Energy units in chemical engineering:\nOne “therm” (as used in fuel and natural gas billing) is equivalent to which of the following energy quantities?

Introduction / Context:
The “therm” is a practical energy unit used widely by gas utilities to bill domestic and industrial consumers. Knowing exact conversions between a therm, British Thermal Units (BTU), kilocalories (kcal), and megajoules (MJ) is essential for quick, error-free energy balances and cost estimations in process engineering.

Given Data / Assumptions:

• By definition in common utility practice, 1 therm = 100,000 BTU (US therm).
• 1 BTU ≈ 1055 J; 1 kcal = 4186.8 J; 1 MJ = 10^6 J.
• We consider the widely adopted “US therm,” not the rarer “international therm.”

Concept / Approach:
Perform consistent unit conversions to cross-check equivalences. Converting 100,000 BTU to joules and then to MJ confirms the size of the therm and helps distinguish it from distractors that are off by orders of magnitude or wrongly expressed in kcal.

Step-by-Step Solution:
Start with definition: 1 therm = 100,000 BTU.Convert to joules: 100,000 BTU * 1055 J/BTU ≈ 1.055×10^8 J.Convert to MJ: 1.055×10^8 J / 10^6 ≈ 105.5 MJ.Cross-check vs kcal: 105.5 MJ / 4.1868 kJ/kcal ≈ 25,200 kcal (not 100,000 kcal).

Verification / Alternative check:
Utility bills often list consumption in therms; multiplying therms by 100,000 BTU gives BTU directly. Converting to kWh: 105.5 MJ / 3.6 MJ/kWh ≈ 29.3 kWh per therm, a common back-of-envelope check.

Why Other Options Are Wrong:
“100,000 kcal” overstates by ~4×. “1,000,000,000 BTU/kcal” are off by four orders of magnitude. “41.868 MJ” corresponds to 10,000 kcal, not a therm.

Common Pitfalls:
Mixing BTU and kcal, or assuming 1 therm equals 100,000 kcal. Also confusing therm with “thm” on bills versus “kWh.”

Final Answer:
100,000 BTU