Thermodynamics: An Engineering Approach

Yunus A. Cengel, Michael A. Boles

Chapter 10

Vapor and Combined Power Cycles - all with Video Answers

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Chapter Questions

Problem 1

Why is the Carnot cycle not a realistic model for steam power plants?

Zulfiqar Ali

Zulfiqar Ali

Numerade Educator

Problem 2

Why is excessive moisture in steam undesirable in steam turbines? What is the highest moisture content allowed?

Saman Zulfiqar

Numerade Educator

Problem 3

A steady-flow Carnot cycle uses water as the working fluid. Water changes from saturated liquid to saturated vapor as heat is transferred to it from a source at $250^{\circ} \mathrm{C}$. Heat rejection takes place at a pressure of $20 \mathrm{kPa}$. Show the cycle on a $T-s$ diagram relative to the saturation lines, and determine $(a)$ the thermal efficiency, $(b)$ the amount of heat rejected, and $(c)$ the net work output.

Anand Jangid

Numerade Educator

Problem 4

Repeat Prob. $10-3$ for a heat rejection pressure of $10 \mathrm{kPa}$.

Zulfiqar Ali

Numerade Educator

Problem 5

Consider a steady-flow Carnot cycle with water as the working fluid. The maximum and minimum temperatures in the cycle are 350 and $60^{\circ} \mathrm{C}$. The quality of water is 0.891 at the beginning of the heat-rejection process and 0.1 at the end. Show the cycle on a $T-s$ diagram relative to the saturation lines, and determine $(a)$ the thermal efficiency, $(b)$ the pressure at the turbine inlet, and $(c)$ the net work output.

Zulfiqar Ali

Numerade Educator

Problem 6

Water enters the boiler of a steady-flow Carnot engine as a saturated liquid at 300 psia and leaves with a quality of $0.95 .$ Steam leaves the turbine at a pressure of 20 psia. Show the cycle on a $T-s$ diagram relative to the saturation lines, and determine $(a)$ the thermal efficiency, $(b)$ the quality at the end of the isothermal heat-rejection process, and (c) the net work output.

Saman Zulfiqar

Numerade Educator

Problem 7

What four processes make up the simple ideal Rankine cycle?

Saman Zulfiqar

Numerade Educator

Problem 8

Consider a simple ideal Rankine cycle with fixed turbine inlet conditions. What is the effect of lowering the condenser pressure on $$
\begin{array}{ll}\hline \text { Pump work input: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Turbine work output: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Heat supplied: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Heat rejected: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Cycle efficiency: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Moisture content at } & (a) \text { increases, }(b) \text { decreases, } \\\text { turbine exit: } & (c) \text { remains the same } \\\hline\end{array}$$

Saman Zulfiqar

Numerade Educator

Problem 9

Consider a simple ideal Rankine cycle with fixed turbine inlet temperature and condenser pressure. What is the effect of increasing the boiler pressure on
$$\begin{array}{ll}\hline \text { Pump work input: } & (a) \text { increases, }(b) \text { decreases, } \\ & (c) \text { remains the same } \\\text { Turbine work output: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\
\text { Heat supplied: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Heat rejected: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Cycle efficiency: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Moisture content at } & (a) \text { increases, }(b) \text { decreases, } \\\text { turbine exit: } & (c) \text { remains the same }\end{array}$$

Saman Zulfiqar

Numerade Educator

Problem 10

Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. What is the effect of superheating the steam to a higher temperature on
$$\begin{array}{ll}\hline \text { Pump work input: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Turbine work output: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Heat supplied: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Heat rejected: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Cycle efficiency: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Moisture content at } & (a) \text { increases, }(b) \text { decreases, } \\\text { turbine exit: } & (c) \text { remains the same }\end{array}$$

Saman Zulfiqar

Numerade Educator

Problem 11

How do actual vapor power cycles differ from idealized ones?

Zulfiqar Ali

Numerade Educator

Problem 12

Compare the pressures at the inlet and the exit of the boiler for $(a)$ actual and $(b)$ ideal cycles

Saman Zulfiqar

Numerade Educator

Problem 13

The entropy of steam increases in actual steam turbines as a result of irreversibilities. In an effort to control entropy increase, it is proposed to cool the steam in the turbine by running cooling water around the turbine casing. It is argued that this will reduce the entropy and the enthalpy of the steam at the turbine exit and thus increase the work output. How would you evaluate this proposal?

Zulfiqar Ali

Numerade Educator

Problem 14

Is it possible to maintain a pressure of $10 \mathrm{kPa}$ in a condenser that is being cooled by river water entering at $20^{\circ} \mathrm{C} ?$

Zulfiqar Ali

Numerade Educator

Problem 15

simple ideal Rankine cycle with water as the working fluid operates between the pressure limits of $3 \mathrm{MPa}$ in the boiler and $30 \mathrm{kPa}$ in the condenser. If the quality at the exit of the turbine cannot be less than 85 percent, what is the maximum thermal efficiency this cycle can have?

Saman Zulfiqar

Numerade Educator

Problem 16

A simple ideal Rankine cycle with water as the working fluid operates between the pressure limits of $4 \mathrm{MPa}$ in the boiler and $20 \mathrm{kPa}$ in the condenser and a turbine inlet temperature of $700^{\circ} \mathrm{C}$. The boiler is sized to provide a steam flow of $50 \mathrm{~kg} / \mathrm{s}$. Determine the power produced by the turbine and consumed by the pump.

Saman Zulfiqar

Numerade Educator

Problem 17

A simple ideal Rankine cycle which uses water as the working fluid operates its condenser at $40^{\circ} \mathrm{C}$ and its boiler at $250^{\circ} \mathrm{C}$. Calculate the work produced by the turbine, the heat supplied in the boiler, and the thermal efficiency of this cycle when the steam enters the turbine without any superheating.

Saman Zulfiqar

Numerade Educator

Problem 18

Consider a solar-pond power plant that operates on a simple ideal Rankine cycle with refrigerant- $134 \mathrm{a}$ as the working fluid. The refrigerant enters the turbine as a saturated vapor at 1.4 MPa and leaves at 0.7 MPa. The mass flow rate of the refrigerant is $3 \mathrm{~kg} / \mathrm{s}$. Show the cycle on a $T-s$ diagram with respect to saturation lines, and determine $(a)$ the thermal efficiency of the cycle and $(b)$ the power output of this plant.

Saman Zulfiqar

Numerade Educator

Problem 19

Consider a 210-MW steam power plant that operates on a simple ideal Rankine cycle. Steam enters the turbine at $10 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$ and is cooled in the condenser at a pressure of $10 \mathrm{kPa}$. Show the cycle on a $T-s$ diagram with respect to saturation lines, and determine $(a)$ the quality of the steam at the turbine exit, $(b)$ the thermal efficiency of the cycle, and $(c)$ the mass flow rate of the steam.

Zulfiqar Ali

Numerade Educator

Problem 20

Repeat Prob. $10-19$ assuming an isentropic efficiency of 85 percent for both the turbine and the pump.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 21

A simple ideal Rankine cycle with water as the working fluid operates between the pressure limits of $15 \mathrm{MPa}$ in the boiler and $100 \mathrm{kPa}$ in the condenser. Saturated steam enters the turbine. Determine the work produced by the turbine, the heat transferred in the boiler, and thermal efficiency of the cycle.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 22

Reconsider Prob. 10-21. Irreversibilities in the turbine cause the steam quality at the outlet of the turbine to be 70 percent. Determine the isentropic efficiency of the turbine and the thermal efficiency of the cycle.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 23

A steam Rankine cycle operates between the pressure limits of 1500 psia in the boiler and 2 psia in the condenser. The turbine inlet temperature is $800^{\circ} \mathrm{F}$. The turbine isentropic efficiency is 90 percent, the pump losses are negligible, and the cycle is sized to produce $2500 \mathrm{~kW}$ of power. Calculate the mass flow rate through the boiler, the power produced by the turbine, the rate of heat supply in the boiler, and the thermal efficiency.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 24

Reconsider Prob. 10-23E. How much error is caused in the thermal efficiency if the power required by the pump were completely neglected?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 25

A simple Rankine cycle uses water as the working fluid. The boiler operates at $6000 \mathrm{kPa}$ and the condenser at $50 \mathrm{kPa}$. At the entrance to the turbine, the temperature is $450^{\circ} \mathrm{C} .$ The isentropic efficiency of the turbine is 94 percent, pressure and pump losses are negligible, and the water leaving the condenser is subcooled by $6.3^{\circ} \mathrm{C}$. The boiler is sized for a mass flow rate of $20 \mathrm{~kg} / \mathrm{s}$. Determine the rate at which heat is added in the boiler, the power required to operate the pumps, the net power produced by the cycle, and the thermal efficiency.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 26

