GATE 2025 ME – Question 52
A thermal power plant is running with no reheat or regeneration. The specific enthalpy and specific entropy of steam at the turbine inlet are 3344 kJ kg$^{-1}$ and 6.5 kJ kg$^{-1}$ K$^{-1}$, respectively. The turbine isentropic efficiency is 0.9, and the mass flow rate of steam at turbine inlet is 102 kg s$^{-1}$. The turbine power output is ____________ MW (rounded off to 1 decimal place).
| Properties of saturated liquid and saturated vapor at turbine exit pressure | |||
|---|---|---|---|
| Saturated liquid water | Saturated water vapor | ||
| Specific enthalpy (kJ kg$^{-1}$) | Specific entropy (kJ kg$^{-1}$ K$^{-1}$) | Specific enthalpy (kJ kg$^{-1}$) | Specific entropy (kJ kg$^{-1}$ K$^{-1}$) |
| 341 | 1.1 | 2645 | 7.6 |
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Show answer and explanation
Correct answer: 99.50 to 100.50
Explanation
For the isentropic expansion, the exit entropy is 6.5, so the dryness fraction is $x = \frac{6.5 - 1.1}{7.6 - 1.1} = 0.8308$. The isentropic exit enthalpy is $h_{2s} = 341 + 0.8308(2645 - 341) = 2255.1$ kJ/kg. The actual work is $0.9 \times (3344 - 2255.1) = 980.0$ kJ/kg. With $102$ kg/s the power is $102 \times 980.0 = 99{,}960$ kW, which is 100.0 MW.