Unit conversion check: 1 kcal per kg per °C is equivalent to how many BTU per lb per °F for specific heat capacity?

Introduction / Context:Specific heat capacity is frequently cited in both SI and English units. Converting correctly between 1 kcal/(kg·°C) and BTU/(lb·°F) prevents significant energy-balance errors in heat-transfer and process calculations.

Given Data / Assumptions:

• 1 kcal = 3.96832 BTU (thermochemical).
• 1 kg = 2.20462 lb.
• Temperature interval: 1 °C = 1.8 °F.

Concept / Approach:Convert the compound unit stepwise: multiply by the energy conversion, divide by the mass conversion, and divide by the temperature-interval conversion. Algebraically, value in BTU/(lb·°F) = 1 * (3.96832 BTU/kcal) * (1 kg / 2.20462 lb) * (1 °C / 1.8 °F). The mass and temperature conversions together cancel the numerical advantage of the energy conversion, yielding very nearly 1.

Step-by-Step Solution:

Verification / Alternative check:Recognize that the “specific heat of water” near room temperature is ≈ 1 kcal/(kg·°C) and ≈ 1 BTU/(lb·°F); the two definitions were historically aligned to make conversions convenient.

Why Other Options Are Wrong:

• 2.42 and 4.97 come from partial conversions (energy only) without accounting for mass and temperature units.
• 0.24 is the conversion between BTU/lb·°F and cal/g·°C, not the value asked here.
• None of these is incorrect because 1 is exact to within rounding.

Common Pitfalls:Forgetting that degrees Celsius and Fahrenheit use different interval sizes; always include the factor of 1.8 when converting per-degree quantities.

Final Answer:1