Power requirement per tonne of refrigeration (PTR) For a vapour-compression plant, express the power per tonne of refrigeration (in kW per TR) in terms of the coefficient of performance (COP). Take 1 TR = 3.5 kW of cooling.
Mechanical Engineering
Heat Transfer, Refrigeration and Air Conditioning
Difficulty: Easy
Choose an option
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A3.5 / COP
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BCOP / 3.5
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C3.5 * COP
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D1 / (3.5 * COP)
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E3.5 * COP^2
Answer
Correct Answer: 3.5 / COP
Explanation
Introduction / Context:Linking COP to input power per unit cooling capacity is essential for comparing chiller and refrigeration plant efficiencies across sizes.
Given Data / Assumptions:
- Definition: COP = Q_L / W_in.
- One tonne of refrigeration (1 TR) = 3.5 kW of cooling capacity.
Concept / Approach:For 1 TR, Q_L = 3.5 kW. Rearranging the COP definition gives W_in = Q_L / COP. Therefore, power per TR is 3.5 / COP (kW per TR).
Step-by-Step Solution:Start with COP = Q_L / W_in.Rearrange: W_in = Q_L / COP.For 1 TR, W_in = 3.5 / COP kW.
Verification / Alternative check:Numerical example: COP = 3 → PTR = 3.5/3 ≈ 1.167 kW/TR. This matches typical plant data.
Why Other Options Are Wrong:
- COP/3.5 or 3.5COP invert or misapply the relationship.
- 1/(3.5COP) has wrong dimensions and magnitude.
Common Pitfalls:Confusing COP with EER or SEER; forgetting that PTR decreases as COP increases.
Final Answer:3.5 / COP