Reversed Carnot refrigerator: The coefficient of performance (COP) in terms of absolute temperatures T1 (low) and T2 (high) is

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:

• Ideal, reversible cycle between T1 (evaporator temperature) and T2 (condenser temperature).
• No pressure drops or non-idealities.
• Temperatures in Kelvin (or Rankine).

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:

• T2/(T2 − T1) is for a heat pump COP, not a refrigerator.
• (T2 − T1)/T2 or /T1 and T1/T2 are not the Carnot refrigerator COP.

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)