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Unformatted text preview: cen84959_ch10.qxd 4/19/05 2:17 PM Page 551 Chapter 10
VAPOR AND COMBINED POWER CYCLES I n Chap. 9 we discussed gas power cycles for which the
working fluid remains a gas throughout the entire cycle. In
this chapter, we consider vapor power cycles in which the
working fluid is alternatively vaporized and condensed. We
also consider power generation coupled with process heating
called cogeneration.
The continued quest for higher thermal efficiencies has
resulted in some innovative modifications to the basic vapor
power cycle. Among these, we discuss the reheat and regenerative cycles, as well as combined gas–vapor power cycles.
Steam is the most common working fluid used in vapor
power cycles because of its many desirable characteristics,
such as low cost, availability, and high enthalpy of vaporization. Therefore, this chapter is mostly devoted to the discussion of steam power plants. Steam power plants are commonly
referred to as coal plants, nuclear plants, or natural gas
plants, depending on the type of fuel used to supply heat to
the steam. However, the steam goes through the same basic
cycle in all of them. Therefore, all can be analyzed in the
same manner. Objectives
The objectives of Chapter 10 are to:
• Analyze vapor power cycles in which the working fluid is
alternately vaporized and condensed.
• Analyze power generation coupled with process heating
called cogeneration.
• Investigate ways to modify the basic Rankine vapor power
cycle to increase the cycle thermal efficiency.
• Analyze the reheat and regenerative vapor power cycles.
• Analyze power cycles that consist of two separate cycles
known as combined cycles and binary cycles.  551 cen84959_ch10.qxd 4/19/05 2:17 PM Page 552 552  Thermodynamics 10–1 THE CARNOT VAPOR CYCLE ■ We have mentioned repeatedly that the Carnot cycle is the most efficient
cycle operating between two specified temperature limits. Thus it is natural
to look at the Carnot cycle first as a prospective ideal cycle for vapor power
plants. If we could, we would certainly adopt it as the ideal cycle. As
explained below, however, the Carnot cycle is not a suitable model for
power cycles. Throughout the discussions, we assume steam to be the working fluid since it is the working fluid predominantly used in vapor power
cycles.
Consider a steadyflow Carnot cycle executed within the saturation dome
of a pure substance, as shown in Fig. 101a. The fluid is heated reversibly
and isothermally in a boiler (process 12), expanded isentropically in a turbine (process 23), condensed reversibly and isothermally in a condenser
(process 34), and compressed isentropically by a compressor to the initial
state (process 41).
Several impracticalities are associated with this cycle:
1. Isothermal heat transfer to or from a twophase system is not difficult to achieve in practice since maintaining a constant pressure in the
device automatically fixes the temperature at the saturation value. Therefore,
processes 12 and 34 can be approached closely in actual boilers and condensers. Limiting the heat transfer processes to twophase systems, however, severely limits the maximum temperature that can be used in the cycle
(it has to remain under the criticalpoint value, which is 374°C for water).
Limiting the maximum temperature in the cycle also limits the thermal efficiency. Any attempt to raise the maximum temperature in the cycle involves
heat transfer to the working fluid in a single phase, which is not easy to
accomplish isothermally.
2. The isentropic expansion process (process 23) can be approximated
closely by a welldesigned turbine. However, the quality of the steam decreases
during this process, as shown on the Ts diagram in Fig. 10–1a. Thus the
turbine has to handle steam with low quality, that is, steam with a high
moisture content. The impingement of liquid droplets on the turbine blades
causes erosion and is a major source of wear. Thus steam with qualities less
than about 90 percent cannot be tolerated in the operation of power plants.
T T
1 1 4 FIGURE 101
Ts diagram of two Carnot vapor
cycles. 4 2 2 3 3 s
(a) s
(b) cen84959_ch10.qxd 4/25/05 3:56 PM Page 553 Chapter 10  553 This problem could be eliminated by using a working fluid with a very
steep saturated vapor line.
3. The isentropic compression process (process 41) involves the compression of a liquid–vapor mixture to a saturated liquid. There are two difficulties associated with this process. First, it is not easy to control the condensation
process so precisely as to end up with the desired quality at state 4. Second, it
is not practical to design a compressor that handles two phases.
Some of these problems could be eliminated by executing the Carnot
cycle in a different way, as shown in Fig. 10–1b. This cycle, however, presents other problems such as isentropic compression to extremely high pressures and isothermal heat transfer at variable pressures. Thus we conclude
that the Carnot cycle cannot be approximated in actual devices and is not a
realistic model for vapor power cycles. 10–2 ■ RANKINE CYCLE: THE IDEAL CYCLE
FOR VAPOR POWER CYCLES INTERACTIVE
TUTORIAL Many of the impracticalities associated with the Carnot cycle can be eliminated by superheating the steam in the boiler and condensing it completely
in the condenser, as shown schematically on a Ts diagram in Fig. 10–2. The
cycle that results is the Rankine cycle, which is the ideal cycle for vapor
power plants. The ideal Rankine cycle does not involve any internal irreversibilities and consists of the following four processes:
12
23
34
41 SEE TUTORIAL CH. 10, SEC. 1 ON THE DVD. Isentropic compression in a pump
Constant pressure heat addition in a boiler
Isentropic expansion in a turbine
Constant pressure heat rejection in a condenser
q in Boiler
T
3 2 wturb,out
Turbine wpump,in 3
Pump wturb,out q in 4
q out 2
1 Condenser
1 q out 4 wpump,in
s FIGURE 10–2
The simple ideal Rankine cycle. cen84959_ch10.qxd 4/19/05 2:17 PM Page 554 554  Thermodynamics
Water enters the pump at state 1 as saturated liquid and is compressed
isentropically to the operating pressure of the boiler. The water temperature
increases somewhat during this isentropic compression process due to a
slight decrease in the specific volume of water. The vertical distance
between states 1 and 2 on the Ts diagram is greatly exaggerated for clarity.
(If water were truly incompressible, would there be a temperature change at
all during this process?)
Water enters the boiler as a compressed liquid at state 2 and leaves as a
superheated vapor at state 3. The boiler is basically a large heat exchanger
where the heat originating from combustion gases, nuclear reactors, or other
sources is transferred to the water essentially at constant pressure. The
boiler, together with the section where the steam is superheated (the superheater), is often called the steam generator.
The superheated vapor at state 3 enters the turbine, where it expands isentropically and produces work by rotating the shaft connected to an electric
generator. The pressure and the temperature of steam drop during this
process to the values at state 4, where steam enters the condenser. At this
state, steam is usually a saturated liquid–vapor mixture with a high quality.
Steam is condensed at constant pressure in the condenser, which is basically
a large heat exchanger, by rejecting heat to a cooling medium such as a
lake, a river, or the atmosphere. Steam leaves the condenser as saturated liquid and enters the pump, completing the cycle. In areas where water is precious, the power plants are cooled by air instead of water. This method of
cooling, which is also used in car engines, is called dry cooling. Several
power plants in the world, including some in the United States, use dry
cooling to conserve water.
Remembering that the area under the process curve on a Ts diagram
represents the heat transfer for internally reversible processes, we see
that the area under process curve 23 represents the heat transferred to the
water in the boiler and the area under the process curve 41 represents
the heat rejected in the condenser. The difference between these two
(the area enclosed by the cycle curve) is the net work produced during the
cycle. Energy Analysis of the Ideal Rankine Cycle
All four components associated with the Rankine cycle (the pump, boiler,
turbine, and condenser) are steadyflow devices, and thus all four processes
that make up the Rankine cycle can be analyzed as steadyflow processes.
The kinetic and potential energy changes of the steam are usually small relative to the work and heat transfer terms and are therefore usually
neglected. Then the steadyflow energy equation per unit mass of steam
reduces to
1 qin qout 2 1 win wout 2 he hi 1 kJ> kg 2 (10–1) The boiler and the condenser do not involve any work, and the pump and
the turbine are assumed to be isentropic. Then the conservation of energy
relation for each device can be expressed as follows:
Pump (q 0): wpump,in h2 h1 (10–2) cen84959_ch10.qxd 4/19/05 2:17 PM Page 555 Chapter 10
or,
wpump,in v 1 P2 P1 2 (10–3) where
h1
Boiler (w hf @ P1 v v1 qin h3 h2 (10–5) wturb,out h3 h4 (10–6) qout h4 h1 (10–7) 0): Turbine (q
Condenser (w and 0):
0): vf @ P1 (10–4) The thermal efficiency of the Rankine cycle is determined from
h th wnet
qin 1 qout
qin (10–8) where
wnet qin qout wturb,out wpump,in The conversion efficiency of power plants in the United States is often
expressed in terms of heat rate, which is the amount of heat supplied, in
Btu’s, to generate 1 kWh of electricity. The smaller the heat rate, the greater
the efficiency. Considering that 1 kWh
3412 Btu and disregarding the
losses associated with the conversion of shaft power to electric power, the
relation between the heat rate and the thermal efficiency can be expressed as
h th 3412 1 Btu> kWh 2 Heat rate 1 Btu> kWh 2 (10–9) For example, a heat rate of 11,363 Btu/kWh is equivalent to 30 percent
efficiency.
The thermal efficiency can also be interpreted as the ratio of the area
enclosed by the cycle on a Ts diagram to the area under the heataddition
process. The use of these relations is illustrated in the following example.
EXAMPLE 10–1 The Simple Ideal Rankine Cycle Consider a steam power plant operating on the simple ideal Rankine cycle.
Steam enters the turbine at 3 MPa and 350°C and is condensed in the condenser at a pressure of 75 kPa. Determine the thermal efficiency of this
cycle. Solution A steam power plant operating on the simple ideal Rankine cycle
is considered. The thermal efficiency of the cycle is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential
energy changes are negligible.
