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.

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