Thermal unit conversion check:\nSelect the correct conversion between British Thermal Units and calories (small-c).

Introduction / Context:
Accurate energy-unit conversions are essential in energy balances, heat-exchanger design, and utility billing. Two common non-SI units are the British Thermal Unit (BTU) and the calorie (small-c, defined relative to heating water).

Given Data / Assumptions:

• Use the common engineering approximation: 1 BTU ≈ 252 cal (small calories).
• Be aware that 1 kcal (Cal, food calorie) = 1000 cal.

Concept / Approach:
Standard reference conversions are: 1 BTU = 1055 J (approx), and 1 cal = 4.186 J. Combining these gives 1 BTU / 1 cal ≈ 1055 / 4.186 ≈ 252. Hence the correct direct conversion is 1 BTU ≈ 252 cal.

Step-by-Step Solution:
Start from SI: 1 cal = 4.186 J.Also: 1 BTU ≈ 1055 J.Compute ratio: 1055 / 4.186 ≈ 252 → 1 BTU ≈ 252 cal.

Verification / Alternative check:
Equivalently, 1 kcal ≈ 3.968 BTU. Multiplying 252 cal by 3.968×10^-3 BTU/cal returns approximately 1 BTU, confirming consistency.

Why Other Options Are Wrong:
453.6 calories: likely confusion with mass conversions (1 lb = 453.6 g); not an energy relation.1 calorie = 252 BTU and 1 calorie = 453.6 BTU invert the ratio and are off by orders of magnitude.

Common Pitfalls:
Mixing calories (cal) with kilocalories (kcal); confusing pound-mass conversion with energy conversion; rounding inconsistently.

Final Answer:
1 BTU = 252 calories