According to the second law of thermodynamics, what must be done to transfer heat from a cooler system to a hotter one?

The second law of thermodynamics states that heat naturally flows from a hotter object to a cooler one, and not the reverse, unless external work is applied. To transfer heat from a cooler system to a hotter system, energy in the form of work is required to move the heat against its natural flow. This principle is utilized in refrigeration and heat pump systems, where work is done by a compressor to extract heat from a cooler area and reject it into a warmer area.

In this context, the requirement for work highlights the concept of energy efficiency and the direction of heat transfer, emphasizing that it is not possible for heat to flow in the opposite direction without intervention. This aligns with the basic tenets of thermodynamic processes and reflects the necessity of external energy input for heat transfer against its spontaneous direction.