Spot the incorrect conversion:\nWhich of the following energy unit conversions is wrong?

Introduction / Context:
Accurate unit conversion is foundational in energy balances and equipment sizing. Small mistakes can lead to large design errors. This question asks you to identify a deliberately incorrect conversion.

Given Data / Assumptions:

• Exact definitions: 1 cal (thermochemical) = 4.184 J; commonly rounded to 4.186 J.
• 1 kWh = 3.6 MJ by definition (3600 s × 1000 W).
• 1 BTU ≈ 1055 J; 1 ft·lbf ≈ 1.356 J.

Concept / Approach:
Check each option against standard references. Focus on directionality (what equals what) and whether power units (hp) are correctly coupled with time when used as energy (hp·h).

Step-by-Step Solution:
Correct relation: 1 calorie ≈ 4.186 J, therefore 1 Joule ≈ 0.239 calorie.Option (a) reverses the relation and is wrong.Option (b): 1 kcal ≈ 3.968 BTU; 1 kcal = 4184 J = 0.00116 kWh; 0.00116 kWh × 1.341 hp/kW ≈ 0.00156 hp·h — consistent.Option (c): 1 ton TNT ≈ 4.184 GJ (rounded as 4.2 GJ) — acceptable.Option (d): 1 ft·lbf = 1.356 J; dividing by 4.186 J/cal gives ≈ 0.324 cal; kg·m relation matches via 1 kg·m = 9.80665 J.Option (e): Identity by definition.

Verification / Alternative check:
Dimensional consistency and cross-conversion among J, cal, BTU, and kWh confirm which entries are correct.

Why Other Options Are Wrong:
Only (a) is wrong; the others match accepted values within rounding.

Common Pitfalls:
Reversing “J per cal” versus “cal per J,” or using hp (power) as energy without including time.

Final Answer:
1 Joule = 4.186 calorie