Calorific value unit conversions:\r Identify the WRONG conversion statement among the following energy-per-mass or energy-per-volume equivalences.

Introduction:
Energy unit conversions appear everywhere from fuel specifications to dryer sizing. Small mistakes in unit factors can produce large design errors. This question asks you to spot the incorrect calorific value conversion among several commonly used relationships.

Given Data / Assumptions:

• Exact factors: 1 kcal = 4.186 kJ; 1 BTU = 1.055 kJ; 1 m^3 = 35.3147 ft^3; 1 MJ = 10^3 kJ; 1 kcal ≈ 3.968 BTU.
• We assume standard conditions for volumetric conversions.

Concept / Approach:
Check each statement using base factors. For (a): 1 kcal/kg equals 3.968 BTU/lb and 4.186 kJ/kg—correct. For (b): 1 BTU/lb equals 1.055 kJ/kg which is 0.252 kcal/kg—rounded to 2.326 kJ/kg for 1 BTU/lb is incorrect unless a typo; the correct figure is about 2.326 kJ per kcal. We adopt the precise pairing 1 BTU/lb ≈ 2.326 kJ/kg = 0.252 kcal/kg as a consistent rounded set used in many handbooks.

Step-by-Step Solution:
Evaluate (c): 1 BTU/ft^3 × 35.3147 ft^3/m^3 × 1.055 kJ/BTU = 37.3 kJ/m^3 ≈ 0.038 MJ/m^3 ≈ 8.9 kcal/m^3 → correct.Evaluate (d): 1 kcal/m^3 in BTU/ft^3 = (3.968 BTU/kcal) / 35.3147 = 0.1124 BTU/ft^3, not 1.124 → WRONG.Evaluate (e): 1 MJ/kg ÷ 4.186 kJ/kcal = 238.9 kcal/kg → rounded 239 is fine.

Verification / Alternative check:
Independent recalculation with SI base units confirms that only statement (d) carries a factor-of-10 error.

Why Other Options Are Wrong:

• Options (a), (b), (c), and (e) are consistent to typical handbook precision; (d) is the sole incorrect statement.

Common Pitfalls:
Dropping or misplacing the 35.3147 ft^3 per m^3 conversion factor often leads to 10× errors, as seen here.

Final Answer:
1 kcal/m^3 = 1.124 BTU/ft^3.