Final answer:
Refrigeration systems have higher efficiency with a smaller temperature difference between the high and outdoor temperatures due to the Coefficient of Performance (COP), which indicates a more cost-effective and energy-efficient operation.
Step-by-step explanation:
Refrigerators, air conditioners, and heat pumps operate most cost-effectively with a small difference between the high temperature, T₁, and the outdoor temperature, To, because the efficiency of these systems is governed by the Coefficient of Performance (COP). The COP is crucial for determining how much cooling effect is achieved per unit of work input. Having a smaller temperature difference between T₁ and To reduces the work required to transport heat from the cooler to the warmer area, consequently increasing the COP and making the cycle more cost-effective and energy-efficient. In the case of refrigerants, recovering and properly managing them is essential due to environmental concerns, including their potential for ozone depletion and their status as greenhouse gases which contribute to global warming. Proper refrigerant management is also important for ensuring a stable supply of materials necessary to maintain refrigeration, which is essential for food storage, medical applications, and various industrial processes.