Which of the following has the minimum value of COP for a given refrigeration effect?

Answer: Option D

For a given refrigeration effect, the system with the minimum value of Coefficient of Performance (COP) is the least efficient in terms of energy usage.

Option A: Reverse Carnot cycle. The Carnot cycle represents the maximum possible efficiency for a given temperature difference. Therefore, the reverse Carnot cycle would have the highest COP among the options.

Option B: Ordinary vapour-compression cycle. While not as efficient as the Carnot cycle, the vapour-compression cycle is commonly used in refrigeration systems and typically has a higher COP compared to other cycles.

Option C: Vapour-compression process with a reversible expansion engine. This would have a higher COP than the air refrigeration cycle because it involves a vapor-compression process.

Option D: Air refrigeration cycle. Air refrigeration cycles typically have the lowest COP among the options due to the lower efficiency of air as a refrigerant compared to vapor-compression cycles.

Therefore, the correct answer is Option D: Air refrigeration cycle.