A Carnot heat pump maintains the temperature in a house at 20C on a day when the temperature outside is 5C. What is the coefficient of performance of the heat pump?

The coefficient of performance (COP) of the Carnot heat pump is 19.5.

The coefficient of performance of a typical heat pump in a british home is around 4.

There is obviously a huge difference between 4 and 19.5 - although a good chunk of this is explained by large temperature differentials in the condenser and evaporator, and a british desire to use a water heating loop.