Using anpropriate software, determine how much the thermal efficiency of the cycle would change if there were a $50 \mathrm{kPa}$ pressure drop across the boiler.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 27

The net work output and the thermal efficiency for the Carnot and the simple ideal Rankine cycles with steam as the working fluid are to be calculated and compared. Steam enters the turbine in both cases at 5 MPa as a saturated vapor, and the condenser pressure is $50 \mathrm{kPa}$. In the Rankine cycle, the condenser exit state is saturated liquid and in the Carnot cycle, the boiler inlet state is saturated liquid. Draw the $T-s$ diagrams for both cycles.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 28

A binary geothermal power plant uses geothermal water at $160^{\circ} \mathrm{C}$ as the heat source. The plant operates on the simple Rankine cycle with isobutane as the working fluid. Heat is transferred to the cycle by a heat exchanger in which geothermal liquid water enters at $160^{\circ} \mathrm{C}$ at a rate of $555.9 \mathrm{~kg} / \mathrm{s}$ and leaves at $90^{\circ} \mathrm{C}$. Isobutane enters the turbine at $3.25 \mathrm{MPa}$ and $147^{\circ} \mathrm{C}$ and leaves at $79.5^{\circ} \mathrm{C}$ and $410 \mathrm{kPa}$. Isobutane is condensed in an air-cooled condenser and pumped to the heat exchanger pressure. Assuming the pump to have an isentropic efficiency of 90 percent, determine $(a)$ the isentropic efficiency of the turbine, $(b)$ the net power output of the plant, and (c) the thermal efficiency of the plant. The properties of isobutane are $h_{1}=273.01 \mathrm{~kJ} / \mathrm{kg}$, $U_{1}=0.001842 \mathrm{~m}^{3} / \mathrm{kg}, h_{3}=761.54 \mathrm{~kJ} / \mathrm{kg}, h_{4}=689.74 \mathrm{~kJ} / \mathrm{kg}$ $h_{4 s}=670.40 \mathrm{~kJ} / \mathrm{kg} .$ Take the specific heat of geothermal water to be $c_{p}=4.258 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$

Mahnoor Amin

Numerade Educator

Problem 29

Consider a coal-fired steam power plant that produces $175 \mathrm{MW}$ of electric power. The power plant operates on a simple ideal Rankine cycle with turbine inlet conditions of 7 MPa and $550^{\circ} \mathrm{C}$ and a condenser pressure of $15 \mathrm{kPa}$. The coal has a heating value (energy released when the fuel is burned) of $29,300 \mathrm{~kJ} / \mathrm{kg} .$ Assuming that 85 percent of this energy is transferred to the steam in the boiler and that the electric generator has an efficiency of 96 percent, determine $(a)$ the overall plant efficiency (the ratio of net electric power output to the energy input as fuel) and $(b)$ the required rate of coal supply.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 30

Show the ideal Rankine cycle with three stages of reheating on a $T$ -s diagram. Assume the turbine inlet temperature is the same for all stages. How does the cycle efficiency vary with the number of reheat stages?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 31

Is there an optimal pressure for reheating the steam of a Rankine cycle? Explain.

Mahnoor Amin

Numerade Educator

Problem 32

How do the following quantities change when a simple ideal Rankine cycle is modified with reheating? Assume the mass flow rate is maintained the same. $$\begin{array}{|ll}\hline \text { Pump work input: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Turbine work output: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Heat supplied: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Heat rejected: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Moisture content at } & (a) \text { increases, }(b) \text { decreases, } \\\text { turbine exit: } & (c) \text { remains the same } \\\hline\end{array}$$

Mahnoor Amin

Numerade Educator

Problem 33

Consider a simple ideal Rankine cycle and an ideal Rankine cycle with three reheat stages. Both cycles operate between the same pressure limits. The maximum temperature is $700^{\circ} \mathrm{C}$ in the simple cycle and $450^{\circ} \mathrm{C}$ in the reheat cycle. Which cycle do you think will have a higher thermal efficiency?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 34

Consider a steam power plant that operates on the ideal reheat Rankine cycle. The plant maintains the boiler at $17.5 \mathrm{MPa}$, the reheater at $2 \mathrm{MPa}$, and the condenser at $50 \mathrm{kPa}$. The temperature is $550^{\circ} \mathrm{C}$ at the entrance of the high-pressure turbine, and $300^{\circ} \mathrm{C}$ at the entrance of the low-pressure turbine. Determine the thermal efficiency of this system.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 35

How much does the thermal efficiency of the cycle change when the temperature at the entrance to the low-pressure turbine is increased to $550^{\circ} \mathrm{C} ?$

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 36

An ideal reheat Rankine cycle with water as the working fluid operates the boiler at $15,000 \mathrm{kPa}$, the reheater at $2000 \mathrm{kPa},$ and the condenser at $100 \mathrm{kPa}$. The temperature is $450^{\circ} \mathrm{C}$ at the entrance of the high-pressure and low-pressure turbines. The mass flow rate through the cycle is $1.74 \mathrm{~kg} / \mathrm{s}$. Determine the power used by pumps, the power produced by the cycle, the rate of heat transfer in the reheater, and the thermal efficiency of this system.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 37

Steam enters the high-pressure turbine of a steam power plant that operates on the ideal reheat Rankine cycle at 800 psia and $900^{\circ} \mathrm{F}$ and leaves as saturated vapor. Steam is then reheated to $800^{\circ} \mathrm{F}$ before it expands to a pressure of 1 psia. Heat is transferred to the steam in the boiler at a rate of $6 \times 10^{4} \mathrm{Btu} / \mathrm{s}$. Steam is cooled in the condenser by the cooling water from a nearby river, which enters the condenser at $45^{\circ} \mathrm{F}$. Show the cycle on a $T-s$ diagram with respect to saturation lines, and determine $(a)$ the pressure at which reheating takes place, $(b)$ the net power output and thermal efficiency, and (c) the minimum mass flow rate of the cooling water required.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 38

An ideal reheat Rankine cycle with water as the working fluid operates the inlet of the high-pressure turbine at $8000 \mathrm{kPa}$ and $450^{\circ} \mathrm{C},$ the inlet of the low-pressure turbine at $500 \mathrm{kPa}$ and $500^{\circ} \mathrm{C},$ and the condenser at $10 \mathrm{kPa}$. Determine the mass flow rate through the boiler needed for this system to produce a net $5000 \mathrm{~kW}$ of power and the thermal efficiency of the cycle.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 39

A steam power plant operates on an ideal reheat Rankine cycle between the pressure limits of $15 \mathrm{MPa}$ and $10 \mathrm{kPa}$. The mass flow rate of steam through the cycle is $12 \mathrm{~kg} / \mathrm{s}$. Steam enters both stages of the turbine at $500^{\circ} \mathrm{C}$. If the moisture content of the steam at the exit of the low-pressure turbine is not to exceed 5 percent, determine $(a)$ the pressure at which reheating takes place, $(b)$ the total rate of heat input in the boiler, and
(c) the thermal efficiency of the cycle. Also, show the cycle on a $T-s$ diagram with respect to saturation lines.

Saman Zulfiqar

Numerade Educator

Problem 40

A steam power plant operates on the reheat Rankine cycle. Steam enters the high-pressure turbine at $12.5 \mathrm{MPa}$ and $550^{\circ} \mathrm{C}$ at a rate of $7.7 \mathrm{~kg} / \mathrm{s}$ and leaves at 2 MPa. Steam is then reheated at constant pressure to $450^{\circ} \mathrm{C}$ before it expands in the low-pressure turbine. The isentropic efficiencies of the turbine and the pump are 85 percent and 90 percent, respectively. Steam leaves the condenser as a saturated liquid. If the moisture content of the steam at the exit of the turbine is not to exceed 5 percent, determine $(a)$ the condenser pressure, $(b)$ the net power output, and $(c)$ the thermal efficiency. This problem is solved using appropriate software.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 41

Consider a steam power plant that operates on a reheat Rankine cycle and has a net power output of $80 \mathrm{MW}$. Steam enters the high-pressure turbine at $10 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$ and the low-pressure turbine at $1 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$. Steam leaves the condenser as a saturated liquid at a pressure of $10 \mathrm{kPa} .$ The isentropic efficiency of the turbine is 80 percent, and that of the pump is 95 percent. Show the cycle on a $T-s$ diagram with respect to saturation lines, and determine ( $a$ ) the quality (or temperature, if superheated) of the steam at the turbine exit, $(b)$ the thermal efficiency of the cycle, and $(c)$ the mass flow rate of the steam.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 42

Repeat Prob. $10-41$ assuming both the pump and the turbine are isentropic.