Analysis The schematic of the power plant and the Ts diagram of the cycle
are shown in Fig. 10–3. We note that the power plant operates on the ideal
Rankine cycle. Therefore, the pump and the turbine are isentropic, there are
no pressure drops in the boiler and condenser, and steam leaves the condenser and enters the pump as saturated liquid at the condenser pressure.  555 cen84959_ch10.qxd 4/25/05 3:56 PM Page 557 Chapter 10  557 qin Boiler
3
2 3 MPa
350°C T, °C 3 MPa Turbine wpump,in 3 350
Pump 75 kPa 4 3M Pa wturb,out qout Condenser 75 kPa 75 kP a 2
1 1
s1 = s2 75 kPa 4 s3 = s4 s FIGURE 10–3
Schematic and Ts diagram for Example 10–1. It is also interesting to note the thermal efficiency of a Carnot cycle operating between the same temperature limits hth,Carnot 1 Tmin
Tmax 1 1 91.76
1 350 273 2 K 273 2 K 0.415 The difference between the two efficiencies is due to the large external irreversibility in Rankine cycle caused by the large temperature difference
between steam and combustion gases in the furnace. 10–3 ■ DEVIATION OF ACTUAL VAPOR POWER
CYCLES FROM IDEALIZED ONES The actual vapor power cycle differs from the ideal Rankine cycle, as illustrated in Fig. 10–4a, as a result of irreversibilities in various components.
Fluid friction and heat loss to the surroundings are the two common sources
of irreversibilities.
Fluid friction causes pressure drops in the boiler, the condenser, and the
piping between various components. As a result, steam leaves the boiler at a
somewhat lower pressure. Also, the pressure at the turbine inlet is somewhat
lower than that at the boiler exit due to the pressure drop in the connecting
pipes. The pressure drop in the condenser is usually very small. To compensate for these pressure drops, the water must be pumped to a sufficiently
higher pressure than the ideal cycle calls for. This requires a larger pump
and larger work input to the pump.
The other major source of irreversibility is the heat loss from the steam to
the surroundings as the steam flows through various components. To maintain the same level of net work output, more heat needs to be transferred to INTERACTIVE
TUTORIAL
SEE TUTORIAL CH. 10, SEC. 2 ON THE DVD. cen84959_ch10.qxd 4/19/05 2:17 PM Page 558 558  Thermodynamics
T T
IDEAL CYCLE
Irreversibility
in the pump Pressure drop
in the boiler
3
3
Irreversibility
in the turbine 2
ACTUAL CYCLE 2a
2s 4
1 1 4s 4a Pressure drop
in the condenser
s s
(b) (a) FIGURE 10–4
(a) Deviation of actual vapor power cycle from the ideal Rankine cycle. (b) The effect of pump and
turbine irreversibilities on the ideal Rankine cycle. the steam in the boiler to compensate for these undesired heat losses. As a
result, cycle efficiency decreases.
Of particular importance are the irreversibilities occurring within the
pump and the turbine. A pump requires a greater work input, and a turbine
produces a smaller work output as a result of irreversibilities. Under ideal
conditions, the flow through these devices is isentropic. The deviation of
actual pumps and turbines from the isentropic ones can be accounted for by
utilizing isentropic efficiencies, defined as
hP ws
wa h 2s
h 2a h1
h1 (10–10) hT wa
ws h3
h3 h 4a
h 4s (10–11) and where states 2a and 4a are the actual exit states of the pump and the turbine,
respectively, and 2s and 4s are the corresponding states for the isentropic
case (Fig. 10–4b).
Other factors also need to be considered in the analysis of actual vapor
power cycles. In actual condensers, for example, the liquid is usually subcooled to prevent the onset of cavitation, the rapid vaporization and condensation of the fluid at the lowpressure side of the pump impeller, which may
damage it. Additional losses occur at the bearings between the moving parts
as a result of friction. Steam that leaks out during the cycle and air that
leaks into the condenser represent two other sources of loss. Finally, the
power consumed by the auxiliary equipment such as fans that supply air to
the furnace should also be considered in evaluating the overall performance
of power plants.
The effect of irreversibilities on the thermal efficiency of a steam power
cycle is illustrated below with an example. cen84959_ch10.qxd 4/19/05 2:17 PM Page 559 Chapter 10
EXAMPLE 10–2  559 An Actual Steam Power Cycle A steam power plant operates on the cycle shown in Fig. 10–5. If the isentropic efficiency of the turbine is 87 percent and the isentropic efficiency of
the pump is 85 percent, determine (a) the thermal efficiency of the cycle
and (b) the net power output of the plant for a mass flow rate of 15 kg/s. Solution A steam power cycle with specified turbine and pump efficiencies
is considered. The thermal efficiency and the net power output are to be
determined.
Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential
energy changes are negligible.
Analysis The schematic of the power plant and the Ts diagram of the cycle
are shown in Fig. 10–5. The temperatures and pressures of steam at various
points are also indicated on the figure. We note that the power plant involves
steadyflow components and operates on the Rankine cycle, but the imperfections at various components are accounted for.
(a) The thermal efficiency of a cycle is the ratio of the net work output to the
heat input, and it is determined as follows: Pump work input:
ws,pump,in wpump,in hp v1 1 P2 P1 2
hp 1 0.001009 m3> kg 2 3 1 16,000
19.0 kJ> kg 15.9 MPa
35°C
3
Boiler 0.85 16 MPa 1 kJ
b
1 kPa # m3 5 T 15 MPa
600°C 4 wturb,out 5 Turbine
η T = 0.87 wpump,in
Pump
ηP = 0.85 1 a 15.2 MPa
625°C
4 2 9 2 kPa 4 9 kPa
38°C 6 10 kPa
2
2s Condenser 3 1 6s 6 s FIGURE 10–5
Schematic and Ts diagram for Example 10–2. cen84959_ch10.qxd 4/19/05 2:17 PM Page 560 560  Thermodynamics
Turbine work output:
hTws,turb,out wturb,out hT 1 h 5 h 6s 2 1277.0 kJ> kg
Boiler heat input: h4 qin h3 Thus, wnet wturb,out h th wnet
qin wpump,in 1258.0 kJ> kg 3487.5 kJ> kg 0.87 1 3583.1
1 3647.6 1 1277.0 2115.3 2 kJ> kg 160.1 2 kJ> kg 19.0 2 kJ> kg 3487.5 kJ> kg 1258.0 kJ> kg 0.361 or 36.1% (b) The power produced by this power plant is #
Wnet #
m 1 wnet 2 1 15 kg> s 2 1 1258.0 kJ> kg 2 18.9 MW Discussion Without the irreversibilities, the thermal efficiency of this cycle
would be 43.0 percent (see Example 10–3c). 10–4 ■ HOW CAN WE INCREASE THE EFFICIENCY
OF THE RANKINE CYCLE? Steam power plants are responsible for the production of most electric
power in the world, and even small increases in thermal efficiency can mean
large savings from the fuel requirements. Therefore, every effort is made to
improve the efficiency of the cycle on which steam power plants operate.
The basic idea behind all the modifications to increase the thermal efficiency of a power cycle is the same: Increase the average temperature at
which heat is transferred to the working fluid in the boiler, or decrease the
average temperature at which heat is rejected from the working fluid in the
condenser. That is, the average fluid temperature should be as high as possible during heat addition and as low as possible during heat rejection. Next
we discuss three ways of accomplishing this for the simple ideal Rankine
cycle. T 3 Lowering the Condenser Pressure (Lowers Tlow,avg)
2
2' 4
1
1' P '4 < Increase in wnet 4' s FIGURE 10–6
The effect of lowering the condenser
pressure on the ideal Rankine cycle. P4 Steam exists as a saturated mixture in the condenser at the saturation
temperature corresponding to the pressure inside the condenser. Therefore,
lowering the operating pressure of the condenser automatically lowers the
temperature of the steam, and thus the temperature at which heat is rejected.
The effect of lowering the condenser pressure on the Rankine cycle efficiency is illustrated on a Ts diagram in Fig. 10–6. For comparison purposes, the turbine inlet state is maintained the same. The colored area on
this diagram represents the increase in net work output as a result of lower¿
ing the condenser pressure from P4 to P4 . The heat input requirements also
increase (represented by the area under curve 2 2), but this increase is very
small. Thus the overall effect of lowering the condenser pressure is an
increase in the thermal efficiency of the cycle. cen84959_ch10.qxd 4/19/05 2:17 PM Page 561 Chapter 10
To take advantage of the increased efficiencies at low pressures, the condensers of steam power plants usually operate well below the atmospheric
pressure. This does not present a major problem since the vapor power
cycles operate in a closed loop. However, there is a lower limit on the condenser pressure that can be used. It cannot be lower than the saturation pressure corresponding to the temperature of the cooling medium. Consider, for
example, a condenser that is to be cooled by a nearby river at 15°C. Allowing a temperature difference of 10°C for effective heat transfer, the steam
temperature in the condenser must be above 25°C; thus the condenser pressure must be above 3.2 kPa, which is the saturation pressure at 25°C.
Lowering the condenser pressure is not without any side effects, however.
For one thing, it creates the possibility of air leakage into the condenser.
