An inventor suggested that a house might be heated in the following manner: A system resembling a refrigerator draws heat from the Earth and rejects heat to the house. The inventor claimed that the heat supplied to the house can exceeds the work done by the engine of the system. What is your comment?

It is not possible, because there is no such engine which produces more than 100% efficiency. In accordance to Planck’s constant, it is impossible to extract heat from a single body and convert the whole of it to work. So, no series of processes is possible whose sole result is the absorption of heat from a thermal reservoir and the complete conversion of this energy to work. Some amount of heat has to be rejected to the sink. Hence whole of the extracted heat cannot be converted into work. There is a definite loss.
The supplied heat to the house will be less than the work done by the engine of the system. Thus the heat supplied to the house cannot exceed the work done by the engine of the system. Therefore it is not possible, which the inventor claimed that the heat supplied to the house can exceed the work done by the engine of the system