Discussion
Steam enters an adiabatic turbine operating at steady state with an enthalpy of 3251.0 kJ/kg and leaves as a saturated mixture at 15 kPa with quality (dryness fraction) 0.9. The enthalpies of the saturated liquid and vapor at 15 kPa are hf = 225.94 kJ/kg and hg = 2598.3 kJ/kg respectively. The mass flow rate of steam is 10 kg/s. Kinetic and potential energy changes are negligible. The power output of the turbine in MW is
Answer: B
The turbine produces about 8.9 MW.
The exit enthalpy follows from the dryness fraction, and the steady-flow energy equation for an adiabatic turbine gives the work:
\[ \begin{aligned} h_{2} &= h_{f}+x(h_{g}-h_{f}) \\ &= 225.94+0.9(2598.3-225.94) \\ &= 2361.06\ \text{kJ/kg} \end{aligned} \]
\[ \begin{aligned} W &= \dot{m}(h_{1}-h_{2}) \\ &= 10(3251.0-2361.06) \\ &= 8899\ \text{kW} \approx 8.9\ \text{MW} \end{aligned} \]
9.1 MW is what you get by taking the exit enthalpy as 0.9 hg and forgetting the enthalpy of the liquid fraction. 6.5 and 27.0 MW do not follow from these data.
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