Unit conversion check (energy and power):\nIdentify the incorrect conversion among the following commonly used engineering unit relations.

Introduction / Context:
Accurate unit conversion is crucial in thermodynamics and energy balances. Some conversions differ by several orders of magnitude if reversed. This question tests recognition of a commonly misstated relation between power units watts and horsepower, along with several standard energy conversions for context.

Given Data / Assumptions:

• SI base and derived units are used (J, W).
• US customary units include BTU and horsepower (hp).
• Thermochemical calorie used: 1 cal = 4.184 J.

Concept / Approach:
The correct relation is 1 horsepower ≈ 746 watts. Therefore, saying “1 W = 746 hp” is off by a factor of 746^2 if compounded in calculations and clearly incorrect dimensionally. Other listed conversions are standard references widely used in energy accounting and equipment specification.

Step-by-Step Solution:

Verification / Alternative check:
Electric meter billing uses kWh; 1 kWh = 3.6 MJ; HVAC conversions use 3412 BTU per kWh—confirming option (d). The joule–calorie relation in (e) is foundational in calorimetry.

Why Other Options Are Wrong or Right:

• (a), (c), (d), and (e) are correct standard conversions.
• (b) is wrong because it reverses the hp–W relationship.

Common Pitfalls:
Confusing power (W) with energy (J), and reversing unit equivalences (hp vs W). Always check which side of the equivalence the larger number belongs to.

Final Answer:
1 W = 746 hp.