More importantly, it increases the moisture content of the steam at the final
stages of the turbine, as can be seen from Fig. 10–6. The presence of large
quantities of moisture is highly undesirable in turbines because it decreases
the turbine efficiency and erodes the turbine blades. Fortunately, this problem can be corrected, as discussed next. Increase in wnet
3'
3 2
1 4 4' s FIGURE 10–7
The effect of superheating the steam to
higher temperatures on the ideal
Rankine cycle. T
Increase
in wnet 3' 3 T max
Decrease
in wnet Increasing the Boiler Pressure (Increases Thigh,avg)
Another way of increasing the average temperature during the heataddition
process is to increase the operating pressure of the boiler, which automatically raises the temperature at which boiling takes place. This, in turn, raises
the average temperature at which heat is transferred to the steam and thus
raises the thermal efficiency of the cycle.
The effect of increasing the boiler pressure on the performance of vapor
power cycles is illustrated on a Ts diagram in Fig. 10–8. Notice that for a
fixed turbine inlet temperature, the cycle shifts to the left and the moisture content of steam at the turbine exit increases. This undesirable side effect can be
corrected, however, by reheating the steam, as discussed in the next section. 561 T Superheating the Steam to High Temperatures
(Increases Thigh,avg)
The average temperature at which heat is transferred to steam can be
increased without increasing the boiler pressure by superheating the steam to
high temperatures. The effect of superheating on the performance of vapor
power cycles is illustrated on a Ts diagram in Fig. 10–7. The colored area on
this diagram represents the increase in the net work. The total area under the
process curve 33 represents the increase in the heat input. Thus both the net
work and heat input increase as a result of superheating the steam to a higher
temperature. The overall effect is an increase in thermal efficiency, however,
since the average temperature at which heat is added increases.
Superheating the steam to higher temperatures has another very desirable
effect: It decreases the moisture content of the steam at the turbine exit, as
can be seen from the Ts diagram (the quality at state 4 is higher than that
at state 4).
The temperature to which steam can be superheated is limited, however, by
metallurgical considerations. Presently the highest steam temperature allowed
at the turbine inlet is about 620°C (1150°F). Any increase in this value
depends on improving the present materials or finding new ones that can
withstand higher temperatures. Ceramics are very promising in this regard.  2'
2
1 4' 4
s FIGURE 10–8
The effect of increasing the boiler
pressure on the ideal Rankine cycle. cen84959_ch10.qxd 4/19/05 2:17 PM Page 562 562  Thermodynamics
Operating pressures of boilers have gradually increased over the years
from about 2.7 MPa (400 psia) in 1922 to over 30 MPa (4500 psia) today,
generating enough steam to produce a net power output of 1000 MW or more
in a large power plant. Today many modern steam power plants operate at
supercritical pressures (P
22.06 MPa) and have thermal efficiencies of
about 40 percent for fossilfuel plants and 34 percent for nuclear plants.
There are over 150 supercriticalpressure steam power plants in operation in
the United States. The lower efficiencies of nuclear power plants are due to
the lower maximum temperatures used in those plants for safety reasons.
The Ts diagram of a supercritical Rankine cycle is shown in Fig. 10–9.
The effects of lowering the condenser pressure, superheating to a higher
temperature, and increasing the boiler pressure on the thermal efficiency of
the Rankine cycle are illustrated below with an example. T
3 Critical
point 2
1 4 s EXAMPLE 10–3 FIGURE 10–9
A supercritical Rankine cycle. Effect of Boiler Pressure
a nd Temperature on Efficiency Consider a steam power plant operating on the ideal Rankine cycle. Steam
enters the turbine at 3 MPa and 350°C and is condensed in the condenser at
a pressure of 10 kPa. Determine (a) the thermal efficiency of this power
plant, (b) the thermal efficiency if steam is superheated to 600°C instead of
350°C, and (c) the thermal efficiency if the boiler pressure is raised to 15
MPa while the turbine inlet temperature is maintained at 600°C. Solution A steam power plant operating on the ideal Rankine cycle is considered. The effects of superheating the steam to a higher temperature and
raising the boiler pressure on thermal efficiency are to be investigated.
Analysis The Ts diagrams of the cycle for all three cases are given in
Fig. 10–10. T T T
T3 = 600°C
3 3 MPa 3 MPa 2 2
10 kPa 10 kPa
1 1 4 10 kPa
1 4 s
( a) T3 = 600°C 15 MPa 3 T = 350°C
3 2 3 4
s s
( b) FIGURE 10–10
Ts diagrams of the three cycles discussed in Example 10–3. ( c) cen84959_ch10.qxd 4/19/05 2:17 PM Page 563 Chapter 10
(a) This is the steam power plant discussed in Example 10–1, except that
the condenser pressure is lowered to 10 kPa. The thermal efficiency is
determined in a similar manner: State 1: P1 10 kPa
f
Sat. liquid State 2: P2
s2 wpump,in h1
v1 191.81 kJ> kg
0.00101 m3> kg hf @ 10 kPa
vf @ 10 kPa 3 MPa
s1 v1 1 P2 P1 2 1 0.00101 m3> kg 2 3 1 3000 3.02 kJ> kg 10 2 kPa 4 a 194.83 kJ> kg h2 h1 wpump,in 1 191.81 State 3: P3
T3 3 MPa
f
350°C h3
s3 State 4: P4
s4 10 kPa
s3 3116.1 kJ> kg
6.7450 kJ> kg # K 1 sat. mixture 2 sf s4 x4 3.02 2 kJ> kg 1 kJ
b
1 kPa # m3 6.7450 0.6492
7.4996 sfg Thus, h4 hf x4hfg 191.81 qin h3 h2 qout h4 h1 1 2136.1 h th 1 qout
qin 1 1 3116.1 and 0.8128 0.8128 1 2392.1 2 194.83 2 kJ> kg
191.81 2 kJ> kg 1944.3 kJ> kg 2921.3 kJ> kg 2136.1 kJ> kg 2921.3 kJ> kg
1944.3 kJ> kg 0.334 or 33.4% Therefore, the thermal efficiency increases from 26.0 to 33.4 percent as a
result of lowering the condenser pressure from 75 to 10 kPa. At the same
time, however, the quality of the steam decreases from 88.6 to 81.3 percent
(in other words, the moisture content increases from 11.4 to 18.7 percent).
(b) States 1 and 2 remain the same in this case, and the enthalpies at
state 3 (3 MPa and 600°C) and state 4 (10 kPa and s4
s3) are determined to be h3
h4
Thus, 3682.8 kJ> kg
2380.3 kJ> kg 1 x4 qin h3 h2 3682.8 194.83 qout h4 h1 2380.3 191.81 and h th 1 qout
qin 1 0.915 2
3488.0 kJ> kg
2188.5 kJ> kg 2188.5 kJ> kg 3488.0 kJ> kg 0.373 or 37.3%  563 cen84959_ch10.qxd 4/25/05 3:56 PM Page 564 564  Thermodynamics
Therefore, the thermal efficiency increases from 33.4 to 37.3 percent as a
result of superheating the steam from 350 to 600°C. At the same time, the
quality of the steam increases from 81.3 to 91.5 percent (in other words,
the moisture content decreases from 18.7 to 8.5 percent).
(c) State 1 remains the same in this case, but the other states change. The
enthalpies at state 2 (15 MPa and s2
s1), state 3 (15 MPa and 600°C),
and state 4 (10 kPa and s4
s3) are determined in a similar manner to be 206.95 kJ> kg h2 3583.1 kJ> kg h3
h4 2115.3 kJ> kg 1 x4 qin h3 h2 3583.1 206.95 qout h4 h1 2115.3 191.81 Thus, and h th 1 qout
qin 1 0.804 2
3376.2 kJ> kg 1923.5 kJ> kg 1923.5 kJ> kg 3376.2 kJ> kg 0.430 or 43.0% Discussion The thermal efficiency increases from 37.3 to 43.0 percent as a
result of raising the boiler pressure from 3 to 15 MPa while maintaining the
turbine inlet temperature at 600°C. At the same time, however, the quality
of the steam decreases from 91.5 to 80.4 percent (in other words, the moisture content increases from 8.5 to 19.6 percent). INTERACTIVE
TUTORIAL
SEE TUTORIAL CH. 10, SEC. 3 ON THE DVD. 10–5 ■ THE IDEAL REHEAT RANKINE CYCLE We noted in the last section that increasing the boiler pressure increases the
thermal efficiency of the Rankine cycle, but it also increases the moisture
content of the steam to unacceptable levels. Then it is natural to ask the following question:
How can we take advantage of the increased efficiencies at higher boiler
pressures without facing the problem of excessive moisture at the final
stages of the turbine? Two possibilities come to mind:
1. Superheat the steam to very high temperatures before it enters the
turbine. This would be the desirable solution since the average temperature
at which heat is added would also increase, thus increasing the cycle efficiency. This is not a viable solution, however, since it requires raising the
steam temperature to metallurgically unsafe levels.
2. Expand the steam in the turbine in two stages, and reheat it in
between. In other words, modify the simple ideal Rankine cycle with a
reheat process. Reheating is a practical solution to the excessive moisture
problem in turbines, and it is commonly used in modern steam power plants.
The Ts diagram of the ideal reheat Rankine cycle and the schematic of
the power plant operating on this cycle are shown in Fig. 10–11. The ideal
reheat Rankine cycle differs from the simple ideal Rankine cycle in that the cen84959_ch10.qxd 4/19/05 2:17 PM Page 565 Chapter 10  expansion process takes place in two stages. In the first stage (the highpressure turbine), steam is expanded isentropically to an intermediate pressure and sent back to the boiler where it is reheated at constant pressure,
usually to the inlet temperature of the first turbine stage. Steam then expands
isentropically in the second stage (lowpressure turbine) to the condenser
pressure. Thus the total heat input and the total turbine work output for a
reheat cycle become
qin qreheat 1 h3 h2 2 1 h5 h4 2 (10–12) wturb,II qprimary 1 h3 h4 2 1 h5 h6 2 (10–13) and
wturb,out wturb,I The incorporation of the single reheat in a modern power plant improves
the cycle efficiency by 4 to 5 percent by increasing the average temperature
at which heat is transferred to the steam.
