Final answer:
Option C. is correct. Refrigerators, air conditioners, and heat pumps are most cost-effective when there is a small temperature difference between Th and To, as this results in a higher Coefficient of Performance (COP) and therefore lower operating costs.
Step-by-step explanation:
Refrigerators, air conditioners, and heat pumps are most cost-effective when they operate with a small difference between the high temperature, Th, and the low temperature, To. This is because the efficiency of these systems heavily depends on the Coefficient of Performance (COP), which is a measure of their effectiveness. The COP for cooling devices is given by the ratio of the heat removed at the low temperature to the work input, and for heat pumps, it is the ratio of the heat delivered at the high temperature to the work input.
When the temperature difference, ΔT (Th - To), is small, the amount of work required to transfer a specific amount of heat is reduced. This improves the COP, thus making the system more efficient and cost-effective. Conversely, if the temperature difference is large, more work is needed to achieve the same amount of heat transfer, which decreases the COP and leads to higher operating costs.