Thermal conductivity conversions:\nWhich of the following conversions for thermal conductivity is incorrect?

Introduction / Context:
Thermal conductivity appears in heat transfer calculations and can be expressed in several equivalent but differently arranged unit sets. When thickness (length) appears in the denominator (e.g., “per ft” or “per inch”), converting between inch and foot must include the factor of 12. This question targets a subtle but common mistake: forgetting that “per inch” differs from “per ft” by a factor of 12.

Given Data / Assumptions:

• Conductivity forms like BTU/ft²·hr·°F per length are equivalent to BTU/ft·hr·°F.
• 1 ft = 12 inches; thus, per inch ≡ 12 × per ft.
• Standard reference: 1 kcal/m·hr·°C ≈ 1.163 W/m·K ≈ 0.672 BTU/ft·hr·°F.

Concept / Approach:
Option (a) expresses “per ft” and option (b) expresses “per inch” but shows the same right-hand side value. Since 1/(inch) = 12/(ft), the numerical constant on the right must be 12 times larger for the “per inch” case than for “per ft.” Leaving it unchanged makes (b) incorrect, while (a), (c), (d), and (e) are consistent with handbook conversions.

Step-by-Step Solution:

Verification / Alternative check:
Convert via SI: 1 W/m·K = 0.5779 BTU/ft·hr·°F (option e). From there, derive all other forms to confirm consistency across (a), (c), and (d).

Why Other Options Are Wrong or Right:

• (a), (c), (d), (e) are correct within rounding.
• (b) fails to apply the 12× factor between inch and foot.

Common Pitfalls:
Confusing area-normalized flux units with conductivity units and forgetting imperial length conversions inside compound units.

Final Answer:
1 BTU/ft²·hr·°F per inch = 1.488 kcal/m²·hr·°C per m.