Example Problem with Complete Solution

8B-2 : Entropy Generation in a Steam Turbine 5 pts
A turbine lets down steam from 5 MPa and 500oC to saturated vapor at 100 kPa while producing 720 kJ/kg of shaft work.  The outer surface of the turbine is at an average temperature of 200oC.  Determine the heat losses from the turbine and the entropy generation in the turbine in kJ/kg-K.
Read: Figure 1a Apply the 1st Law to determine Q and the 2nd Law to get Sgen.  Properties come fomr the steam tables or the NIST Webbook.  The key is that the heat losses occur at the constant, average surface temperature and this must be taken into account when evaluating Sgen for the turbine.
Given: P1 5000 kPa Find:
T1 500 oC (Sgen)turb ??? kJ/kg-K
P2 100 kPa
x2 1
THT 200 oC
WS 720 kJ/kg-K
Diagram: Figure 1b
Assumptions:
- The turbine operates at steady-state.
- Kinetic and potential energy changes are negligible.
- Shaft work and flow work are the only forms of work that cross the system boundary.
- Heat loss from the turbine occurs at a constant and uniform temperature of 200oC.
Equations / Data / Solve :
We can determine the entropy generation from an entropy balance on the turbine.
The entropy balance equation for a SISO process operating at steady-state that exchanges heat only with the surroundings is:
Equation 1 Eqn 1
The temperature at which heat transfer occurs is the surface temperature of the turbine, 200oC.
We can lookup S1 and S2 inn the steam tables or the NIST Webbook because states 1 and 2 are completely determined by the information given in the problem statement.
S1 6.9781 kJ/kg-K S2 7.3558 kJ/kg-K
Now, use the 1st Law for a steady-state process with negligible changes in kinetic and potential energies to determine Q.
Equation 2 Eqn 2
Solve Eqn 2 for Q : Equation 3 Eqn 3
We can now lookup H1 and H2 in the steam tables or the NIST Webbook because, again, states 1 and 2 are completely determined by the information given in the problem statement.
H1 3434.7 kJ/kg H2 2674.9 kJ/kg
Now we can plug values into Eqn 2 to evaluate Q: Q -39.80 kJ/kg
We can now evaluate the entropy generation within the turbine using Eqn 1. (Sgen)turb 0.4618 kJ/kg-K
Equation 4
Verify : The assumptions made in the solution of this problem cannot be verified with the given information.
Answers: Q -39.8 kJ/kg Sgen 0.4618 kJ/kg-K