# Example Problem with Complete Solution

5C-2 : Heat Losses From a Steam Turbine 5 pts
At steady-state, a steam turbine produces 1,050 MW by letting the pressure down from 50 bar to 1 bar. The steam enters the turbine at 320oC with a velocity of 8 m/s and a mass flow rate of 150 kg/min.
The steam leaves the turbine with a quality of 0.94 kg vapor/kg and a velocity of 65 m/s. Determine the rate of heat loss from the turbine to the surroundings in kW.

Read : Apply the steady-state form of the 1st Law for open systems and solve for Q.  Assume changes in potential energy are negligible.  We know the values of two intensive variables for state 1, so we can look up H1.  We know the pressure and quality for state 2, so we can also determine H2.  Then, just plug back into the 1st Law to get Q !
Given: m 150 kg/min v1 8 m/s
2.500 kg/s P2 100 kPa
Ws 1050 kW x2 0.94
P1 5000 kPa v2 65 m/s
T1 320 oC
Find: Q ??? kW
Diagram:  Assumptions: 1 - The turbine operates at steady-state.
2 - The change in the potential energy of the fluid from the inlet to the outlet is negligible.
Equations / Data / Solve:
Let's begin by writing the steady-state form of the 1st Law for open systems. Eqn 1
Solve Eqn 1 for Q : Eqn 2
We must use the Steam Tables to determine H2 and H1 : Eqn 3
H1 2986.2 kJ/kg
At P2 = 100 kPa : Hsat liq 417.50 kJ/kg
Hsat vap 2674.95 kJ/kg
H2 2539.5 kJ/kg
Now, we can plug values into Eqn 2 to evaluate Q : Q -61.62 kW
Verify: None of the assumptions made in this problem solution can be verified.
Answers : Q -61.6 kW 