Topic: Thermodynamics
The inlet and outlet conditions of steam for an adiabatic steam turbine are as indicated in the figure. The notations are as usually followed. If the mass rate of steam through the turbine is 20 kg/s, the power output of the turbine is (Inlet: $h_1=3200$ kJ/kg, $V_1=160$ m/s, $Z_1=10$ m; Outlet: $h_2=2600$ kJ/kg, $V_2=100$ m/s, $Z_2=6$ m)
- A. 12.157 MW
- B. 12.941 MW
- C. 168.001 MW
- D. 168.785 MW
Answer: A. 12.157 MW
Explanation: Applying the Steady Flow Energy Equation (SFEE) for an adiabatic process ($Q = 0$): $m(h_1 + V_1^2/2000 + gZ_1/1000) = m(h_2 + V_2^2/2000 + gZ_2/1000) + W$. Substituting the given values yields $W = 20 \times [(3200 - 2600) + (160^2 - 100^2)/2000 + 9.81 \times (10 - 6)/1000]$. Evaluating this gives $W = 20 \times [600 + 7.8 + 0.03924] = 20 \times 607.83924 = 12156.78$ kW, which is approximately 12.157 MW.