Question

can you use a heat pump to provide the temperature difference to run a heat engine?
multiple choice
no, heat is not created.
yes, but the work generated by the heat engine will be less than the work used to run the heat pump.
yes, because heat engines are more efficient than heat pumps.
no, the heat supplied does not create a large enough temperature difference.

Explanation:

A heat pump requires work input to transfer heat from a low - temperature reservoir to a high - temperature reservoir. A heat engine operates between a high - temperature and a low - temperature reservoir and produces work. The second law of thermodynamics (Kelvin - Planck statement: No heat engine can operate in a cycle while transferring heat with a single reservoir) implies that we cannot have a net work output in a cycle if we only have one heat reservoir. When using a heat pump to create a temperature difference, the work input to the heat pump is greater than the work output of the heat engine (because of the inefficiencies in both devices and the fact that the heat pump needs to consume work to create the temperature difference).

Answer:

Yes, but the work generated by the heat engine will be less than the work used to run the heat pump.