Define the coefficient of performance (COP) for a refrigerator.

• A. COP = W / Q_L
• B. COP = Q_L / Q_H
• C. COP = Q_L / W
• D. COP = Q_H / W

Answer: (C)

The main idea is that the coefficient of performance for a refrigerator measures how much heat is removed from the cold space per unit of work you have to do. The useful effect is the heat taken out of the refrigerated area, Q_L, and the effort you supply is the work input, W. So the COP is defined as Q_L divided by W: COP = Q_L / W.

This aligns with the energy balance of a refrigeration cycle, where the heat dumped to the surroundings is Q_H = Q_L + W. A larger Q_L (more cooling) or a smaller W (less work) improves COP. The other expressions don’t describe the refrigerator’s performance in the same way: W/Q_L is the inverse of COP, Q_L/Q_H doesn’t quantify cooling performance per unit work, and Q_H/W is the COP for a heat pump, not a refrigerator.