Refrigeration cycles – COP ranking for a fixed refrigeration effect A refrigeration cycle is a reversed heat engine. For the same refrigeration effect, which cycle offers the maximum theoretical coefficient of performance (COP)?

Introduction / Context:
The COP is a key metric for comparing refrigeration cycles. It measures cooling provided per unit of work input. Theoretical limits help benchmark real systems such as vapor compression units and gas cycles.

Given Data / Assumptions:

• Same cold and hot reservoir temperatures for all cycles compared.
• Ideal, reversible operation defines the theoretical upper bound.
• Air and vapor compression cycles have practical irreversibilities.

Concept / Approach:
The Carnot refrigeration cycle is the ideal reversible cycle operating between two temperature reservoirs. Its COP for refrigeration is COP_Carnot = Tc / (Th − Tc), which is the maximum achievable for any cycle between the same reservoir temperatures. Real vapor compression systems that use an expansion valve suffer throttling losses; using an expansion (work-recovering) turbine improves COP but still falls short of the Carnot limit. Air cycles (reverse Brayton) typically have lower COPs at common refrigeration temperatures and pressures.

Step-by-Step Solution:

Verification / Alternative check:
Any real cycle must satisfy COP_real ≤ COP_Carnot. Textbook comparisons show Carnot > vapor compression with expander > vapor compression with valve > air cycle (typical conditions).

Why Other Options Are Wrong:

• Expansion valve: Irreversible throttling reduces COP.
• Air cycle: Generally lowest COP for given temperature lift.
• Expansion engine improves COP but cannot surpass Carnot.

Common Pitfalls:
Comparing COPs at different temperature lifts; always compare at identical Tc and Th.

Final Answer:
Carnot refrigeration cycle