Steam enters an adiabatic turbine steadily at 7 MPa, 500°C, and 45 m/s and leaves at 100 kPa and 75 m/s. If the power output of the turbine is 5 MW and the isentropic efficiency is 77 percent, determine (a) the mass flow rate of steam through the turbine, (b) the temperature at the turbine exit, and (c) the rate of entropy generation during this process.
FIGURE P7–137
a)
The mass flow rate of the steam.
Answer to Problem 137P
The mass flow rate of the steam is
Explanation of Solution
Write the expression for the energy balance equation for closed system.
Here, rate of net energy transfer in to the control volume is
Write the expression to calculate the power output for the isentropic process.
Here, the power output for the isentropic process is
Conclusion:
The rate of change in internal energy of the system is zero at steady state.
Substitute 0 for
Here, mass flow rate is
From the Table A-6, “superheated water table”, select the initial enthalpy
The entropy remains constant since the process is isentropic
From the Table A-6, “superheated water table”, select the enthalpy at final state in isentropic process
Substitute 5,000 kW for
Substitute
Thus, the mass flow rate of the steam is
b)
The exit temperature of the steam.
Answer to Problem 137P
The exit temperature of the steam is
Explanation of Solution
Write the expression to calculate the mass flow rate of the steam.
Here, rate of actual work is
Conclusion:
Substitute
From the Table A-6, “superheated water table”, obtain final entropy at pressure of
From the Table A-6, “Superheated water”, obtain the value of exit temperature
Write the formula of interpolation method of two variables.
Here, the variables denoted by x and y are exit temperature and enthalpy.
Show exit temperature and enthalpy values from the Table A-6.
Temperature | Enthalpy |
2675 | 100 |
2683.5 | ? |
2776.6 | 150 |
Substitute
The value of exit temperature
Thus, the exit temperature of the steam is
c)
The entropy generation in the turbine.
Answer to Problem 137P
The entropy generation in the turbine is
Explanation of Solution
Write the expression to calculate the entropy generation in the turbine.
Here, entropy generation in the turbine is
Conclusion:
Substitute
Thus, the entropy generation in the turbine is
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