The average temperature during the reheat process can be increased by
increasing the number of expansion and reheat stages. As the number of
stages is increased, the expansion and reheat processes approach an isothermal process at the maximum temperature, as shown in Fig. 10–12. The use
of more than two reheat stages, however, is not practical. The theoretical
improvement in efficiency from the second reheat is about half of that
which results from a single reheat. If the turbine inlet pressure is not high
enough, double reheat would result in superheated exhaust. This is undesirable as it would cause the average temperature for heat rejection to increase
and thus the cycle efficiency to decrease. Therefore, double reheat is used
only on supercriticalpressure (P 22.06 MPa) power plants. A third reheat
stage would increase the cycle efficiency by about half of the improvement
attained by the second reheat. This gain is too small to justify the added cost
and complexity. T
Highpressure
turbine 3 Reheating
3 5
Lowpressure
turbine Boiler
Reheater 4 HighP
turbine LowP
turbine 4 P4 = P5 = Preheat
6 2 5
Condenser
2 1 6 Pump
1 FIGURE 10–11
The ideal reheat Rankine cycle. s 565 cen84959_ch10.qxd 4/19/05 2:17 PM Page 566 566  Thermodynamics T Tavg,reheat The reheat cycle was introduced in the mid1920s, but it was abandoned
in the 1930s because of the operational difficulties. The steady increase in
boiler pressures over the years made it necessary to reintroduce single
reheat in the late 1940s and double reheat in the early 1950s.
The reheat temperatures are very close or equal to the turbine inlet temperature. The optimum reheat pressure is about onefourth of the maximum
cycle pressure. For example, the optimum reheat pressure for a cycle with a
boiler pressure of 12 MPa is about 3 MPa.
Remember that the sole purpose of the reheat cycle is to reduce the moisture content of the steam at the final stages of the expansion process. If we
had materials that could withstand sufficiently high temperatures, there
would be no need for the reheat cycle. s FIGURE 10–12
The average temperature at which heat
is transferred during reheating
increases as the number of reheat
stages is increased. EXAMPLE 10–4 The Ideal Reheat Rankine Cycle Consider a steam power plant operating on the ideal reheat Rankine cycle.
Steam enters the highpressure turbine at 15 MPa and 600°C and is condensed in the condenser at a pressure of 10 kPa. If the moisture content of
the steam at the exit of the lowpressure turbine is not to exceed 10.4 percent, determine (a) the pressure at which the steam should be reheated and
(b) the thermal efficiency of the cycle. Assume the steam is reheated to the
inlet temperature of the highpressure turbine. Solution A steam power plant operating on the ideal reheat Rankine cycle
is considered. For a specified moisture content at the turbine exit, the reheat
pressure and the thermal efficiency are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential
energy changes are negligible.
Analysis The schematic of the power plant and the Ts diagram of the cycle
are shown in Fig. 10–13. We note that the power plant operates on the ideal
reheat Rankine cycle. Therefore, the pump and the turbines are isentropic,
there are no pressure drops in the boiler and condenser, and steam leaves
the condenser and enters the pump as saturated liquid at the condenser
pressure.
(a) The reheat pressure is determined from the requirement that the
entropies at states 5 and 6 be the same: P6 10 kPa x6 0.896 s6 sf x6sfg 0.6492 0.896 1 7.4996 2 7.3688 kJ> kg # K h6 State 6: hf x6hfg 191.81 0.896 1 2392.1 2 2335.1 kJ> kg T5
s5 600°C
f
s6 1 sat. mixture 2 Also, Thus, State 5: P5
h5 4.0 MPa
3674.9 kJ> kg Therefore, steam should be reheated at a pressure of 4 MPa or lower to prevent a moisture content above 10.4 percent. cen84959_ch10.qxd 4/19/05 2:17 PM Page 567 Chapter 10  (b) To determine the thermal efficiency, we need to know the enthalpies at
all other states: State 1: P1 10 kPa
f
Sat. liquid State 2: P2
s2 s1 191.81 kJ> kg
0.00101 m3> kg 15 MPa
v1 1 P2 wpump,in h1
v1 h f @ 10 kPa
vf @ 10 kPa P1 2 1 0.00101 m3> kg 2 3 1 15,000 10 2 kPa 4 a 15.14 kJ> kg
h2 h1 State 3: P3
T3 15 MPa
f
600°C State 4: P4
s4 4 MPa
f
s3 Thus 1 h3 qin 1 191.81 wpump,in h2 2 h3
s3 15.14 2 kJ> kg 3583.1 kJ> kg
6.6796 kJ> kg # K 1 h5 h4 2 206.95 2 kJ> kg h6 1 2335.1 3896.1 kJ> kg
h1 206.95 kJ> kg h4 3155.0 kJ> kg
1 T4 375.5°C 2 1 3583.1 qout 1 kJ
b
1 kPa # m3 2143.3 kJ> kg 1 3674.9 3155.0 2 kJ> kg 191.81 2 kJ> kg T, °C
Reheating
15 MPa 3 3 600 5 15 MPa Boiler HighP
turbine 4 LowP
turbine 15 MPa 4 Reheater
P4 = P5 = Preheat 6 5
Condenser 15 MPa 10 kPa 2
10 kPa
1 6 Pump
10 kPa
s 2
1 FIGURE 10–13
Schematic and Ts diagram for Example 10–4. 567 cen84959_ch10.qxd 4/25/05 3:56 PM Page 568 568  Thermodynamics
and h th 1 qout
qin 1 2143.3 kJ> kg 3896.1 kJ> kg 0.450 or 45.0% Discussion This problem was solved in Example 10–3c for the same pressure and temperature limits but without the reheat process. A comparison of
the two results reveals that reheating reduces the moisture content from
19.6 to 10.4 percent while increasing the thermal efficiency from 43.0 to
45.0 percent. 10–6 INTERACTIVE
TUTORIAL
SEE TUTORIAL CH. 10, SEC. 4 ON THE DVD. T Steam exiting
boiler
Lowtemperature
heat addition 3 2'
Steam entering
boiler 2
1 4 s FIGURE 10–14
The first part of the heataddition
process in the boiler takes place at
relatively low temperatures. ■ THE IDEAL REGENERATIVE RANKINE CYCLE A careful examination of the Ts diagram of the Rankine cycle redrawn in
Fig. 10–14 reveals that heat is transferred to the working fluid during
process 22 at a relatively low temperature. This lowers the average heataddition temperature and thus the cycle efficiency.
To remedy this shortcoming, we look for ways to raise the temperature of
the liquid leaving the pump (called the feedwater) before it enters the boiler.
One such possibility is to transfer heat to the feedwater from the expanding
steam in a counterflow heat exchanger built into the turbine, that is, to use
regeneration. This solution is also impractical because it is difficult to
design such a heat exchanger and because it would increase the moisture
content of the steam at the final stages of the turbine.
A practical regeneration process in steam power plants is accomplished by
extracting, or “bleeding,” steam from the turbine at various points. This steam,
which could have produced more work by expanding further in the turbine, is
used to heat the feedwater instead. The device where the feedwater is heated
by regeneration is called a regenerator, or a feedwater heater (FWH).
Regeneration not only improves cycle efficiency, but also provides a convenient means of deaerating the feedwater (removing the air that leaks in at
the condenser) to prevent corrosion in the boiler. It also helps control the
large volume flow rate of the steam at the final stages of the turbine (due to
the large specific volumes at low pressures). Therefore, regeneration has
been used in all modern steam power plants since its introduction in the
early 1920s.
A feedwater heater is basically a heat exchanger where heat is transferred
from the steam to the feedwater either by mixing the two fluid streams
(open feedwater heaters) or without mixing them (closed feedwater heaters).
Regeneration with both types of feedwater heaters is discussed below. Open Feedwater Heaters
An open (or directcontact) feedwater heater is basically a mixing chamber, where the steam extracted from the turbine mixes with the feedwater
exiting the pump. Ideally, the mixture leaves the heater as a saturated liquid
at the heater pressure. The schematic of a steam power plant with one open
feedwater heater (also called singlestage regenerative cycle) and the Ts
diagram of the cycle are shown in Fig. 10–15.
In an ideal regenerative Rankine cycle, steam enters the turbine at the
boiler pressure (state 5) and expands isentropically to an intermediate pres cen84959_ch10.qxd 4/19/05 2:17 PM Page 569 Chapter 10  569 sure (state 6). Some steam is extracted at this state and routed to the feedwater heater, while the remaining steam continues to expand isentropically
to the condenser pressure (state 7). This steam leaves the condenser as a saturated liquid at the condenser pressure (state 1). The condensed water,
which is also called the feedwater, then enters an isentropic pump, where it
is compressed to the feedwater heater pressure (state 2) and is routed to the
feedwater heater, where it mixes with the steam extracted from the turbine.
The fraction of the steam extracted is such that the mixture leaves the heater
as a saturated liquid at the heater pressure (state 3). A second pump raises
the pressure of the water to the boiler pressure (state 4). The cycle is completed by heating the water in the boiler to the turbine inlet state (state 5).
In the analysis of steam power plants, it is more convenient to work with
quantities expressed per unit mass of the steam flowing through the boiler.