Saman Zulfiqar

Numerade Educator

Problem 43

Devise an ideal regenerative Rankine cycle that has the same thermal efficiency as the Carnot cycle. Show the cycle on a $T-s$ diagram.

Saman Zulfiqar

Numerade Educator

Problem 44

During a regeneration process. some steam is extracted from the turbine and is used to heat the liquid water leaving the pump. This does not seem like a smart thing to do since the extracted steam could produce some more work in the turbine. How do you justify this action?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 45

Consider a simple ideal Rankine cycle and an ideal regenerative Rankine cycle with one open feedwater heater. The two cycles are very much alike, except the feedwater in the regenerative cycle is heated by extracting some steam just before it enters the turbine. How would you compare the efficiencies of these two cycles?

Saman Zulfiqar

Numerade Educator

Problem 46

How do open feedwater heaters differ from closed feedwater heaters?

Saman Zulfiqar

Numerade Educator

Problem 47

How do the following quantities change when the simple ideal Rankine cycle is modified with regeneration? Assume the mass flow rate through the boiler is the same.
$$\begin{array}{|ll}\hline \text { Turbine work output: } & (a) \text { increases, }(b) \text { decreases } \\& (c) \text { remains the same } \\\text { Heat supplied: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Heat rejected: } & (a) \text { increases, }(b) \text { decreases, } \\& (c) \text { remains the same } \\\text { Moisture content at } & (a) \text { increases, }(b) \text { decreases, } \\\text { turbine exit: } & (c) \text { remains the same } \\\hline\end{array}$$

Saman Zulfiqar

Numerade Educator

Problem 48

Cold feedwater enters a $200-\mathrm{kPa}$ open feedwater heater of a regenerative Rankine cycle at $70^{\circ} \mathrm{C}$ with a flow rate of $10 \mathrm{~kg} / \mathrm{s} .$ Bleed steam is available from the turbine at $200 \mathrm{kPa}$ and $160^{\circ} \mathrm{C}$. At what rate must bleed steam be supplied to the open feedwater heater so the feedwater leaves this unit as a saturated liquid?

Saman Zulfiqar

Numerade Educator

Problem 49

$10-49 E$ In a regenerative Rankine cycle. the closed feedwater heater with a pump as shown in the figure is arranged so that the water at state 5 is mixed with the water at state 2 to form a feedwater which is a saturated liquid at 200 psia. Feedwater enters this heater at $350^{\circ} \mathrm{F}$ and 200 psia with a flow rate of $2 \mathrm{lbm} / \mathrm{s} .$ Bleed steam is taken from the turbine at 160 psia and $400^{\circ} \mathrm{F}$ and enters the pump as a saturated liquid at 160 psia. Determine the mass flow rate of bleed steam required to operate this unit.

Saman Zulfiqar

Numerade Educator

Problem 50

A steam power plant operates on an ideal regenerative Rankine cycle. Steam enters the turbine at $6 \mathrm{MPa}$ and $450^{\circ} \mathrm{C}$ and is condensed in the condenser at $20 \mathrm{kPa}$. Steam is extracted from the turbine at 0.4 MPa to heat the feedwater in an open feedwater heater. Water leaves the feedwater heater as a saturated liquid. Show the cycle on a $T-s$ diagram, and determine $(a)$ the net work output per kilogram of steam flowing through the boiler and $(b)$ the thermal efficiency of the cycle.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 51

Repeat Prob. $10-50$ by replacing the open feedwater heater with a closed feedwater heater. Assume that the feed-
water leaves the heater at the condensation temperature of the extracted steam and that the extracted steam leaves the heater as a saturated liquid and is pumped to the line carrying the feedwater.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 52

A steam power plant operates on an ideal regenerative Rankine cycle with two open feedwater heaters. Steam enters the turbine at $8 \mathrm{MPa}$ and $550^{\circ} \mathrm{C}$ and exhausts to the condenser at $15 \mathrm{kPa}$. Steam is extracted from the turbine at 0.6 and 0.2 MPa. Water leaves both feedwater heaters as a saturated liquid. The mass flow rate of steam through the boiler is $24 \mathrm{~kg} / \mathrm{s}$. Show the cycle on a $T-s$ diagram, and determine ( $a$ ) the net power output of the power plant and $(b)$ the thermal efficiency of the cycle.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 53

Consider an ideal steam regenerative Rankine cycle with two feedwater heaters, one closed and one open. Steam enters the turbine at $10 \mathrm{MPa}$ and $600^{\circ} \mathrm{C}$ and exhausts to the condenser at $10 \mathrm{kPa}$. Steam is extracted from the turbine at 1.2 MPa for the closed feedwater heater and at 0.6 MPa for the open one. The feedwater is heated to the condensation temperature of the extracted steam in the closed feedwater heater. The extracted steam leaves the closed feedwater heater as a saturated liquid, which is subsequently throttled to the open feedwater heater. Show the cycle on a $T-s$ diagram with respect to saturation lines, and determine $(a)$ the mass flow rate of steam through the boiler for a net power output of 400 MW and $(b)$ the thermal efficiency of the cycle.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 54

Using appropriate software, investigate the effects of turbine and pump efficiencies as they are varied from 70 percent to 100 percent on the mass flow rate and thermal efficiency. Plot the mass flow rate and the thermal efficiency as a function of turbine efficiency for pump efficiencies of $70,85,$ and 100 percent, and discuss the results. Also plot the $T-s$ diagram for turbine and pump efficiencies of 85 percent.

Jincy M Saji

Numerade Educator

Problem 55

Consider a steam power plant that operates on the ideal regenerative Rankine cycle with a closed feedwater heater as shown in the figure. The plant maintains the turbine inlet at $3000 \mathrm{kPa}$ and $350^{\circ} \mathrm{C}$ and operates the condenser at $20 \mathrm{kPa}$ Steam is extracted at $1000 \mathrm{kPa}$ to serve the closed feedwater heater, which discharges into the condenser after being throttled to condenser pressure. Calculate the work produced by the turbine, the work consumed by the pump, and the heat supply in the boiler for this cycle per unit of boiler flow rate.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 56

Using appropriate software, determine the optimum bleed pressure for the closed feedwater heater that maximizes the thermal efficiency of the cycle.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 57

Determine the thermal efficiency of the regenerative Rankine cycle when the isentropic efficiency of the turbine is 90 percent before and after the steam extraction point.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 58

Determine the thermal efficiency of the regenerative Rankine cycle when the isentropic efficiency of the turbine before and after the steam extraction point is 90 percent and the condenser condensate is subcooled by $10^{\circ} \mathrm{C}$.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 59

Using appropriate software, determine how much additional heat must be supplied to the boiler when the turbine isentropic efficiency before and after the extraction point is 90 percent and there is a $10 \mathrm{kPa}$ pressure drop across the boiler.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 60

A steam power plant operates on an ideal reheatregenerative Rankine cycle and has a net power output of $80 \mathrm{MW}$. Steam enters the high-pressure turbine at $10 \mathrm{MPa}$ and $550^{\circ} \mathrm{C}$ and leaves at $0.8 \mathrm{MPa}$. Some steam is extracted at this pressure to heat the feedwater in an open feedwater heater. The rest of the steam is reheated to $500^{\circ} \mathrm{C}$ and is expanded in the low-pressure turbine to the condenser pressure of $10 \mathrm{kPa}$. Show the cycle on a $T-s$ diagram with respect to saturation lines, and determine $(a)$ the mass flow rate of steam through the boiler and $(b)$ the thermal efficiency of the cycle.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 61

Repeat Prob. $10-60,$ but replace the open feedwater heater with a closed feedwater heater. Assume that the feedwater leaves the heater at the condensation temperature of the extracted steam and that the extracted steam leaves the heater as a saturated liquid and is pumped to the line carrying the feedwater.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 62

A steam power plant operates on an ideal reheat regenerative Rankine cycle with one reheater and two open feedwater heaters. Steam enters the high-pressure turbine at 1500 psia and $1100^{\circ} \mathrm{F}$ and leaves the low-pressure turbine at 1 psia. Steam is extracted from the turbine at 250 and 40 psia, and it is reheated to $1000^{\circ} \mathrm{F}$ at a pressure of 140 psia. Water leaves both feedwater heaters as a saturated liquid. Heat is transferred to the steam in the boiler at a rate of $4 \times 10^{5} \mathrm{Btu} / \mathrm{s}$. Show the cycle on a $T-s$ diagram with respect to saturation lines, and determine $(a)$ the mass flow rate of steam through the boiler, $(b)$ the net power output of the plant, and $(c)$ the thermal efficiency of the cycle.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 63

