A Rankine steam cycle modified for reheat, a closed feedwater heater, and an open feedwater heater is shown below. The high-pressure turbine receives 100 kg/s of steam from the steam boiler. The feedwater heater exit states for the boiler feedwater and the condensed steam are the normally assumed ideal states. The following data tables give the saturation data for the pressures and data for h and s at selected states. (a) Sketch the T-s diagram for the ideal cycle. (b) Determine the net power output of the cycle, in MW. (c) If cooling water is available at 25°C, what is the minimum flow rate of the cooling water required for the ideal cycle, in kg/s? Take cp,water = 4.18 kJ/kg·K.
Process states and selected data | ||||
State | P, kPa | T, °C | h, kJ/kg | s, kJ/kg·K |
1 | 20 | |||
2 | 1400 | |||
3 | 1400 | |||
4 | 1400 | |||
5 | 5000 | |||
6 | 5000 | 700 | 3894 | 7.504 |
7 | 1400 | 3400 | 7.504 | |
8 | 1200 | 3349 | 7.504 | |
9 | 1200 | 600 | 3692 | 7.938 |
10 | 245 | 3154 | 7.938 | |
11 | 20 | 2620 | 7.938 |
(a)
Sketch the T-s diagram for the ideal cycle.
Answer to Problem 111RP
Sketch the T-s diagram for the ideal cycle is shown in Figure 1.
Explanation of Solution
Draw the
Figure 1.
(b)
The net power output of the cycle.
Answer to Problem 111RP
The net power output of the cycle is
Explanation of Solution
Write the formula for work done by the pump during process 1-2.
Here, the specific volume is
Write the formula for enthalpy
Write the formula for work done by the pump during process 3-4.
Here, the specific volume is
Write the formula for enthalpy
Write the formula for an energy balance on the open feed water heater.
Here, the fraction of steam extracted is
Rewrite the Equation (V) to find out the value of
Write the formula for an energy balance on the closed feed water heater.
Here, the fraction of steam extracted is
Rewrite the Equation (V) to find out the value of
Write the formula for heat input in the boiler.
Write the formula for work output from the turbine.
Write the formula for net work output from the cycle.
Write the net power output of the cycle.
Conclusion:
From the Table A-5, “Saturated water-temperature Table” obtains the value of the enthalpy
Substitute
Substitute
From the Table A-5, “Saturated water-temperature Table” obtains the value of the enthalpy
Substitute
Substitute
Refer Table A-5, “Saturated water-temperature Table”, and write the enthalpy at state 12 at pressure of
Here, enthalpy of saturation liquid at pressure of
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y is pressure and specific enthalpy at state 12 respectively.
Show the specific enthalpy at state 12 corresponding to temperature as in Table (1).
Pressure at state 12 |
Specific enthalpy at state 12 |
225 | 520.71 |
245 | |
250 | 535.35 |
Substitute
Substitute
Here, the throttle valve operation of specific enthalpy at the state 13 is equal to specific enthalpy at the state 12.
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the net power output of the cycle is
(c)
The minimum flow rate of the cooling water.
Answer to Problem 111RP
The minimum flow rate of the cooling water is
Explanation of Solution
Write the formula for heat rejected from the condenser.
The mass flow rate cooling water will be minimum when the cooling water exit temperature is a maximum as
Write the formula for an energy balance on the condenser.
Conclusion:
Substitute 0.1039 for
Substitute
Thus, the minimum flow rate of the cooling water is
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Chapter 10 Solutions
Thermodynamics: An Engineering Approach
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