Which equation best describes the boiler efficiency relation used in the given example (Furnace temperature = 3200°F, Stack temperature = 750°F)?

Which equation best describes the boiler efficiency relation used in the given example (Furnace temperature = 3200°F, Stack temperature = 750°F)?

• A. Efficiency = (Stack Temperature / Furnace Temperature) × 100
• B. Efficiency = ((Furnace Temperature - Stack Temperature) / Furnace Temperature) × 100
• C. Efficiency = ((Stack Temperature - Furnace Temperature) / Stack Temperature) × 100
• D. Efficiency = (Furnace Temperature + Stack Temperature) / 2

Answer: (B)

Boiler efficiency in this simplified example is the fraction of the input energy that remains as useful heat after losses up the stack. It’s calculated as the difference between the furnace temperature (input heat) and the stack temperature (heat carried away), divided by the furnace temperature, then converted to a percent.

With a furnace at 3200°F and a stack at 750°F, the useful heat is 3200 − 750 = 2450. Dividing by the input heat 3200 and multiplying by 100 gives 2450/3200 × 100 ≈ 76.6%. This shows why the form using (Furnace Temperature − Stack Temperature) divided by Furnace Temperature best represents the efficiency in this scenario.

The other forms don’t fit because they either swap the numerator and denominator in a way that would represent the exhaust heat instead of useful heat, use a difference over a different base, or compute an average that doesn’t correspond to how much energy is retained versus lost.