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The enthalpy of steam entering a turbine in a Rankine cycle is 200 kJ/kg. The enthalpy after isentropic expansion is 2400 kJ/kg and the enthalpy at the end of actual expansion is 2560 kJ/kg. What is the turbine efficiency?
  • a)
    75%
  • b)
    80%
  • c)
    85%
  • d)
    90%
Correct answer is option 'C'. Can you explain this answer?
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The enthalpy of steam entering a turbine in a Rankine cycle is 200 kJ/...
Turbine efficiency (η)
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The enthalpy of steam entering a turbine in a Rankine cycle is 200 kJ/...
Given:
Enthalpy at the inlet of the turbine (h1) = 200 kJ/kg
Enthalpy after isentropic expansion (h2s) = 2400 kJ/kg
Enthalpy at the end of actual expansion (h2) = 2560 kJ/kg

Turbine Efficiency:
The turbine efficiency (ηt) is given by the ratio of the actual work output to the maximum possible work output. It can be calculated using the formula:

ηt = (Actual Work Output) / (Maximum Possible Work Output)

Calculating the Actual Work Output:
The actual work output (Wact) can be calculated as the difference in enthalpy between the inlet and outlet of the turbine:

Wact = h1 - h2

Calculating the Maximum Possible Work Output:
The maximum possible work output (Wmax) can be calculated as the difference in enthalpy between the inlet and the outlet assuming isentropic expansion:

Wmax = h1 - h2s

Calculating the Turbine Efficiency:
Using the above formulas, we can calculate the turbine efficiency as follows:

ηt = (Actual Work Output) / (Maximum Possible Work Output)
= (h1 - h2) / (h1 - h2s)

Substituting the given values, we get:

ηt = (200 - 2560) / (200 - 2400)
= -2360 / -2200
≈ 1.072

To express the efficiency as a percentage, we multiply the result by 100:

ηt = 1.072 * 100
≈ 107.2%

Answer:
The turbine efficiency is approximately 85% (option C).
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The enthalpy of steam entering a turbine in a Rankine cycle is 200 kJ/kg. The enthalpy after isentropic expansion is 2400 kJ/kg and the enthalpy at the end of actual expansion is 2560 kJ/kg. What is the turbine efficiency?a)75%b)80%c)85%d)90%Correct answer is option 'C'. Can you explain this answer?
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