Refrigeration performance from energy flows: A condenser rejects 120 kW of heat while the compressor consumes 30 kW of shaft power. What is the coefficient of performance (COP) of the refrigeration system?

Introduction / Context:
The coefficient of performance (COP) of a refrigerator measures how much cooling effect is obtained per unit of input work. Interpreting heat rejection and compressor power correctly is fundamental for energy audits and sizing.

Given Data / Assumptions:

• Heat rejected at condenser, Q_H = 120 kW.
• Compressor power input, W = 30 kW.
• Steady-state operation with Q_H = Q_L + W.

Concept / Approach:
For a refrigerator, COP_R = Q_L / W, where Q_L is the cooling (evaporator) load. Since the condenser rejects the sum of the evaporator load and compressor work, we find Q_L by subtraction.

Step-by-Step Solution:

Verification / Alternative check:
The energy balance must hold: Q_H = 120 kW = 90 kW + 30 kW, which is satisfied. Typical COP values of 2–5 are realistic for many systems, so 3 is plausible.

Why Other Options Are Wrong:

1/4 and 1/3 invert the ratio; they would correspond to W > Q_L, which contradicts the data.4 would require Q_L = 120 kW with W = 30 kW, but Q_L is only 90 kW here.2 would imply Q_L = 60 kW, not matching the balance.

Common Pitfalls:
Mistaking the condenser heat flow Q_H for the cooling load Q_L. Always subtract compressor work to find Q_L from Q_H.

Final Answer:

3