Steam engine performance terms: definition of relative efficiency Relative efficiency is defined as which of the following ratios?

Introduction / Context:
Several efficiency measures appear in steam plant calculations: thermal efficiency, mechanical efficiency, Rankine (ideal cycle) efficiency, and relative efficiency. Disentangling these helps compare real engines with their idealized counterparts and identify where the major losses occur.

Given Data / Assumptions:

• Rankine efficiency refers to the ideal cycle efficiency at the same boiler and condenser conditions.
• Thermal efficiency refers to actual cycle efficiency of the engine or plant.
• We are not evaluating mechanical losses or generator efficiency in this definition.

Concept / Approach:
Relative efficiency benchmarks the real (actual) thermal efficiency against the ideal Rankine cycle efficiency for the same temperature and pressure limits. It answers the question: how close is the real plant to the ideal cycle, ignoring purely mechanical losses?

Step-by-Step Solution:
Let η_th = actual thermal efficiency of the engine/plant.Let η_R = Rankine efficiency (ideal).Define relative efficiency η_rel = η_th / η_R.Interpretation: η_rel = 1 means the plant matches ideal Rankine limits; values less than 1 show deviation due to irreversibilities like throttling, superheat utilization, wetness losses, etc.

Verification / Alternative check:
Common textbooks present “efficiency ratio” or “relative efficiency” exactly as the ratio of actual to ideal thermal efficiency for steam engines and turbines, enabling sensible comparison across differing operating conditions.

Why Other Options Are Wrong:
Brake power to indicated power is mechanical efficiency. “Heat equivalent of IP to energy in steam” is indicated thermal efficiency, not relative efficiency to Rankine. The product η_th * η_R has no standard meaning in this context.

Common Pitfalls:
Mixing plant-level thermal efficiency with component-level mechanical efficiency; forgetting that Rankine is an ideal reference, not a measured quantity.

Final Answer:
ratio of thermal efficiency to Rankine efficiency