Final answer:
Refrigerators, air conditioners, and heat pumps operate most cost-effectively for cycles with a small temperature difference between the cold and hot reservoirs. Purge units can help maintain a small temperature difference by removing non-condensable gases, including refrigerant, from the system.
Step-by-step explanation:
Refrigerators, air conditioners, and heat pumps operate most cost-effectively for cycles with a small difference between T₁ and To because the effectiveness or coefficient of performance (COP) of a refrigerator is measured by the heat removed from the cold reservoir divided by the work input. The smaller the temperature difference between the cold and hot reservoir, the higher the COP and the more efficient the device.
By discharging a low percentage of refrigerant with the air they remove, purge units can help maintain a small temperature difference. These units are designed to remove any non-condensable gases, including refrigerant, from the system. The presence of these gases can increase the temperature difference and reduce the efficiency of the refrigerator, air conditioner, or heat pump.
Overall, maintaining a small temperature difference is essential for optimizing the performance and energy efficiency of refrigeration and air conditioning systems.