Coil performance in sensible cooling For a sensible cooling process across a cooling coil, the coil efficiency equals which of the following expressions in terms of by-pass factor (BPF)?

Introduction / Context:
Cooling coil performance is often expressed via by-pass factor (BPF) and coil efficiency. Understanding their relationship streamlines quick estimates of outlet air conditions relative to the apparatus dew point (ADP).

Given Data / Assumptions:

• Sensible cooling (moisture change negligible for the relation).
• Standard definition of BPF and ADP; uniform face velocity and distribution.

Concept / Approach:
By definition, for cooling: BPF = (t_out − t_ADP) / (t_in − t_ADP). Coil efficiency measures approach to the ADP: efficiency = (t_in − t_out) / (t_in − t_ADP) = 1 − BPF.

Step-by-Step Solution:
Write BPF in terms of temperatures.Rearrange for (t_in − t_out) / (t_in − t_ADP).Obtain coil efficiency = 1 − BPF.

Verification / Alternative check:
If BPF = 0 (perfect coil with no bypass), efficiency = 1 (100%); if BPF = 1 (complete bypass), efficiency = 0—consistent with the formula.

Why Other Options Are Wrong:

• BPF − 1 and 1 + BPF can yield negative or >1 values, not physically meaningful.
• Equaling BPF or 1/BPF does not match the standard definition.

Common Pitfalls:
Mixing heating and cooling forms; forgetting that efficiency measures approach to ADP, not to entering air.

Final Answer:
Coil efficiency = 1 − BPF