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?
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A1/4
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B1/3
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C3
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D4
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E2
Answer
Correct Answer: 3
Explanation
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:
Compute evaporator load: Q_L = Q_H − W = 120 − 30 = 90 kW.Compute COP: COP_R = Q_L / W = 90 / 30 = 3.Therefore, COP = 3.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