Unit conversion check (energy and power): Identify the incorrect conversion among the following commonly used engineering unit relations.
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A1 J = 1 W·s ≈ 10^7 ergs ≈ 9.48×10^-4 BTU ≈ 0.239 cal
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B1 W = 746 hp
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C1 hp ≈ 746 W (exactly 745.7 W in SI)
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D1 kWh = 3.6×10^6 J ≈ 3412 BTU
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E1 cal ≈ 4.184 J
Answer
Correct Answer: 1 W = 746 hp
Explanation
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:
Recall: 1 hp = 745.7 W (often rounded to 746 W).Therefore: 1 W = 1/746 hp ≈ 0.00134 hp, not 746 hp.Check the remaining statements; they are standard and consistent with handbooks.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.