For each 1 kg of steam leaving the boiler, y kg expands partially in the turbine
and is extracted at state 6. The remaining (1 y) kg expands completely to
the condenser pressure. Therefore, the mass flow rates are different in dif.
ferent components. If the mass flow rate through the boiler is m , for exam. through the condenser. This aspect of the regenerative
ple, it is (1
y)m
Rankine cycle should be considered in the analysis of the cycle as well as in
the interpretation of the areas on the Ts diagram. In light of Fig. 10–15, the
heat and work interactions of a regenerative Rankine cycle with one feedwater heater can be expressed per unit mass of steam flowing through the
boiler as follows:
qin h5 11 qout 1 h5 wturb,out 11 wpump,in h4 (10–14) y 2 1 h7
h6 2 h1 2 (10–15) 11 y 2 1 h6 y 2 wpump I,in h7 2 wpump II,in (10–16)
(10–17) 5
T
Turbine Boiler 5
y 1–y
6 7 Open
FWH 4 4
6 3 3
2 Pump II 2 Condenser 1 7 1
Pump I FIGURE 10–15
The ideal regenerative Rankine cycle with an open feedwater heater. s cen84959_ch10.qxd 4/19/05 2:17 PM Page 570 570  Thermodynamics
where
y
wpump I,in
wpump II,in ##
m6> m5 v1 1 P2 P1 2 v3 1 P4 1 fraction of steam extracted 2 P3 2 The thermal efficiency of the Rankine cycle increases as a result of regeneration. This is because regeneration raises the average temperature at
which heat is transferred to the steam in the boiler by raising the temperature of the water before it enters the boiler. The cycle efficiency increases
further as the number of feedwater heaters is increased. Many large plants
in operation today use as many as eight feedwater heaters. The optimum
number of feedwater heaters is determined from economical considerations.
The use of an additional feedwater heater cannot be justified unless it saves
more from the fuel costs than its own cost. Closed Feedwater Heaters
Another type of feedwater heater frequently used in steam power plants is
the closed feedwater heater, in which heat is transferred from the extracted
steam to the feedwater without any mixing taking place. The two streams
now can be at different pressures, since they do not mix. The schematic of a
steam power plant with one closed feedwater heater and the Ts diagram of
the cycle are shown in Fig. 10–16. In an ideal closed feedwater heater, the
feedwater is heated to the exit temperature of the extracted steam, which
ideally leaves the heater as a saturated liquid at the extraction pressure. In
actual power plants, the feedwater leaves the heater below the exit tempera T 6 6
Boiler Turbine
9 7
Mixing
chamber 8 Closed
FWH 9 4
7
3 2 1 5 5 8 2
4 3
Condenser
1
Pump II Pump I FIGURE 10–16
The ideal regenerative Rankine cycle with a closed feedwater heater. s cen84959_ch10.qxd 4/19/05 2:17 PM Page 571 Chapter 10 Turbine Boiler
Condenser
Deaerating Closed
FWH Closed
FWH Open
FWH Closed
FWH Pump Pump Trap Trap Trap FIGURE 10–17
A steam power plant with one open and three closed feedwater heaters. ture of the extracted steam because a temperature difference of at least a
few degrees is required for any effective heat transfer to take place.
The condensed steam is then either pumped to the feedwater line or routed
to another heater or to the condenser through a device called a trap. A trap
allows the liquid to be throttled to a lower pressure region but traps the
vapor. The enthalpy of steam remains constant during this throttling process.
The open and closed feedwater heaters can be compared as follows. Open
feedwater heaters are simple and inexpensive and have good heat transfer
characteristics. They also bring the feedwater to the saturation state. For
each heater, however, a pump is required to handle the feedwater. The
closed feedwater heaters are more complex because of the internal tubing
network, and thus they are more expensive. Heat transfer in closed feedwater heaters is also less effective since the two streams are not allowed to be
in direct contact. However, closed feedwater heaters do not require a separate pump for each heater since the extracted steam and the feedwater can
be at different pressures. Most steam power plants use a combination of
open and closed feedwater heaters, as shown in Fig. 10–17.
EXAMPLE 10–5 The Ideal Regenerative Rankine Cycle Consider a steam power plant operating on the ideal regenerative Rankine
cycle with one open feedwater heater. Steam enters the turbine at 15 MPa
and 600°C and is condensed in the condenser at a pressure of 10 kPa.  571 cen84959_ch10.qxd 4/19/05 2:17 PM Page 572 572  Thermodynamics
Some steam leaves the turbine at a pressure of 1.2 MPa and enters the open
feedwater heater. Determine the fraction of steam extracted from the turbine
and the thermal efficiency of the cycle. Solution A steam power plant operates on the ideal regenerative Rankine
cycle with one open feedwater heater. The fraction of steam extracted from
the turbine and the thermal efficiency are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential
energy changes are negligible.
Analysis The schematic of the power plant and the Ts diagram of the cycle
are shown in Fig. 10–18. We note that the power plant operates on the ideal
regenerative Rankine cycle. Therefore, the pumps and the turbines are isentropic; there are no pressure drops in the boiler, condenser, and feedwater
heater; and steam leaves the condenser and the feedwater heater as saturated liquid. First, we determine the enthalpies at various states: State 1: P1 10 kPa
f
Sat. liquid State 2: P2 191.81 kJ> kg
0.00101 m3> kg 1.2 MPa s2 h1
v1 hf @ 10 kPa
vf @ 10 kPa s1
v1 1 P2 wpump I,in P1 2 1 0.00101 m3> kg 2 3 1 1200 1.20 kJ> kg
h2 h1 wpump I,in 1 191.81 1.20 2 kJ> kg 10 2 kPa 4 a 1 kJ
b
1 kPa # m3 193.01 kJ> kg T 5
15 MPa
600°C
Boiler 5
wturb,out Turbine
4 q in 1.2 MPa 7 3 10 kPa 2
1 7 1.2 MPa
1
10 kPa Pump II 3 qout 1.2 MPa
2 4
15 MPa 6 6 Open
FWH Pump I FIGURE 10–18
Schematic and Ts diagram for Example 10–5. Condenser s cen84959_ch10.qxd 4/19/05 2:17 PM Page 573 Chapter 10
State 3: P3 1.2 MPa
f
Sat. liquid
State 4: P4 v3
h3 vf @ 1.2 MPa
h f @ 1.2 MPa 0.001138 m3> kg
798.33 kJ> kg 15 MPa s4 s3 v3 1 P4 wpump II,in P3 2 1 0.001138 m3> kg 2 3 1 15,000 15.70 kJ> kg
h3 h4 1200 2 kPa 4 a 1 798.33 wpump II,in State 5: P5
T5 15 MPa
f
600°C
1.2 MPa
f
s5 h6
1 T6 State 7: P7 814.03 kJ> kg 3583.1 kJ> kg
6.6796 kJ> kg # K h5
s5 State 6: P6
s6 15.70 2 kJ> kg 1 kJ
b
1 kPa # m3 10 kPa
sf s7 s7 s5 x7 h7 hf x7h fg 2860.2 kJ> kg
218.4°C 2 6.6796 0.6492
7.4996 sfg 0.8041 1 2392.1 2 191.81 0.8041
2115.3 kJ> kg The energy analysis of open feedwater heaters is identical to the energy
analysis. of mixing chambers. The feedwater heaters are generally well insu.
lated (Q
0), and they do not involve any work interactions (W
0). By
neglecting the kinetic and potential energies of the streams, the energy balance reduces for a feedwater heater to #
E in #
#
E out S a mh
in or yh 6 11 y 2 h2 #
a mh
out 1 1 h3 2 ..
where y is the fraction of steam extracted from the turbine ( m 6 /m 5). Solving for y and substituting the enthalpy values, we find y h3
h6 Thus, qin
qout h5 11 h4 y 2 1 h7 h2
h2 1 3583.1 1486.9 kJ> kg h1 2 798.33
2860.2 814.03 2 kJ> kg 11 and h th 1 qout
qin 193.01
193.01 1 0.2270
2769.1 kJ> kg 0.2270 2 1 2115.3 1486.9 kJ> kg 2769.1 kJ> kg 191.81 2 kJ> kg 0.463 or 46.3%  573 cen84959_ch10.qxd 4/27/05 5:49 PM Page 574 574  Thermodynamics
Discussion This problem was worked out in Example 10–3c for the same
pressure and temperature limits but without the regeneration process. A
comparison of the two results reveals that the thermal efficiency of the cycle
has increased from 43.0 to 46.3 percent as a result of regeneration. The net
work output decreased by 171 kJ/kg, but the heat input decreased by
607 kJ/kg, which results in a net increase in the thermal efficiency. EXAMPLE 10–6 The Ideal Reheat–Regenerative Rankine Cycle Consider a steam power plant that operates on an ideal reheat–regenerative
Rankine cycle with one open feedwater heater, one closed feedwater heater,
and one reheater. Steam enters the turbine at 15 MPa and 600°C and is
condensed in the condenser at a pressure of 10 kPa. Some steam is
extracted from the turbine at 4 MPa for the closed feedwater heater, and the
remaining steam is reheated at the same pressure to 600°C. The extracted
steam is completely condensed in the heater and is pumped to 15 MPa
before it mixes with the feedwater at the same pressure. Steam for the open
feedwater heater is extracted from the lowpressure turbine at a pressure of
0.5 MPa. Determine the fractions of steam extracted from the turbine as
well as the thermal efficiency of the cycle. Solution A steam power plant operates on the ideal reheat–regenerative
Rankine cycle with one open feedwater heater, one closed feedwater heater,
and one reheater. The fractions of steam extracted from the turbine and the
thermal efficiency are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential
energy changes are negligible. 3 In both open and closed feedwater heaters,
feedwater is heated to the saturation temperature at the feedwater heater
pressure. (Note that this is a conservative assumption since extracted steam
enters the closed feedwater heater at 376°C and the saturation temperature
at the closed feedwater pressure of 4 MPa is 250°C).
