Unit conversion in thermodynamics: 1 BTU per cubic foot is approximately equal to how many kilocalories per cubic meter?

Introduction / Context:Unit conversion is a foundational thermodynamics skill for chemical and mechanical engineers. This question asks you to convert an energy density expressed in British units (BTU per cubic foot) to SI-compatible units (kilocalories per cubic meter). Such conversions are common when comparing fuel values, heating values, or designing energy systems where consistent units are essential.

Given Data / Assumptions:

• 1 BTU ≈ 252 cal = 0.252 kcal.
• 1 ft^3 = 0.0283168 m^3.
• We assume standard definitions without temperature-dependent corrections.

Concept / Approach:Convert the numerator (energy) and the denominator (volume) separately and then combine. The goal is to express BTU/ft^3 as kcal/m^3 by multiplying by appropriate conversion factors that equal 1 in value but change units.

Step-by-Step Solution:

Verification / Alternative check:Since 1 m^3 is ~35.3147 ft^3, 1 BTU/ft^3 equals 35.3147 BTU/m^3. Multiply by 0.252 kcal/BTU: 35.3147 * 0.252 ≈ 8.9 kcal/m^3. This matches the earlier computation.

Why Other Options Are Wrong:

• 1 kcal/m^3: Underestimates by roughly a factor of 9.
• 4 kcal/m^3: About half the correct value.
• 252 kcal/m^3: Confuses BTU-to-cal conversion without accounting for volume.
• 0.252 kcal/m^3: Converts BTU to kcal but ignores ft^3 to m^3 scaling.

Common Pitfalls:Mixing up 1 BTU = 252 cal with 252 kcal, forgetting to convert ft^3 to m^3, or inverting the volume ratio. Always keep track of units explicitly in every step.

Final Answer:9 kcal/m^3