A simple ideal Rankine cycle with water as the working fluid operates between the pressure limits of $4 \mathrm{MPa}$ in the boiler and $20 \mathrm{kPa}$ in the condenser and a turbine inlet temperature of $700^{\circ} \mathrm{C}$. Calculate the exergy destruction in each of the components of the cycle when heat is being rejected to the atmospheric air at $15^{\circ} \mathrm{C}$ and heat is supplied from an energy reservoir at $750^{\circ} \mathrm{C}$

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 64

Consider a steam power plant that operates on a simple ideal Rankine cycle. Steam enters the turbine at $10 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$ and is cooled in the condenser at a pressure of $10 \mathrm{kPa}$. Determine the exergy destruction associated with each of the processes of the cycle assuming a source temperature of $1500 \mathrm{~K}$ and a sink temperature of $290 \mathrm{~K}$.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 65

An ideal reheat Rankine cycle with water as the work ing fluid operates the inlet of the high-pressure turbine at $8000 \mathrm{kPa}$ and $450^{\circ} \mathrm{C}$; the inlet of the low-pressure turbine at $500 \mathrm{kPa}$ and $500^{\circ} \mathrm{C}$; and the condenser at $10 \mathrm{kPa}$. Which component of the cycle offers the greatest opportunity to regain lost power potential? The sink is at $10^{\circ} \mathrm{C}$ and the source is at $600^{\circ} \mathrm{C}$.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 66

An ideal reheat Rankine cycle with water as the work reheat Rankine cycle. Steam enters the high-pressure turbine at $10 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$ and the low-pressure turbine at $1 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$. Steam leaves the condenser as a saturated liquid at a pressure of $10 \mathrm{kPa}$. The isentropic efficiency of the turbine is 80 percent, and that of the pump is 95 percent. Determine the exergy destruction associated with the heat addition process and the expansion process. Assume a source temperature of $1600 \mathrm{~K}$ and a sink temperature of $285 \mathrm{~K}$. Also, determine the exergy of the steam at the boiler exit. Take $P_{0}=100 \mathrm{kPa}$.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 67

A steam power plant operates on an ideal regenerative Rankine cycle. Steam enters the turbine at $6 \mathrm{MPa}$ and $450^{\circ} \mathrm{C}$ and is condensed in the condenser at $20 \mathrm{kPa}$. Steam is extracted from the turbine at 0.4 MPa to heat the feedwater in an open feedwater heater. Water leaves the feedwater heater as a saturated liquid. Determine the exergy destruction associated with the cycle. Assume a source temperature of $1350 \mathrm{~K}$ and a sink temperature of $290 \mathrm{~K}$.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 68

A steam power plant operates on an ideal reheat-regenerative Rankine cycle. Steam enters the high-pressure turbine at $10 \mathrm{MPa}$ and $550^{\circ} \mathrm{C}$ and leaves at $0.8 \mathrm{MPa}$. Some steam is extracted at this pressure to heat the feedwater in an open feedwater heater. The rest of the steam is reheated to $500^{\circ} \mathrm{C}$ and is expanded in the low-pressure turbine to the condenser pressure of $10 \mathrm{kPa}$. Determine the exergy destruction associated with the reheating and regeneration processes. Assume a source temperature of $1800 \mathrm{~K}$ and a sink temperature of $290 \mathrm{~K}$.

Km Neeraj

Numerade Educator

Problem 69

The schematic of a single-flash geothermal power plant with state numbers is given in Fig. $\mathrm{P} 10-69 .$ Geothermal resource exists as saturated liquid at $230^{\circ} \mathrm{C}$. The geothermal liquid is withdrawn from the production well at a rate of $230 \mathrm{~kg} / \mathrm{s}$ and is flashed to a pressure of $500 \mathrm{kPa}$ by an essentially isenthalpic flashing process where the resulting vapor is separated from the liquid in a separator and is directed to the turbine. The steam leaves the turbine at $10 \mathrm{kPa}$ with a moisture content of 5 percent and enters the condenser where it is condensed; it is routed to a reinjection well along with the liquid coming off the separator. Determine $(a)$ the power output of the turbine and the thermal efficiency of the plant, $(b)$ the exergy of the geothermal liquid at the exit of the flash chamber, and the exergy destructions and the second-law efficiencies for $(c)$ the turbine and $(d)$ the entire plant.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 70

What is the difference between cogeneration and regeneration?

Mahnoor Amin

Numerade Educator

Problem 71

How is the utilization factor $\epsilon_{u}$ for cogeneration plants defined? Could $\epsilon_{u}$ be unity for a cogeneration plant that does not produce any power?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 72

Consider a cogeneration plant for which the utilization factor is $1 .$ Is the irreversibility associated with this cycle necessarily zero? Explain.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 73

Consider a cogeneration plant for which the utilization factor is $0.5 .$ Can the exergy destruction associated with this plant be zero? If yes, under what conditions?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 74

Steam is generated in the boiler of a cogeneration plant at 600 psia and $650^{\circ} \mathrm{F}$ at a rate of $32 \mathrm{lbm} / \mathrm{s} .$ The plant is to produce power while meeting the process steam requirements for a certain industrial application. One-third of the steam leaving the boiler is throttled to a pressure of 120 psia and is routed to the process heater. The rest of the steam is expanded in an isentropic turbine to a pressure of 120 psia and is also routed to the process heater. Steam leaves the process heater at $240^{\circ} \mathrm{F}$. Neglecting the pump work, determine $(a)$ the net power produced, $(b)$ the rate of process heat supply, and $(c)$ the utilization factor of this plant.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 75

A large food-processing plant requires $1.5 \mathrm{lbm} / \mathrm{s}$ of saturated or slightly superheated steam at 140 psia, which is extracted from the turbine of a cogeneration plant. The boiler generates steam at 800 psia and $1000^{\circ} \mathrm{F}$ at a rate of $10 \mathrm{lbm} / \mathrm{s}$ and the condenser pressure is 2 psia. Steam leaves the process heater as a saturated liquid. It is then mixed with the feedwater at the same pressure, and this mixture is pumped to the boiler pressure. Assuming both the pumps and the turbine have isentropic efficiencies of 91 percent, determine $(a)$ the rate of heat transfer to the boiler and $(b)$ the power output of the cogeneration plant.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 76

An ideal cogeneration steam plant is to generate power and $8600 \mathrm{~kJ} / \mathrm{s}$ of process heat. Steam enters the turbine from the boiler at $7 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$. One-fourth of the steam is extracted from the turbine at 600 -kPa pressure for process heating. The remainder of the steam continues to expand and exhausts to the condenser at $10 \mathrm{kPa}$. The steam extracted for the process heater is condensed in the heater and mixed with the feedwater at $600 \mathrm{kPa}$. The mixture is pumped to the boiler pressure of 7 MPa. Show the cycle on a $T-s$ diagram with respect to saturation lines, and determine $(a)$ the mass flow rate of steam that must be supplied by the boiler, $(b)$ the net power produced by the plant, and $(c)$ the utilization factor.

Narayan Hari

Numerade Educator

Problem 77

Steam is generated in the boiler of a cogeneration plant at $10 \mathrm{MPa}$ and $450^{\circ} \mathrm{C}$ at a steady rate of $5 \mathrm{~kg} / \mathrm{s}$. In normal operation, steam expands in a turbine to a pressure of $0.5 \mathrm{MPa}$ and is then routed to the process heater, where it supplies the process heat. Steam leaves the process heater as a saturated liquid and is pumped to the boiler pressure. In this mode, no steam passes through the condenser, which operates at $20 \mathrm{kPa}$.
(a) Determine the power produced and the rate at which process heat is supplied in this mode.
(b) Determine the power produced and the rate of process heat supplied if only 60 percent of the steam is routed to the process heater and the remainder is expanded to the condenser pressure.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 78

Consider a cogeneration power plant modified with regeneration. Steam enters the turbine at $9 \mathrm{MPa}$ and $400^{\circ} \mathrm{C}$ and expands to a pressure of 1.6 MPa. At this pressure, 35 percent of the steam is extracted from the turbine, and the remainder expands to $10 \mathrm{kPa}$. Part of the extracted steam is used to heat the feedwater in an open feedwater heater. The rest of the extracted steam is used for process heating and leaves the process heater as a saturated liquid at $1.6 \mathrm{MPa}$. It is subsequently mixed with the feedwater leaving the feedwater heater, and the mixture is pumped to the boiler pressure. Assuming the turbines and the pumps to be isentropic, show the cycle on a $T-s$ diagram with respect to saturation lines, and determine the mass flow rate of steam through the boiler for a net power output of $25 \mathrm{MW}$.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 79

Using appropriate software, investigate the effect of the extraction pressure for removing steam from the turbine to be used for the process heater and open feedwater heater on the required mass flow rate. Plot the mass flow rate through the boiler as a function of the extraction pressure, and discuss the results.