Analysis The schematic of the power plant and the Ts diagram of the cycle
are shown in Fig. 10–19. The power plant operates on the ideal reheat–
regenerative Rankine cycle and thus the pumps and the turbines are isentropic; there are no pressure drops in the boiler, reheater, condenser, and feedwater heaters; and steam leaves the condenser and the feedwater heaters as
saturated liquid.
The enthalpies at the various states and the pump work per unit mass of
fluid flowing through them are h1
h2
h3
h4
h5
h6
h7
h8 191.81 kJ> kg
192.30 kJ> kg
640.09 kJ> kg
643.92 kJ> kg
1087.4 kJ> kg
1087.4 kJ> kg
1101.2 kJ> kg
1089.8 kJ> kg h9
h10
h11
h12
h13
wpump I,in
wpump II,in
wpump III,in 3155.0 kJ> kg
3155.0 kJ> kg
3674.9 kJ> kg
3014.8 kJ> kg
2335.7 kJ> kg
0.49 kJ> kg
3.83 kJ> kg 13.77 kJ> kg cen84959_ch10.qxd 4/19/05 2:17 PM Page 575 Chapter 10  575 The fractions of steam extracted are determined from the mass and energy
balances of the feedwater heaters:
Closed feedwater heater: 11 yh10
y h4
1 h5 h5
h6 2 1 h10 #
Ein #
Eout y 2 h4 h4 2 #
E out h2 2 11 y 2 h5 1087.4
1087.4 2 1 3155.0 #
E in 11 yh6
643.92
1 1087.4 643.92 2 0.1766 Open feedwater heater: zh 12
z 11 11 y y 2 1 h3 h12 h2 z 2 h2 11 y 2 h3 0.1766 2 1 640.09
3014.8 192.30 192.30 2 0.1306 The enthalpy at state 8 is determined by applying the mass and energy
equations to the mixing chamber, which is assumed to be insulated: #
E in 1 1 2 h8
h8 #
E out
11
11 y 2 h5 yh 7 0.1766 2 1 1087.4 2 kJ> kg 0.1766 1 1101.2 2 kJ> kg 1089.8 kJ> kg 1 kg y
1– Reheater 11 9 LowP
turbine g HighP
turbine
10 1k Boiler T 15 MPa
600°C 9 15 MPa
y P10 = P11 = 4 MPa z
12 1–y 11 4 MPa 0.5 MPa 8
Mixing
chamber 600°C Closed
FWH 8 1–y –z 5
4 13
10 kPa Open
FWH 7 4
6 Pump III 3
Pump II FIGURE 10–19
Schematic and Ts diagram for Example 10–6. Pump I Condenser
1 y 10 1–y 6
0.5 MPa 2 2 4 MPa 3 z 12
1–y–z 10 kPa
1 5 7 13
s cen84959_ch10.qxd 4/19/05 2:17 PM Page 576 576  Thermodynamics
Thus, 1 h9 qin h8 2 11 1 3583.1 y 2 1 h 11 1089.8 2 kJ> kg 2921.4 kJ> kg
11 qout z 2 1 h 13 y 11 1485.3 kJ> kg h1 2 and qout
qin 1 11 0.1306 2 1 2335.7 0.1766 h th h 10 2 0.1766 2 1 3674.9 191.81 2 kJ> kg 1485.3 kJ> kg 2921.4 kJ> kg 1 3155.0 2 kJ> kg 0.492 or 49.2% Discussion This problem was worked out in Example 10–4 for the same pressure and temperature limits with reheat but without the regeneration process.
A comparison of the two results reveals that the thermal efficiency of the cycle
has increased from 45.0 to 49.2 percent as a result of regeneration.
The thermal efficiency of this cycle could also be determined from where 1 h9 wturb,out 11 wpump,in h 10 2
y wturb,out wnet
qin hth 11 wpump,in
qin y 2 1 h 11 z 2 wpump I,in h 12 2 11 11 y 2 wpump II,in y z 2 1 h 12 1 y 2 wpump III,in h 13 2 Also, if we assume that the feedwater leaves the closed FWH as a saturated liquid at 15 MPa (and thus at T5
342°C and h5
1610.3 kJ/kg), it
can be shown that the thermal efficiency would be 50.6. 10–7 ■ SECONDLAW ANALYSIS
OF VAPOR POWER CYCLES The ideal Carnot cycle is a totally reversible cycle, and thus it does not
involve any irreversibilities. The ideal Rankine cycles (simple, reheat, or
regenerative), however, are only internally reversible, and they may involve
irreversibilities external to the system, such as heat transfer through a finite
temperature difference. A secondlaw analysis of these cycles reveals where
the largest irreversibilities occur and what their magnitudes are.
Relations for exergy and exergy destruction for steadyflow systems are
developed in Chap. 8. The exergy destruction for a steadyflow system can
be expressed, in the rate form, as
#
X dest #
T0 S gen #
T0 1 S out #
S in 2 #
T0 a a m s
out #
Q out
Tb,out #
a ms
in #
Q in
b
Tb,in 1 kW 2
(10–18) or on a unit mass basis for a oneinlet, oneexit, steadyflow device as
xdest T0sgen T0 a se si qout
Tb,out qin
b
Tb,in 1 kJ> kg 2 (10–19) cen84959_ch10.qxd 4/19/05 2:17 PM Page 577 Chapter 10
where Tb,in and Tb,out are the temperatures of the system boundary where
heat is transferred into and out of the system, respectively.
The exergy destruction associated with a cycle depends on the magnitude
of the heat transfer with the high and lowtemperature reservoirs involved,
and their temperatures. It can be expressed on a unit mass basis as
T0 a a xdest qin
aT b qout
Tb,out 1 kJ> kg 2 b,in (10–20) For a cycle that involves heat transfer only with a source at TH and a sink at
TL , the exergy destruction becomes
xdest T0 a qin
b
TH qout
TL 1 kJ> kg 2 (10–21) The exergy of a fluid stream c at any state can be determined from
1h c h0 2 T0 1 s s0 2 V2
2 1 kJ> kg 2 gz (10–22) where the subscript “0” denotes the state of the surroundings.
EXAMPLE 10–7 SecondLaw Analysis of an Ideal Rankine Cycle Determine the exergy destruction associated with the Rankine cycle (all four
processes as well as the cycle) discussed in Example 10–1, assuming that
heat is transferred to the steam in a furnace at 1600 K and heat is rejected
to a cooling medium at 290 K and 100 kPa. Also, determine the exergy of
the steam leaving the turbine. Solution The Rankine cycle analyzed in Example 10–1 is reconsidered. For
specified source and sink temperatures, the exergy destruction associated
with the cycle and exergy of the steam at turbine exit are to be determined.
Analysis In Example 10–1, the heat input was determined to be 2728.6 kJ/kg,
and the heat rejected to be 2018.6 kJ/kg.
Processes 12 and 34 are isentropic (s1
s2, s3
s4) and therefore do
not involve any internal or external irreversibilities, that is, 0 xdest,12 and xdest,34 0 Processes 23 and 41 are constantpressure heataddition and heatrejection processes, respectively, and they are internally reversible. But the
heat transfer between the working fluid and the source or the sink takes
place through a finite temperature difference, rendering both processes irreversible. The irreversibility associated with each process is determined from
Eq. 10–19. The entropy of the steam at each state is determined from the
steam tables: s2 s1 s4 s3 sf @ 75 kPa 1.2132 kJ> kg # K 6.7450 kJ> kg # K 1 at 3 MPa, 350°C 2 Thus, xdest,23 T0 a s3 s2 qin,23
Tsource 1 290 K 2 c 1 6.7450
1110 kJ/kg b
1.2132 2 kJ> kg # K 2728.6 kJ> kg
1600 K d  577 cen84959_ch10.qxd 4/19/05 2:17 PM Page 578 578  Thermodynamics
xdest,41 T0 a s1 qout,41 s4 Tsink 1 290 K 2 c 1 1.2132 b
6.7450 2 kJ> kg # K 2018.6 kJ> kg
290 K d 414 kJ/kg
Therefore, the irreversibility of the cycle is x dest,cycle xdest,12
0 xdest,23 1110 kJ> kg xdest,34
0 xdest,41 414 kJ> kg 1524 kJ/kg
The total exergy destroyed during the cycle could also be determined from
Eq. 10–21. Notice that the largest exergy destruction in the cycle occurs
during the heataddition process. Therefore, any attempt to reduce the
exergy destruction should start with this process. Raising the turbine inlet
temperature of the steam, for example, would reduce the temperature difference and thus the exergy destruction.
The exergy (work potential) of the steam leaving the turbine is determined
from Eq. 10–22. Disregarding the kinetic and potential energies, it reduces to 1 h4 h0 2 T0 1 s4 s0 2 1 h4 c4 h0 2 T0 1 s4 s0 2 where h0 c4 h f @ 290 K s0
Thus, h @ 290 K,100 kPa
s@ 290 K,100 kPa sf @ 290 K 1 2403.0 71.355 2 kJ> kg 0
0
V2 Q
4
gz4Q
2 71.355 kJ> kg 0.2533 kJ> kg # K 1 290 K 2 3 1 6.7450 0.2533 2 kJ> kg # K 4 449 kJ/kg
Discussion Note that 449 kJ/kg of work could be obtained from the steam
leaving the turbine if it is brought to the state of the surroundings in a
reversible manner. 10–8 ■ COGENERATION In all the cycles discussed so far, the sole purpose was to convert a portion
of the heat transferred to the working fluid to work, which is the most valuable form of energy. The remaining portion of the heat is rejected to rivers,
lakes, oceans, or the atmosphere as waste heat, because its quality (or grade)
is too low to be of any practical use. Wasting a large amount of heat is a
price we have to pay to produce work, because electrical or mechanical
work is the only form of energy on which many engineering devices (such
as a fan) can operate.
