance, is TL over (TH-TL). For this specific cases between -20 degree and 30 degree, the coefficient of performance is 5.06. So QL is 5.06 times W provided. What does that mean? We can extract the heat more than the work we provided. Heat pump operates similar to refrigerator, but the purpose of heat pump is to deliver heat to high temperature side. Therefore, the efficiency is defined differently. Output here is the heat delivered to the high temperature side the -QH, and the input is the work provided. So the efficiency is TH over (TH-TL). If it operates between -20 degree and 30 degree, the efficiency is 6.06. It is a highly efficient method to heat up a room.