Mahnoor Amin

Numerade Educator

Problem 80

In combined gas-steam cycles, what is the energy source for the steam?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 81

Why is the combined gas-steam cycle more efficient than either of the cycles operated alone?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 82

The gas-turbine portion of a combined gas-steam power plant has a pressure ratio of $16 .$ Air enters the compressor at $300 \mathrm{~K}$ at a rate of $14 \mathrm{~kg} / \mathrm{s}$ and is heated to $1500 \mathrm{~K}$ in the combustion chamber. The combustion gases leaving the gas turbine are used to heat the steam to $400^{\circ} \mathrm{C}$ at $10 \mathrm{MPa}$ in a heat exchanger. The combustion gases leave the heat exchanger at $420 \mathrm{~K}$. The steam leaving the turbine is condensed at $15 \mathrm{kPa}$. Assuming all the compression and expansion processes to be isentropic, determine $(a)$ the mass flow rate of the steam, (b) the net power output, and ( $c$ ) the thermal efficiency of the combined cycle. For air, assume constant specific heats at room temperature.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 83

A combined gas-steam power cycle uses a simple gas turbine for the topping cycle and simple Rankine cycle for the bottoming cycle. Atmospheric air enters the gas turbine at $101 \mathrm{kPa}$ and $20^{\circ} \mathrm{C},$ and the maximum gas cycle temperature is $1100^{\circ} \mathrm{C}$. The compressor pressure ratio is 8 ; the compressor isentropic efficiency is 85 percent; and the gas turbine isentropic efficiency is 90 percent. The gas stream leaves the heat exchanger at the saturation temperature of the steam flowing through the heat exchanger. Steam flows through the heat exchanger with a pressure of $6000 \mathrm{kPa}$ and leaves at $320^{\circ} \mathrm{C}$. The steam-cycle condenser operates at $20 \mathrm{kPa},$ and the isentropic efficiency of the steam turbine is 90 percent. Determine the mass flow rate of air through the air compressor required for this system to produce $100 \mathrm{MW}$ of power. Use constant specific heats for air at room temperature.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 84

An ideal regenerator is added to the gas cycle portion of the combined cycle. How much does this change the efficiency of this combined cycle?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 85

Determine which components of the combined cycle are the most wasteful of work potential.

Mahnoor Khan

Numerade Educator

Problem 86

Consider a combined gas-steam power plant that has a net power output of $280 \mathrm{MW}$. The pressure ratio of the gasturbine cycle is $11 .$ Air enters the compressor at $300 \mathrm{~K}$ and the turbine at $1100 \mathrm{~K}$. The combustion gases leaving the gas turbine are used to heat the steam at $5 \mathrm{MPa}$ to $350^{\circ} \mathrm{C}$ in a heat exchanger. The combustion gases leave the heat exchanger at $420 \mathrm{~K}$. An open feedwater heater incorporated with the steam cycle operates at a pressure of 0.8 MPa. The condenser pressure is $10 \mathrm{kPa}$. Assuming isentropic efficiencies of 100 percent for the pump, 82 percent for the compressor, and 86 percent for the gas and steam turbines, determine $(a)$ the mass flow rate ratio of air to steam, $(b)$ the required rate of heat input in the combustion chamber, and (c) the thermal efficiency of the combined cycle.

Penny Riley

Numerade Educator

Problem 87

Using appropriate software, study the effects of the gas cycle pressure ratio as it is varied from 10 to 20 on the ratio of gas flow rate to steam flow rate and cycle thermal efficiency. Plot your results as functions of gas cycle pressure ratio, and discuss the results.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 88

Consider a combined gas-steam power cycle The topping cycle is a simple Brayton cycle that has a pressure ratio of 7 . Air enters the compressor at $15^{\circ} \mathrm{C}$ at a rate of $40 \mathrm{~kg} / \mathrm{s}$ and the gas turbine at $950^{\circ} \mathrm{C}$. The bottoming cycle is a reheat Rankine cycle between the pressure limits of 6 MPa and $10 \mathrm{kPa}$. Steam is heated in a heat exchanger at a rate of $4.6 \mathrm{~kg} / \mathrm{s}$ by the exhaust gases leaving the gas turbine, and the exhaust gases leave the heat exchanger at $200^{\circ} \mathrm{C}$. Steam leaves the high-pressure turbine at $1.0 \mathrm{MPa}$ and is reheated to $400^{\circ} \mathrm{C}$ in the heat exchanger before it expands in the low-pressure turbine. Assuming 80 percent isentropic efficiency for all pumps and turbines, determine $(a)$ the moisture content at the exit of the low-pressure turbine, $(b)$ the steam temperature at the inlet of the high-pressure turbine, $(c)$ the net power output and the thermal efficiency of the combined plant. This problem is solved using appropriate software.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 89

What is a binary power cycle? What is its purpose?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 90

What is the difference between the binary vapor power cycle and the combined gas-steam power cycle?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 91

Why is mercury a suitable working fluid for the topping portion of a binary vapor cycle but not for the bottoming cycle?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 92

Why is steam not an ideal working fluid for vapor power cycles?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 93

By writing an energy balance on the heat exchanger of a binary vapor power cycle, obtain a relation for the ratio of mass flow rates of two fluids in terms of their enthalpies.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 94

Feedwater at $4000 \mathrm{kPa}$ is heated at a rate of $6 \mathrm{~kg} / \mathrm{s}$ from $200^{\circ} \mathrm{C}$ to $245^{\circ} \mathrm{C}$ in a closed feedwater heater of a regenerative Rankine cycle. Bleed steam enters this unit at $3000 \mathrm{kPa}$ with a quality of 90 percent and leaves as a saturated liquid. Calculate the rate at which bleed steam is required.

Mahnoor Amin

Numerade Educator

Problem 95

Steam enters the turbine of a steam power plant that operates on a simple ideal Rankine cycle at a pressure of $6 \mathrm{MPa}$, and it leaves as a saturated vapor at $7.5 \mathrm{kPa}$. Heat is transferred to the steam in the boiler at a rate of $40,000 \mathrm{~kJ} / \mathrm{s}$ Steam is cooled in the condenser by the cooling water from a nearby river, which enters the condenser at $15^{\circ} \mathrm{C}$. Show the cycle on a $T-s$ diagram with respect to saturation lines, and determine $(a)$ the turbine inlet temperature, $(b)$ the net power output and thermal efficiency, and $(c)$ the minimum mass flow rate of the cooling water required.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 96

Consider a steam power plant operating on the ideal Rankine cycle with reheat between the pressure limits of $30 \mathrm{MPa}$ and $10 \mathrm{kPa}$ with a maximum cycle temperature of $700^{\circ} \mathrm{C}$ and a moisture content of 5 percent at the turbine exit. For a reheat temperature of $700^{\circ} \mathrm{C}$, determine the reheat pressures of the cycle for the cases of $(a)$ single and $(b)$ double reheat.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 97

A steam power plant operates on an ideal Rankine cycle with two stages of reheat and has a net power output of $75 \mathrm{MW}$. Steam enters all three stages of the turbine at $550^{\circ} \mathrm{C}$ The maximum pressure in the cycle is $10 \mathrm{MPa}$, and the minimum pressure is $30 \mathrm{kPa}$. Steam is reheated at 4 MPa the first time and at 2 MPa the second time. Show the cycle on a $T-s$ diagram with respect to saturation lines, and determine $(a)$ the thermal efficiency of the cycle and $(b)$ the mass flow rate of the steam.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 98

Consider a steam power plant that operates on a regenerative Rankine cycle and has a net power output of $150 \mathrm{MW}$. Steam enters the turbine at $10 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$ and the condenser at $10 \mathrm{kPa} .$ The isentropic efficiency of the turbine is 80 percent, and that of the pumps is 95 percent. Steam is extracted from the turbine at 0.5 MPa to heat the feedwater in an open feedwater heater. Water leaves the feedwater heater as a saturated liquid. Show the cycle on a $T-s$ diagram, and determine $(a)$ the mass flow rate of steam through the boiler and $(b)$ the thermal efficiency of the cycle. Also, determine the exergy destruction associated with the regeneration process. Assume a source temperature of $1300 \mathrm{~K}$ and a sink temperature of $303 \mathrm{~K}$.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 99

Repeat Prob. $10-98$ assuming both the pump and the turbine are isentropic.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 100

Consider an ideal reheat-regenerative Rankine cycle with one open feedwater heater. The boiler pressure is $10 \mathrm{MPa}$ the condenser pressure is $15 \mathrm{kPa},$ the reheater pressure is 1 MPa, and the feedwater pressure is 0.6 MPa. Steam enters both the high- and low-pressure turbines at $500^{\circ} \mathrm{C}$. Show the cycle on a $T-s$ diagram with respect to saturation lines, and determine ( $a$ ) the fraction of steam extracted for regeneration and $(b)$ the thermal efficiency of the cycle.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 101