Many systems or devices, however, require energy input in the form of
heat, called process heat. Some industries that rely heavily on process heat
are chemical, pulp and paper, oil production and refining, steel making, cen84959_ch10.qxd 4/19/05 2:17 PM Page 579 Chapter 10
food processing, and textile industries. Process heat in these industries is
usually supplied by steam at 5 to 7 atm and 150 to 200°C (300 to 400°F).
Energy is usually transferred to the steam by burning coal, oil, natural gas,
or another fuel in a furnace.
Now let us examine the operation of a processheating plant closely. Disregarding any heat losses in the piping, all the heat transferred to the steam in the
boiler is used in the processheating units, as shown in Fig. 10–20. Therefore,
process heating seems like a perfect operation with practically no waste of
energy. From the secondlaw point of view, however, things do not look so perfect. The temperature in furnaces is typically very high (around 1400°C), and
thus the energy in the furnace is of very high quality. This highquality energy
is transferred to water to produce steam at about 200°C or below (a highly irreversible process). Associated with this irreversibility is, of course, a loss in
exergy or work potential. It is simply not wise to use highquality energy to
accomplish a task that could be accomplished with lowquality energy.
Industries that use large amounts of process heat also consume a large
amount of electric power. Therefore, it makes economical as well as engineering sense to use the alreadyexisting work potential to produce power
instead of letting it go to waste. The result is a plant that produces electricity while meeting the processheat requirements of certain industrial processes. Such a plant is called a cogeneration plant. In general, cogeneration
is the production of more than one useful form of energy (such as process
heat and electric power) from the same energy source.
Either a steamturbine (Rankine) cycle or a gasturbine (Brayton) cycle or
even a combined cycle (discussed later) can be used as the power cycle in a
cogeneration plant. The schematic of an ideal steamturbine cogeneration
.
plant is shown in Fig. 10–21. Let us say this plant is to supply process heat Qp
at 500 kPa at a rate of 100 kW. To meet this demand, steam is expanded in the
turbine to a pressure of 500 kPa, producing power at a rate of, say, 20 kW.
The flow rate of the steam can be adjusted such that steam leaves the processheating section as a saturated liquid at 500 kPa. Steam is then pumped to the
boiler pressure and is heated in the boiler to state 3. The pump work is usually
very small and can be neglected. Disregarding any heat losses, the rate of heat
input in the boiler is determined from an energy balance to be 120 kW.
Probably the most striking feature of the ideal steamturbine cogeneration
plant shown in Fig. 10–21 is the absence of a condenser. Thus no heat is
rejected from this plant as waste heat. In other words, all the energy transferred to the steam in the boiler is utilized as either process heat or electric
power. Thus it is appropriate to define a utilization factor u for a cogeneration plant as
u Net work output Process heat delivered
Total heat input #
Wnet
#
Q in #
Qp (10–23) or
u 1 #
Q out
#
Q in (10–24) .
where Qout represents the heat rejected in the condenser. Strictly speaking,
.
Qout also includes all the undesirable heat losses from the piping and other
components, but they are usually small and thus neglected. It also includes
combustion inefficiencies such as incomplete combustion and stack losses  579 Boiler
Process
heater
Qp
Pump
Qin FIGURE 10–20
A simple processheating plant. 3 Turbine Boiler 20 kW
4
Process
heater 120 kW
2 Pump 100 kW
1
W pump ~ 0
= FIGURE 10–21
An ideal cogeneration plant. cen84959_ch10.qxd 4/19/05 2:17 PM Page 580 580  Thermodynamics 4
Expansion
valve
Turbine Boiler
5 6
7
Process
heater 3 Pump II Condenser
8
1 2 Pump I FIGURE 10–22
A cogeneration plant with adjustable
loads. when the utilization factor is defined on the basis of the heating value of the
fuel. The utilization factor of the ideal steamturbine cogeneration plant is
obviously 100 percent. Actual cogeneration plants have utilization factors as
high as 80 percent. Some recent cogeneration plants have even higher utilization factors.
Notice that without the turbine, we would need to supply heat to the
steam in the boiler at a rate of only 100 kW instead of at 120 kW. The additional 20 kW of heat supplied is converted to work. Therefore, a cogeneration power plant is equivalent to a processheating plant combined with a
power plant that has a thermal efficiency of 100 percent.
The ideal steamturbine cogeneration plant described above is not practical because it cannot adjust to the variations in power and processheat
loads. The schematic of a more practical (but more complex) cogeneration
plant is shown in Fig. 10–22. Under normal operation, some steam is
extracted from the turbine at some predetermined intermediate pressure P6.
The rest of the steam expands to the condenser pressure P7 and is then
cooled at constant pressure. The heat rejected from the condenser represents
the waste heat for the cycle.
At times of high demand for process heat, all the steam is routed to the
.
processheating units and none to the condenser (m 7 0). The waste heat is
zero in this mode. If this is not sufficient, some steam leaving the boiler is
throttled by an expansion or pressurereducing valve (PRV) to the extraction
pressure P6 and is directed to the processheating unit. Maximum process
heating is realized when all the steam leaving the boiler passes through the
.
.
m 4). No power is produced in this mode. When there is no
PRV (m 5
demand for process heat, all the steam passes through the turbine and the
.
.
m6
0), and the cogeneration plant operates as an ordicondenser (m 5
nary steam power plant. The rates of heat input, heat rejected, and process
heat supply as well as the power produced for this cogeneration plant can be
expressed as follows:
#
Q in
#
Q out
#
Qp
#
Wturb #
m3 1 h4 h3 2
#
m7 1 h7 h1 2
#
#
m5 h5 m6 h6
#
#
1 m4 m5 2 1 h4 (10–25)
(10–26) #
m8 h8
h6 2 (10–27) #
m7 1 h6 h7 2 (10–28) Under optimum conditions, a cogeneration plant simulates the ideal
cogeneration plant discussed earlier. That is, all the steam expands in the
turbine to the extraction pressure and continues to the processheating unit.
No steam passes through the PRV or the condenser; thus, no waste heat is
.
.
.
.
m 6 and m 5
m7
0). This condition may be difficult to
rejected (m 4
achieve in practice because of the constant variations in the processheat
and power loads. But the plant should be designed so that the optimum
operating conditions are approximated most of the time.
The use of cogeneration dates to the beginning of this century when
power plants were integrated to a community to provide district heating,
that is, space, hot water, and process heating for residential and commercial
buildings. The district heating systems lost their popularity in the 1940s
owing to low fuel prices. However, the rapid rise in fuel prices in the 1970s
brought about renewed interest in district heating. cen84959_ch10.qxd 4/19/05 2:17 PM Page 581 Chapter 10  581 Cogeneration plants have proved to be economically very attractive. Consequently, more and more such plants have been installed in recent years,
and more are being installed.
EXAMPLE 10–8 An Ideal Cogeneration Plant Consider the cogeneration plant shown in Fig. 10–23. Steam enters the turbine
at 7 MPa and 500°C. Some steam is extracted from the turbine at 500 kPa for
process heating. The remaining steam continues to expand to 5 kPa. Steam is
then condensed at constant pressure and pumped to the boiler pressure of
7 MPa. At times of high demand for process heat, some steam leaving the
boiler is throttled to 500 kPa and is routed to the process heater. The extraction fractions are adjusted so that steam leaves the process heater as a saturated liquid at 500 kPa. It is subsequently pumped to 7 MPa. The mass flow
rate of steam through the boiler is 15 kg/s. Disregarding any pressure drops
and heat losses in the piping and assuming the turbine and the pump to be
isentropic, determine (a) the maximum rate at which process heat can be
supplied, (b) the power produced and the utilization factor when no process
heat is supplied, and (c) the rate of process heat supply when 10 percent of
the steam is extracted before it enters the turbine and 70 percent of the
steam is extracted from the turbine at 500 kPa for process heating. Solution A cogeneration plant is considered. The maximum rate of process
heat supply, the power produced and the utilization factor when no process
heat is supplied, and the rate of process heat supply when steam is extracted
from the steam line and turbine at specified ratios are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Pressure drops and heat
losses in piping are negligible. 3 Kinetic and potential energy changes are
negligible.
Analysis The schematic of the cogeneration plant and the Ts diagram of
the cycle are shown in Fig. 10–23. The power plant operates on an ideal 7 MPa
500°C
1 T
1, 2, 3
3 2 Boiler Expansion
valve
4
500 kPa Turbine
5 4 500 kPa
6 Process
heater 10 5 kPa 11 11
10 Mixing
chamber 7 5 9 Pump II
Condenser 7 8 6 Pump I 9 8 7 MPa
5 kPa FIGURE 10–23
Schematic and Ts diagram for Example 10–8. s cen84959_ch10.qxd 4/19/05 2:17 PM Page 582 582  Thermodynamics
cycle and thus the pumps and the turbines are isentropic; there are no pressure drops in the boiler, process heater, and condenser; and steam leaves
the condenser and the process heater as saturated liquid.
