Difficulty: Easy
Correct Answer: COP = T1 / (T2 - T1)
Explanation:
Introduction / Context:
The reversed Carnot cycle represents the upper theoretical limit of refrigeration performance operating between a cold reservoir at T1 and a hot reservoir at T2 (absolute temperatures). Its COP provides a benchmark for real systems.
Given Data / Assumptions:
Concept / Approach:
For a refrigerator, COP = desired effect / input = Q_L / W. For the Carnot refrigerator, Q_L / Q_H = T1 / T2 and W = Q_H − Q_L. Combine relations to obtain COP in terms of T1 and T2 only.
Step-by-Step Derivation:
Verification / Alternative check:
Dimensionless check: temperatures cancel to a pure number; as T2 approaches T1, COP → ∞, consistent with the limiting reversible case.
Why Other Options Are Wrong:
Common Pitfalls:
Confusing refrigerator COP with heat pump COP; always confirm whether the numerator is Q_L or Q_H.
Final Answer:
COP = T1 / (T2 - T1)
Discussion & Comments