Steam power plant efficiencies: The ratio of the heat equivalent of brake power (useful output at the shaft) to the energy supplied in the steam to the engine is called the __________.

Introduction / Context:
Performance metrics for steam engines and turbines include several efficiencies that compare inputs and outputs at different boundaries: thermal, mechanical, and overall. Selecting the correct definition ensures meaningful analysis and benchmarking.

Given Data / Assumptions:

• Brake power B.P. is measured at the shaft output.
• Energy supplied in steam is based on mass flow and steam enthalpy rise relative to feedwater.
• Steady-state operation.

Concept / Approach:
Brake thermal efficiency η_bt is defined as: η_bt = (heat equivalent of brake power) / (rate of heat supplied in steam). Indicated thermal efficiency uses indicated power in the numerator, while mechanical efficiency is B.P. / I.P. Overall efficiency often includes the boiler, i.e., useful power divided by fuel energy rate. Therefore, when comparing B.P. directly to steam energy supplied to the engine, we refer specifically to brake thermal efficiency.

Step-by-Step Solution:
Identify numerator: B.P. converted to heat equivalent (B.P. in kW corresponds to kJ/s).Identify denominator: steam energy input rate = m_dot * (h_in − h_ref).Form ratio: η_bt = (B.P. in kW) / (steam heat rate in kW).Select the term matching this ratio: brake thermal efficiency.

Verification / Alternative check:
Cross-check with definitions: η_it uses I.P.; η_mech = B.P./I.P.; η_overall = B.P./(fuel heat rate).

Why Other Options Are Wrong:
Mechanical efficiency does not reference steam energy; it compares B.P. to I.P.

Indicated thermal efficiency uses I.P. as output.

Overall efficiency uses fuel energy as input, not steam energy.

Nozzle efficiency is for nozzles, not whole engines.

Common Pitfalls:
Mixing up “thermal” qualifiers at indicated vs brake levels; forgetting boundary definitions.

Final Answer:
brake thermal efficiency