Final answer:
The minimum work required by a refrigerator to extract 50 J per cycle from a space at -10°C and exhaust heat at 25°C is calculated using Carnot efficiency. The work required is derived from the temperatures of the heat exchange and the second law of thermodynamics, which dictates that the work will always be more than the energy extracted due to inevitable inefficiencies.
Step-by-step explanation:
To calculate the minimum work required by a refrigerator to extract heat, we rely on thermodynamic principles. Given that the refrigerator extracts 50 J per cycle from inside at a temperature of -10°C (263 K) and rejects heat at 25°C (298 K), we can use the second law of thermodynamics and the concept of Carnot efficiency. For a Carnot refrigerator, efficiency is determined by the temperatures of the heat reservoirs it interacts with.
The Carnot efficiency (e) is defined as e = 1 - (T_Cold/T_Hot), thus the efficiency for this refrigerator would be e = 1 - (263/298). After finding the efficiency, we can then calculate the work input (W) needed for each cycle using W = Q_Cold/e, where Q_Cold is the amount of heat extracted from the cold space.
Upon computing, we find that the work needed for each cycle is more than the energy extracted (50 J) due to the laws of thermodynamics, which ensure that no real refrigerator can be perfectly efficient. To ensure safe and proper operation of refrigeration equipment, always ventilate the area and follow manufacturers' instructions, as indicated in safety guidelines for handling substances that might release pollutants or require specific conditions for operation.