Repeat Prob. $10-100$ assuming an isentropic efficiency of 84 percent for the turbines and 89 percent for the pumps.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 102

A textile plant requires $4 \mathrm{~kg} / \mathrm{s}$ of saturated steam at 2 MPa, which is extracted from the turbine of a cogeneration plant. Steam enters the turbine at $8 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$ at a rate of $11 \mathrm{~kg} / \mathrm{s}$ and leaves at $20 \mathrm{kPa}$. The extracted steam leaves the process heater as a saturated liquid and mixes with the feedwater at constant pressure. The mixture is pumped to the boiler pressure. Assuming an isentropic efficiency of 88 percent for both the turbine and the pumps, determine $(a)$ the rate of process heat supply, $(b)$ the net power output, and $(c)$ the utilization factor of the plant.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 103

Consider a cogeneration power plant that is modified with reheat and that produces 3 MW of power and supplies 7 MW of process heat. Steam enters the high-pressure turbine at $8 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$ and expands to a pressure of 1 MPa. At this pressure, part of the steam is extracted from the turbine and routed to the process heater, while the remainder is reheated to $500^{\circ} \mathrm{C}$ and expanded in the low-pressure turbine to the condenser pressure of $15 \mathrm{kPa}$. The condensate from the condenser is pumped to 1 MPa and is mixed with the extracted steam, which leaves the process heater as a compressed liquid at $120^{\circ} \mathrm{C}$. The mixture is then pumped to the boiler pressure. Assuming the turbine to be isentropic, show the cycle on a $T-s$ diagram with respect to saturation lines, and disregarding pump work, determine $(a)$ the rate of heat input in the boiler and $(b)$ the fraction of steam extracted for process heating.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 104

Steam is to be supplied from a boiler to a high-pressure turbine whose isentropic efficiency is 85 percent at conditions to be determined. The steam is to leave the high pressure turbine as a saturated vapor at $1.4 \mathrm{MPa}$, and the turbine is to produce $5.5 \mathrm{MW}$ of power. Steam at the turbine exit is extracted at a rate of $1000 \mathrm{~kg} / \mathrm{min}$ and routed to a process heater while the rest of the steam is supplied to a low-pressure turbine whose isentropic efficiency is 80 percent. The low pressure turbine allows the steam to expand to $10 \mathrm{kPa}$ pressure and produces $1.5 \mathrm{MW}$ of power. Determine the temperature, pressure, and the flow rate of steam at the inlet of the high pressure turbine.

Mohammad Mehran

Mohammad Mehran

Numerade Educator

Problem 105

Atmospheric air enters the air compressor of a simple combined gas-steam power system at 14.7 psia and $80^{\circ} \mathrm{F}$. The air compressor's compression ratio is $10 ;$ the gas cycle's maximum temperature is $2100^{\circ} \mathrm{F}$; and the air compressor and turbine have an isentropic efficiency of 90 percent. The gas leaves the heat exchanger $50^{\circ} \mathrm{F}$ hotter than the saturation temperature of the steam in the heat exchanger. The steam pressure in the heat exchanger is 800 psia, and the steam leaves the heat exchanger at $600^{\circ} \mathrm{F}$. The steam-condenser pressure is 5 psia and the isentropic efficiency of the steam turbine is 95 percent. Determine the overall thermal efficiency of this combined cycle. For air, use constant specific heats at room temperature.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 106

It has been suggested that the steam passing through the condenser of the combined cycle be routed to buildings during the winter to heat them. When this is done, the pressure in the heating system where the steam is now condensed will have to be increased to 10 psia. How does this change the overall thermal efficiency of the combined cycle?

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 107

During winter, the system must supply $2 \times 10^{6} \mathrm{Btu} / \mathrm{h}$ of heat to the buildings. What is the mass flow rate of air through the air compressor and the system's total electrical power production in winter?

Jincy M Saji

Numerade Educator

Problem 108

The gas-turbine cycle of a combined gas-steam power plant has a pressure ratio of $12 .$ Air enters the compressor at $310 \mathrm{~K}$ and the turbine at $1400 \mathrm{~K}$. The combustion gases leaving the gas turbine are used to heat the steam at 12.5 MPa to $500^{\circ} \mathrm{C}$ in a heat exchanger. The combustion gases leave the heat exchanger at $247^{\circ} \mathrm{C}$. Steam expands in a high-pressure turbine to a pressure of 2.5 MPa and is reheated in the combustion chamber to $550^{\circ} \mathrm{C}$ before it expands in a low-pressure turbine to $10 \mathrm{kPa}$. The mass flow rate of steam is $12 \mathrm{~kg} / \mathrm{s}$. Assuming all the compression and expansion processes to be isentropic, determine $(a)$ the mass flow rate of air in the gas-turbine cycle, (b) the rate of total heat input, and $(c)$ the thermal efficiency of the combined cycle.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 109

Repeat Prob. $10-108$ assuming isentropic efficiencies of 100 percent for the pump, 85 percent for the compressor, and 90 percent for the gas and steam turbines.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 110

A steam power plant operates on an ideal reheat-regenerative Rankine cycle with one reheater and two feedwater heaters, one open and one closed. Steam enters the high-pressure turbine at $15 \mathrm{MPa}$ and $600^{\circ} \mathrm{C}$ and the lowpressure turbine at $1 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$. The condenser pressure is $5 \mathrm{kPa}$. Steam is extracted from the turbine at $0.6 \mathrm{MPa}$ for the closed feedwater heater and at 0.2 MPa for the open feedwater heater. In the closed feedwater heater, the feedwater is heated to the condensation temperature of the extracted steam. The extracted steam leaves the closed feedwater heater as a saturated liquid, which is subsequently throttled to the open feedwater heater. Show the cycle on a $T-s$ diagram with respect to saturation lines. Determine $(a)$ the fraction of steam extracted from the turbine for the open feedwater heater, $(b)$ the thermal efficiency of the cycle, and $(c)$ the net power output for a mass flow rate of $42 \mathrm{~kg} / \mathrm{s}$ through the boiler.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 111

A Rankine steam cycle modified for reheat, a closed feedwater heater, and an open feedwater heater is shown below. The high-pressure turbine receives $100 \mathrm{~kg} / \mathrm{s}$ 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 $25^{\circ} \mathrm{C},$ what is the minimum flow rate of the cooling water required for the ideal cycle, in $\mathrm{kg} / \mathrm{s} ?$ Take $c_{p, \text { water }}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}$

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 112

A Rankine steam cycle modified for reheat and three closed feedwater heaters is shown below. The high-pressure turbine receives $100 \mathrm{~kg} / \mathrm{s}$ 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 the cooling water is limited to a $10^{\circ} \mathrm{C}$ temperature rise, what is the flow rate of the cooling water required for the ideal cycle, in $\mathrm{kg} / \mathrm{s}$ ? Take $c_{p, \text { water }}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}$.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 113

Using appropriate software, investigate the effect of the boiler pressure on the performance of a simple ideal Rankine cycle. Steam enters the turbine at $500^{\circ} \mathrm{C}$ and exits at $10 \mathrm{kPa}$. The boiler pressure is varied from 0.5 to 20 MPa. Determine the thermal efficiency of the cycle and plot it against the boiler pressure, and discuss the results.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 114

Using appropriate software, investigate the effect of the condenser pressure on the performance of a simple ideal Rankine cycle. Turbine inlet conditions of steam are maintained constant at $10 \mathrm{MPa}$ and $550^{\circ} \mathrm{C}$ while the condenser pressure is varied from 5 to $100 \mathrm{kPa}$. Determine the thermal efficiency of the cycle and plot it against the condenser pressure, and discuss the results.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 115

Using appropriate software, investigate the effect of superheating the steam on the performance of a simple ideal Rankine cycle. Steam enters the turbine at 3 MPa and exits at $10 \mathrm{kPa}$. The turbine inlet temperature is varied from 250 to $1100^{\circ} \mathrm{C}$. Determine the thermal efficiency of the cycle and plot it against the turbine inlet temperature, and discuss the results.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 116

Using appropriate software, investigate the effect of reheat pressure on the performance of an ideal Rankine cycle. The maximum and minimum pressures in the cycle are $15 \mathrm{MPa}$ and $10 \mathrm{kPa}$, respectively, and steam enters both stages of the turbine at $500^{\circ} \mathrm{C}$. The reheat pressure is varied from 12.5 to 0.5 MPa. Determine the thermal efficiency of the cycle and plot it against the reheat pressure, and discuss the results.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 117

Show that the thermal efficiency of a combined gas steam power plant $\eta_{\mathrm{cc}}$ can be expressed as $$\eta_{\mathrm{cc}}=\eta_{g}+\eta_{s}-\eta_{g} \eta_{s}$$ where $\eta_{g}=W_{g} / Q_{\text {in }}$ and $\eta_{s}=W_{s} / Q_{\text {gout }}$ are the thermal efficiencies of the gas and steam cycles, respectively. Using this relation, determine the thermal efficiency of a combined power cycle that consists of a topping gas-turbine cycle with an efficiency of 40 percent and a bottoming steam-turbine cycle with an efficiency of 30 percent.

