Definition check: efficiency of a steam boiler Which statement correctly defines boiler efficiency from an energy perspective?

Introduction / Context:Boiler efficiency is a fundamental metric for power and process plants. It quantifies how effectively the chemical energy in fuel is converted into thermal energy of steam delivered by the boiler.

Given Data / Assumptions:

• Energy-in basis: fuel heat input as measured by calorific value and mass flow.
• Energy-out basis: enthalpy rise of water to steam at delivery conditions relative to feedwater.
• Steady-state operation during the measurement period.

Concept / Approach:Boiler efficiency = useful energy to steam / fuel energy input. The useful energy is m * (h − hf1). The fuel energy input is mf * C. This definition reflects first-law efficiency and provides a basis for comparing different designs and fuels.

Step-by-Step Solution:Identify useful heat: increase of water/steam enthalpy.Identify input: fuel chemical energy released in furnace.Form the ratio: η = useful heat / fuel heat.Select the statement that matches this definition: option (a).

Verification / Alternative check:Heat balance sheets for boiler trials allocate losses (stack, moisture, radiation); efficiency equals 1 minus total fractional losses, consistent with option (a).

Why Other Options Are Wrong:Option (b) compares masses, not energies. Option (c) is the inverse of the correct definition. Option (e) refers to a specific loss instead of overall efficiency; (d) is therefore incorrect.

Common Pitfalls:Ignoring feedwater temperature in the useful heat term; comparing boilers without correcting for steam pressure and quality.

Final Answer:ratio of heat actually used in producing steam to the heat liberated in the furnace