Final answer:
A heat pump is the system that provides both heating and cooling through the same ducts. It is efficient as it serves as both an air conditioner and a heating unit using a single set of ductwork, and its performance is optimized when the indoor and outdoor temperature difference is small.
Step-by-step explanation:
The system that delivers both heating and cooling through the same ducts is known as a heat pump. Heat pumps act as an air conditioner during hot periods and a heating unit during cold periods, making them exceptionally versatile. In the heating mode, the system moves thermal energy from outside the house into the interior space for warming. On the other hand, in the cooling mode, the heat pump extracts heat from inside the house and releases it outside, thus cooling the interior.
Electric heat pumps are efficient for this purpose as they can perform both to heat and cool a space, using the same ductwork to distribute conditioned air throughout the home. This efficiency often results in lower operational costs, especially when the temperature difference between the outside and inside (Th and To) is small, which is optimal for the Coefficient of Performance (COP) of heat pumps.