Saman Zulfiqar

Numerade Educator

Problem 118

It can be shown that the thermal efficiency of a combined gas-steam power plant $\eta_{\mathrm{cc}}$ can be expressed in terms of the thermal efficiencies of the gas- and the steam-turbine cycles as $$\eta_{\mathrm{cc}}=\eta_{g}+\eta_{s}-\eta_{g} \eta_{s}$$
Prove that the value of $\eta_{\mathrm{cc}}$ is greater than either $\eta_{g}$ or $\eta_{s} .$ That is, the combined cycle is more efficient than either the gas turbine or steam-turbine cycle alone.

Saman Zulfiqar

Numerade Educator

Problem 119

A solar collector system delivers heat to a power plant. It is well known that the thermal collection efficiency $\eta_{\mathrm{sc}}$ of a solar collector diminishes with increasing solar collection output temperature $T_{H},$ or $\eta_{\mathrm{sc}}=A-B T_{H}$ where $A$ and $B$ are known constants. The thermal efficiency of the power plant $\eta_{\text {th }}$ is a fixed fraction of the Carnot thermal efficiency, such that $\eta_{\mathrm{th}}=F\left(1-T_{L} / T_{H}\right)$ where $F$ is a known constant assumed here independent of temperatures and $T_{L}$ is the condenser temperature, also constant for this problem. Here, the solar collection temperature $T_{H}$ is also taken to be the source temperature for the power plant.
(a) At what temperature $T_{H}$ should the solar collector be operated to obtain the maximum overall system efficiency?
(b) Develop an expression for the maximum overall system efficiency.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 120

Starting with Eq. $10-20,$ show that the exergy destruction associated with a simple ideal Rankine cycle can be expressed as $x_{\text {dest }}=q_{\text {in }}\left(\eta_{\text {th.Carnot }}-\eta_{\text {th }}\right),$ where $\eta_{\text {th }}$ is the efficiency of the Rankine cycle and $\eta_{\text {th,Carnot }}$ is the efficiency of the Carnot cycle operating between the same temperature limits.

Saman Zulfiqar

Numerade Educator

Problem 121

Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. If the steam is superheated to
a higher temperature,
(a) the turbine work output will decrease.
(b) the amount of heat rejected will decrease.
(c) the cycle efficiency will decrease.
( $d$ ) the moisture content at turbine exit will decrease.
( $e$ ) the amount of heat input will decrease.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 122

Consider a simple ideal Rankine cycle. If the condenser pressure is lowered while keeping the turbine inlet state the same,
( $a$ ) the turbine work output will decrease.
(b) the amount of heat rejected will decrease.
(c) the cycle efficiency will decrease.
( $d$ ) the moisture content at turbine exit will decrease.
( $e$ ) the pump work input will decrease.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 123

Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. If the cycle is modified with reheating,
( $a$ ) the turbine work output will decrease.
(b) the amount of heat rejected will decrease.
(c) the pump work input will decrease.
( $d$ ) the moisture content at turbine exit will decrease.
(e) the amount of heat input will decrease.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 124

Consider a simple ideal Rankine cycle with fixed boiler and condenser pressures. If the cycle is modified with regeneration that involves one open feedwater heater (select the correct statement per unit mass of steam flowing through the boiler),
( $a$ ) the turbine work output will decrease.
(b) the amount of heat rejected will increase.
(c) the cycle thermal efficiency will decrease.
(d) the quality of steam at turbine exit will decrease.
( $e$ ) the amount of heat input will increase.

Dominador Tan

Numerade Educator

Problem 125

Consider a steady-flow Carnot cycle with water as the working fluid executed under the saturation dome between the pressure limits of $1 \mathrm{MPa}$ and $10 \mathrm{kPa}$. Water changes from saturated liquid to saturated vapor during the heat addition process. The net work output of this cycle is
(a) $596 \mathrm{~kJ} / \mathrm{kg}$
(b) $666 \mathrm{~kJ} / \mathrm{kg}$
(c) $708 \mathrm{~kJ} / \mathrm{kg}$
(d) $822 \mathrm{~kJ} / \mathrm{kg}$
(e) $1500 \mathrm{~kJ} / \mathrm{kg}$

Mahnoor Amin

Numerade Educator

Problem 126

A simple ideal Rankine cycle operates between the pressure limits of $10 \mathrm{kPa}$ and $5 \mathrm{MPa}$, with a turbine inlet temperature of $600^{\circ} \mathrm{C}$. The mass fraction of steam that condenses at the turbine exit is
( $a$ ) 6 percent
(b) 9 percent
(c) 12 percent
(d) 15 percent
(e) 18 percent

Mahnoor Amin

Numerade Educator

Problem 127

A steam power plant operates on the simple ideal Rankine cycle between the pressure limits of $10 \mathrm{kPa}$ and $5 \mathrm{MPa},$ with a turbine inlet temperature of $600^{\circ} \mathrm{C} .$ The rate of heat transfer in the boiler is $450 \mathrm{~kJ} / \mathrm{s}$. Disregarding the pump work, the power output of this plant is
(a) $118 \mathrm{~kW}$
(b) $140 \mathrm{~kW}$
(c) $177 \mathrm{~kW}$
(d) $286 \mathrm{~kW}$
(e) $450 \mathrm{~kW}$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 128

A simple ideal Rankine cycle operates between the pressure limits of $10 \mathrm{kPa}$ and $3 \mathrm{MPa}$, with a turbine inlet temperature of $600^{\circ} \mathrm{C}$. Disregarding the pump work, the cycle efficiency is
(a) 24 percent
(b) 37 percent
(c) 52 percent
(d) 63 percent
(e) 71 percent

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 129

An ideal reheat Rankine cycle operates between the pressure limits of $10 \mathrm{kPa}$ and $8 \mathrm{MPa}$, with reheat occurring at 4 MPa. The temperature of steam at the inlets of both turbines is $500^{\circ} \mathrm{C},$ and the enthalpy of steam is $3185 \mathrm{~kJ} / \mathrm{kg}$ at the exit of the high-pressure turbine and $2247 \mathrm{~kJ} / \mathrm{kg}$ at the exit of the low-pressure turbine. Disregarding the pump work, the cycle efficiency is
(a) 29 percent
(b) 32 percent
(c) 36 percent
(d) 41 percent
(e) 49 percent

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 130

Pressurized feedwater in a steam power plant is to be heated in an ideal open feedwater heater that operates at a pressure of 2 MPa with steam extracted from the turbine. If the enthalpy of the feedwater is $252 \mathrm{~kJ} / \mathrm{kg}$ and the enthalpy of the extracted steam is $2810 \mathrm{~kJ} / \mathrm{kg},$ the mass fraction of steam extracted from the turbine is
(a) 10 percent
(b) 14 percent
(c) 26 percent
(d) 36 percent
(e) 50 percent

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 131

Consider a steam power plant that operates on the regenerative Rankine cycle with one open feedwater heater. The enthalpy of the steam is $3374 \mathrm{~kJ} / \mathrm{kg}$ at the turbine inlet, $2797 \mathrm{~kJ} / \mathrm{kg}$ at the location of bleeding, and $2346 \mathrm{~kJ} / \mathrm{kg}$ at the turbine exit. The net power output of the plant is $120 \mathrm{MW},$ and the fraction of steam bled off the turbine for regeneration is 0.172. If the pump work is negligible, the mass flow rate of steam at the turbine inlet is
(a) $117 \mathrm{~kg} / \mathrm{s}$
(b) $126 \mathrm{~kg} / \mathrm{s}$
(c) $219 \mathrm{~kg} / \mathrm{s}$
(d) $268 \mathrm{~kg} / \mathrm{s}$
(e) $679 \mathrm{~kg} / \mathrm{s}$

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 132

Consider a combined gas-steam power plant. Water for the steam cycle is heated in a well-insulated heat exchanger by the exhaust gases that enter at $800 \mathrm{~K}$ at a rate of $60 \mathrm{~kg} / \mathrm{s}$ and leave at $400 \mathrm{~K}$. Water enters the heat exchanger at $200^{\circ} \mathrm{C}$ and 8 MPa and leaves at $350^{\circ} \mathrm{C}$ and $8 \mathrm{MPa}$. If the exhaust gases are treated as air with constant specific heats at room temperature, the mass flow rate of water through the heat exchanger becomes
(a) $11 \mathrm{~kg} / \mathrm{s}$
(b) $24 \mathrm{~kg} / \mathrm{s}$
(c) $46 \mathrm{~kg} / \mathrm{s}$
(d) $53 \mathrm{~kg} / \mathrm{s}$
(e) $60 \mathrm{~kg} / \mathrm{s}$

