Sensible heating coil performance: For air heated sensibly across a coil, the coil efficiency (or effectiveness) in terms of the by-pass factor (B.P.F.) is:

Introduction / Context:
By-pass factor (B.P.F.) quantifies the fraction of air that effectively “misses” contact with the coil surface temperature, while coil efficiency (or apparatus dew-point effectiveness for sensible heating) tells how close the outlet approaches the coil surface temperature.

Given Data / Assumptions:

• Sensible heating (no moisture change).
• Well-mixed outlet air.
• Coil surface temperature is uniform.

Concept / Approach:
For sensible processes, coil efficiency ε = (T_out - T_in) / (T_surface - T_in). The by-pass factor is defined as B.P.F. = (T_surface - T_out) / (T_surface - T_in). From these definitions, ε + B.P.F. = 1.

Step-by-Step Solution:

Verification / Alternative check:
Limiting cases: perfect coil contact gives B.P.F. → 0, so ε → 1; fully bypassed air gives B.P.F. → 1 and ε → 0, which is consistent.

Why Other Options Are Wrong:
Other algebraic forms contradict the standard definitions; for example, B.P.F. - 1 is negative for normal coils, which is nonphysical for an efficiency.

Common Pitfalls:
Mixing signs or inverting temperatures; forgetting that efficiency must lie between 0 and 1.

Final Answer:
1 - B.P.F.