Rankine (turbine) efficiency dependence A statement about Rankine (turbine) efficiency says: it depends upon the total useful heat drop and the total isentropic heat drop across the turbine stage or machine. Is this statement correct?

Difficulty: Easy

Correct Answer: Correct

Explanation:


Introduction / Context:
Rankine efficiency (often called turbine efficiency or internal efficiency for the whole turbine or stage) compares the actual work output to the ideal (isentropic) work output between the same inlet and exit states. It provides a thermodynamic measure independent of mechanical losses.


Given Data / Assumptions:

  • Same inlet pressure/temperature and exit pressure for actual and isentropic reference processes.
  • Negligible changes in kinetic and potential energy across the control volume for the basic definition.
  • Moisture effects may exist but are folded into the enthalpy changes.


Concept / Approach:

The internal (Rankine) efficiency is defined as η_internal = (actual heat drop utilized) / (isentropic heat drop). Because actual turbine work equals the actual enthalpy drop (neglecting KE/PE), and the ideal work equals the isentropic enthalpy drop, the efficiency indeed depends on the ratio of these two “heat drops.” Hence the statement is correct and applies to both impulse and reaction turbines.


Step-by-Step Solution:

Write actual work per kg: W_actual ≈ h_in − h_out(actual).Write ideal work per kg: W_ideal ≈ h_in − h_out(isentropic).Form η_internal = W_actual / W_ideal = (useful heat drop) / (isentropic heat drop).


Verification / Alternative check:

Performance tests compute isentropic outlet enthalpy from measured exit pressure and assumed isentropic expansion; comparing with measured exit enthalpy yields turbine internal efficiency consistent with the definition.


Why Other Options Are Wrong:

Limiting the definition to impulse or reaction types is unnecessary; it is a general thermodynamic definition.Moisture content affects values but not the definition.


Common Pitfalls:

Mixing internal efficiency with mechanical efficiency (shaft vs. internal power) or with stage/diagram efficiency; each metric has different denominators.


Final Answer:

Correct

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