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 133

Consider a cogeneration power plant modified with regeneration. Steam enters the turbine at $6 \mathrm{MPa}$ and $450^{\circ} \mathrm{C}$ at a rate of $20 \mathrm{~kg} / \mathrm{s}$ and expands to a pressure of $0.4 \mathrm{MPa}$. At this pressure, 60 percent of the steam is extracted from the turbine, and the remainder expands to a pressure of $10 \mathrm{kPa}$. Part of the extracted steam is used to heat feedwater in an open feedwater heater. The rest of the extracted steam is used for process heating and leaves the process heater as a saturated liquid at $0.4 \mathrm{MPa} .$ It is subsequently mixed with the feedwater leaving the feedwater heater, and the mixture is pumped to the boiler pressure. The steam in the condenser is cooled and condensed by the cooling water from a nearby river, which enters the adiabatic condenser at a rate of $463 \mathrm{~kg} / \mathrm{s}$.
1. The total power output of the turbine is
(a) $17.0 \mathrm{MW}$
(b) $8.4 \mathrm{MW}$
(c) $12.2 \mathrm{MW}$
(d) $20.0 \mathrm{MW}$
(e) $3.4 \mathrm{MW}$
2. The temperature rise of the cooling water from the river in the condenser is
(a) $8.0^{\circ} \mathrm{C}$
(b) $5.2^{\circ} \mathrm{C}$
(c) $9.6^{\circ} \mathrm{C}$
(d) $12.9^{\circ} \mathrm{C}$
(e) $16.2^{\circ} \mathrm{C}$
3. The mass flow rate of steam through the process heater is
(a) $1.6 \mathrm{~kg} / \mathrm{s}$
(b) $3.8 \mathrm{~kg} / \mathrm{s}$
(c) $5.2 \mathrm{~kg} / \mathrm{s}$
(d) $7.6 \mathrm{~kg} / \mathrm{s}$
(e) $10.4 \mathrm{~kg} / \mathrm{s}$
4. The rate of heat supply from the process heater per unit mass of steam passing through it is
(a) $246 \mathrm{~kJ} / \mathrm{kg}$
(b) $893 \mathrm{~kJ} / \mathrm{kg}$
(c) $1344 \mathrm{~kJ} / \mathrm{kg}$
(d) $1891 \mathrm{~kJ} / \mathrm{kg}$
(e) $2060 \mathrm{~kJ} / \mathrm{kg}$
5. The rate of heat transfer to the steam in the boiler is
(a) $26.0 \mathrm{MJ} / \mathrm{s}$
(b) $53.8 \mathrm{MJ} / \mathrm{s}$
(c) $39.5 \mathrm{MJ} / \mathrm{s}$
(d) $62.8 \mathrm{MJ} / \mathrm{s}$
(e) $125.4 \mathrm{MJ} / \mathrm{s}$

Andrew C

Numerade Educator

Problem 134

Stack gases exhausting from electrical power plants are at approximately $150^{\circ} \mathrm{C}$. Design a basic Rankine cycle that uses water, refrigerant- $134 \mathrm{a}$, or ammonia as the working fluid and that produces the maximum amount of work from this energy source while rejecting heat to the ambient air at $40^{\circ} \mathrm{C}$. You are to use a turbine whose efficiency is 92 percent and whose exit quality cannot be less than 85 percent.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 135

Design a steam power cycle that can achieve a cycle thermal efficiency of at least 40 percent under the conditions that all turbines have isentropic efficiencies of 85 percent and all pumps have isentropic efficiencies of 60 percent. Prepare an engineering report describing your design. Your design report must include, but is not limited to, the following:
(a) Discussion of various cycles attempted to meet the goal as well as the positive and negative aspects of your design.
(b) System figures and $T-s$ diagrams with labeled states and temperature, pressure, enthalpy, and entropy information for your design.
(c) Sample calculations.

Eric Mockensturm

Eric Mockensturm

Numerade Educator

Problem 136

A natural gas-fired furnace in a textile plant is used to provide steam at $130^{\circ} \mathrm{C}$. At times of high demand, the furnace supplies heat to the steam at a rate of $30 \mathrm{MJ} / \mathrm{s}$. The plant also uses up to $6 \mathrm{MW}$ of electrical power purchased from the local power company. The plant management is considering converting the existing process plant into a cogeneration plant to meet both their process-heat and power requirements. Your job is to come up with some designs. Designs based on a gas turbine or a steam turbine are to be considered. First decide whether a system based on a gas turbine or a steam turbine will best serve the purpose, considering the cost and the complexity. Then propose your design for the cogeneration plant complete with pressures and temperatures and the mass flow rates. Show that the proposed design meets the power and processheat requirements of the plant.

Jincy M Saji

Numerade Educator

Problem 137

Design the condenser of a steam power plant that has a thermal efficiency of 40 percent and generates $10 \mathrm{MW}$ of net electric power. Steam enters the condenser as saturated vapor at $10 \mathrm{kPa},$ and it is to be condensed outside horizontal tubes through which cooling water from a nearby river flows. The temperature rise of the cooling water is limited to $8^{\circ} \mathrm{C},$ and the velocity of the cooling water in the pipes is limited to $6 \mathrm{~m} / \mathrm{s}$ to keep the pressure drop at an acceptable level. From prior experience, the average heat flux based on the outer surface of the tubes can be taken to be $12,000 \mathrm{~W} / \mathrm{m}^{2}$. Specify the pipe diameter, total pipe length, and the arrangement of the pipes to minimize the condenser volume.

Jincy M Saji

Numerade Educator

Problem 138

Several geothermal power plants are in operation in the United States. Heat source of a geothermal plant is hot geothermal water, which is "free energy." An 8-MW geothermal power plant is being considered at a location where geothermal water at $160^{\circ} \mathrm{C}$ is available. Geothermal water is to serve as the heat source for a closed Rankine power cycle with refrigerant$134 \mathrm{a}$ as the working fluid. Specify suitable temperatures and pressures for the cycle, and determine the thermal efficiency of the cycle. Justify your selections.

Nicholas Mogoi

Numerade Educator

Problem 139

A 10-MW geothermal power plant is being considered at a site where geothermal water at $230^{\circ} \mathrm{C}$ is available. Geothermal water is to be flashed into a chamber to a lower pressure where part of the water evaporates. The liquid is returned to the ground while the vapor is used to drive the steam turbine. The pressures at the turbine inlet and the turbine exit are to remain above $200 \mathrm{kPa}$ and $8 \mathrm{kPa}$, respectively. Highpressure flash chambers yield a small amount of steam with high exergy whereas lower-pressure flash chambers yield considerably more steam but at a lower exergy. By trying several pressures, determine the optimum pressure of the flash chamber to maximize the power production per unit mass of geothermal water withdrawn. Also, determine the thermal efficiency for each case assuming 10 percent of the power produced is used to drive the pumps and other auxiliary equipment.

Narayan Hari

Numerade Educator

Problem 140

A photographic equipment manufacturer uses a flow of $64,500 \mathrm{lbm} / \mathrm{h}$ of steam in its manufacturing process. Currently the spent steam at 3.8 psia and $224^{\circ} \mathrm{F}$ is exhausted to the atmosphere. Do the preliminary design of a system to use the energy in the waste steam economically. If electricity is produced, it can be generated about $8000 \mathrm{~h} / \mathrm{yr},$ and its value is $\$ 0.08 / \mathrm{kWh} .$ If the energy is used for space heating, the value is also $\$ 0.08 / \mathrm{kWh},$ but it can only be used about $3000 \mathrm{~h} / \mathrm{yr}$ (only during the "heating season"). If the steam is condensed and the liquid $\mathrm{H}_{2} \mathrm{O}$ is recycled through the process, its value is $\$ 0.70 / 100$ gal. Make all assumptions as realistic as possible. Sketch the system you propose. Make a separate list of required components and their specifications (capacity, efficiency, etc.). The final result will be the calculated annual dollar value of the energy use plan (actually a saving because it will replace electricity or heat and/or water that would otherwise have to be purchased).

Manik Pulyani

Numerade Educator

Problem 141

Contact your power company and obtain information on the thermodynamic aspects of their most recently built power plant. If it is a conventional power plant, find out why it is preferred over a highly efficient combined power plant.

Naman Kumar

Numerade Educator