Question

The efficiency of a furnace is defined as:

• A. (Heat supplied Heat utilized) $\times$ 100
• B. (Heat utilized Heat supplied) $\times$ 100
• C. (Heat losses Heat supplied) $\times$ 100
• D. (Heat utilized Total heat supplied) $\times$ 100

Hint:

Thermodynamic efficiency is always defined as "what you want (utilized energy)" divided by "what you pay for (supplied energy)".
This principle makes it easy to remember the correct ratio for any thermal system.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the standard thermodynamic definition of the thermal efficiency ($\eta$) of an industrial furnace.

Step 2: Key Formula or Approach:

• By first-law thermodynamic definition, efficiency ($\eta$) is the ratio of useful output energy to total input energy: \[ \eta = \frac{\text{Useful Energy Output}}{\text{Energy Input}} \times 100\% \]
• In the context of a furnace, the "useful output" is the heat absorbed/utilized by the material being heated (the charge).

• The "energy input" is the total heat supplied by fuel combustion or electrical energy.

Step 3: Detailed Explanation:

• An industrial furnace converts chemical energy of fuel or electrical energy into thermal energy to heat, melt, or heat-treat materials.

• Not all heat supplied to the furnace is absorbed by the stock (charge). Significant heat is lost through flue gases, furnace walls, radiation, and cooling water.

• The thermal efficiency of the furnace is: \[ \text{Efficiency } (\eta) = \frac{\text{Heat utilized by the stock}}{\text{Total heat supplied to the furnace}} \times 100 \]
• Comparing the options:
Option (B) states "(Heat utilized Heat supplied) $\times$ 100", which perfectly matches this definition.

Step 4: Final Answer:
The efficiency of a furnace is defined as (Heat utilized Heat supplied) $\times$ 100.