The work inputs to the pumps and the enthalpies at various states are as
follows: wpump I,in v8 1 P9 P8 2 1 0.001005 m3> kg 2 3 1 7000 5 2 kPa 4 a 1 0.001093 m3> kg 2 3 17000 500 2 kPa 4 a 7.03 kJ> kg
wpump II,in v7 1 P10 P7 2 7.10 kJ> kg
h1
h5 h2 h3 2739.3 kJ> kg
2073.0 kJ> kg h7 h f @ 500 kPa h8 h f @ 5 kPa h9 h8 wpump I,in h 10 h7 1 kJ
b
1 kPa # m3 3411.4 kJ> kg h4 h6 1 kJ
b
1 kPa # m3 wpump II,in 640.09 kJ> kg 137.75 kJ> kg 1 137.75 1 640.09 7.03 2 kJ> kg 7.10 2 kJ> kg 144.78 kJ> kg 647.19 kJ> kg (a) The maximum rate of process heat is achieved when all the steam leaving
the boiler is throttled and sent to the process heater and none is sent to the
.
.
.
.
.
.
turbine (that is, m 4
m7
m1
15 kg/s and m 3
m5
m6
0). Thus, #
Q p,max #
m1 1 h4 h7 2 1 15 kg> s 2 3 1 3411.4 640.09 2 kJ> kg 4 41,570 kW The utilization factor is 100 percent in this case since no heat is rejected in
the condenser, heat losses from the piping and other components are
assumed to be negligible, and combustion losses are not considered.
(b) When no process heat is supplied, all the steam leaving the boiler passes
through the turbine and expands to the condenser pressure of 5 kPa (that is,
.
.
.
.
.
m3
m6
m1
15 kg/s and m 2
m5
0). Maximum power is produced
in this mode, which is determined to be #
Wturb,out
#
Wpump,in
#
Wnet,out
#
Q in #
m 1 h3 h6 2 1 15 kg> s 2 3 1 3411.4 2073.0 2 kJ> kg 4 20,076 kW 1 15 kg> s 2 1 7.03 kJ> kg 2
105 kW
#
#
Wturb,out Wpump,in
1 20,076 105 2 kW 19,971 kW
20.0 MW
#
m 1 1 h1 h 11 2
1 15 kg> s 2 3 1 3411.4 144.78 2 kJ> kg 4
48,999 kW Thus, #
Wnet
u #
Q in #
Qp 1 19,971 0 2 kW 48,999 kW 0.408 or 40.8% That is, 40.8 percent of the energy is utilized for a useful purpose. Notice
that the utilization factor is equivalent to the thermal efficiency in this case.
(c) Neglecting any kinetic and potential energy changes, an energy balance
on the process heater yields cen84959_ch10.qxd 4/19/05 2:17 PM Page 583 Chapter 10
#
Ein
#
m 4h 4 #
m5h5 #
Eout
#
Q p,out #
Qp,out #
m 4h4 #
m 5h 5 #
m7h 7
#
m 7h7 or where #
m4
#
m5
#
m7 1 0.1 2 1 15 kg> s 2 1 0.7 2 1 15 kg> s 2
#
#
m 4 m 5 1.5 1.5 kg> s 10.5 kg> s
10.5 12 kg> s Thus #
Q p,out 1 1.5 kg> s 2 1 3411.4 kJ> kg 2 1 12 kg> s 2 1 640.09 kJ> kg 2 1 10.5 kg> s 2 1 2739.3 kJ> kg 2 26.2 MW
Discussion Note that 26.2 MW of the heat transferred will be utilized in the
process heater. We could also show that 11.0 MW of power is produced in
this case, and the rate of heat input in the boiler is 43.0 MW. Thus the utilization factor is 86.5 percent. 10–9 ■ COMBINED GAS–VAPOR POWER CYCLES The continued quest for higher thermal efficiencies has resulted in rather
innovative modifications to conventional power plants. The binary vapor
cycle discussed later is one such modification. A more popular modification
involves a gas power cycle topping a vapor power cycle, which is called the
combined gas–vapor cycle, or just the combined cycle. The combined
cycle of greatest interest is the gasturbine (Brayton) cycle topping a steamturbine (Rankine) cycle, which has a higher thermal efficiency than either of
the cycles executed individually.
Gasturbine cycles typically operate at considerably higher temperatures
than steam cycles. The maximum fluid temperature at the turbine inlet is
about 620°C (1150°F) for modern steam power plants, but over 1425°C
(2600°F) for gasturbine power plants. It is over 1500°C at the burner exit
of turbojet engines. The use of higher temperatures in gas turbines is made
possible by recent developments in cooling the turbine blades and coating
the blades with hightemperatureresistant materials such as ceramics. Because
of the higher average temperature at which heat is supplied, gasturbine
cycles have a greater potential for higher thermal efficiencies. However, the
gasturbine cycles have one inherent disadvantage: The gas leaves the gas
turbine at very high temperatures (usually above 500°C), which erases any
potential gains in the thermal efficiency. The situation can be improved
somewhat by using regeneration, but the improvement is limited.
It makes engineering sense to take advantage of the very desirable characteristics of the gasturbine cycle at high temperatures and to use the hightemperature exhaust gases as the energy source for the bottoming cycle such
as a steam power cycle. The result is a combined gas–steam cycle, as shown  583 cen84959_ch10.qxd 4/19/05 2:17 PM Page 584 584  Thermodynamics
in Fig. 10–24. In this cycle, energy is recovered from the exhaust gases by
transferring it to the steam in a heat exchanger that serves as the boiler. In
general, more than one gas turbine is needed to supply sufficient heat to the
steam. Also, the steam cycle may involve regeneration as well as reheating.
Energy for the reheating process can be supplied by burning some additional fuel in the oxygenrich exhaust gases.
Recent developments in gasturbine technology have made the combined
gas–steam cycle economically very attractive. The combined cycle increases
the efficiency without increasing the initial cost greatly. Consequently, many
new power plants operate on combined cycles, and many more existing
steam or gasturbine plants are being converted to combinedcycle power
plants. Thermal efficiencies well over 40 percent are reported as a result of
conversion.
A 1090MW Tohoku combined plant that was put in commercial operation
in 1985 in Niigata, Japan, is reported to operate at a thermal efficiency of
44 percent. This plant has two 191MW steam turbines and six 118MW gas
turbines. Hot combustion gases enter the gas turbines at 1154°C, and steam
enters the steam turbines at 500°C. Steam is cooled in the condenser by cooling water at an average temperature of 15°C. The compressors have a pressure
ratio of 14, and the mass flow rate of air through the compressors is 443 kg/s. Qin
T
Combustion
chamber
6 7
GAS CYCLE Air
in 5
Exhaust
gases 7 Gas
turbine Compressor 9 Heat exchanger GAS
CYCLE Qin 8 8
3
6 2 3 STEAM
CYCLE 9 Pump Steam
turbine Condenser STEAM
CYCLE 2
5
1 4
Qout 1
Qout FIGURE 10–24
Combined gas–steam power plant. 4
s cen84959_ch10.qxd 4/19/05 2:17 PM Page 585 Chapter 10  A 1350MW combinedcycle power plant built in Ambarli, Turkey, in
1988 by Siemens of Germany is the first commercially operating thermal
plant in the world to attain an efficiency level as high as 52.5 percent at
design operating conditions. This plant has six 150MW gas turbines and
three 173MW steam turbines. Some recent combinedcycle power plants
have achieved efficiencies above 60 percent.
EXAMPLE 10–9 A Combined Gas–Steam Power Cycle Consider the combined gas–steam power cycle shown in Fig. 10–25. The topping cycle is a gasturbine cycle that has a pressure ratio of 8. Air enters the
compressor at 300 K and the turbine at 1300 K. The isentropic efficiency of
the compressor is 80 percent, and that of the gas turbine is 85 percent. The
bottoming cycle is a simple ideal Rankine cycle operating between the pressure
limits of 7 MPa and 5 kPa. Steam is heated in a heat exchanger by the exhaust
gases to a temperature of 500°C. The exhaust gases leave the heat exchanger
at 450 K. Determine (a) the ratio of the mass flow rates of the steam and the
combustion gases and (b) the thermal efficiency of the combined cycle. Solution A combined gas–steam cycle is considered. The ratio of the mass
flow rates of the steam and the combustion gases and the thermal efficiency
are to be determined.
Analysis The Ts diagrams of both cycles are given in Fig. 10–25. The gasturbine cycle alone was analyzed in Example 9–6, and the steam cycle in
Example 10–8b, with the following results: Gas cycle: ¿
h4 880.36 kJ> kg qin 790.58 kJ> kg h5
¿ h @ 450 K 1 T4
¿ wnet 853 K 2 210.41 kJ> kg 451.80 kJ> kg h th 26.6% T, K
3' 1300 4'
3 500°C
7 MPa 2'
7 MPa
450 5'
2 300 5 kPa 1'
1 4 s FIGURE 10–25
Ts diagram of the gas–steam
combined cycle described in
Example 10–9. 585 cen84959_ch10.qxd 4/19/05 2:17 PM Page 586 586  Thermodynamics
Steam cycle: h2
h3
wnet 144.78 kJ> kg 1 T2 33°C 2 1331.4 kJ> kg hth 40.8% 3411.4 kJ> kg 1 T3 500°C 2 (a) The ratio of mass flow rates is determined from an energy balance on the
heat exchanger: #
E in
#
#
¿
ms h3
mg h5
#
ms 1 h3 h2 2 #
m s 1 3411.4 144.78 2 #
E out
#
#
mg h4
¿
ms h2
#
mg 1 h ¿
h5 2
¿
4
#
mg 1 880.36 451.80 2 Thus, #
ms
#
mg y 0.131 That is, 1 kg of exhaust gases can heat only 0.131 kg of steam from 33 to
500°C as they are cooled from 853 to 450 K. Then the total net work output per kilogram of combustion gases becomes wnet wnet,gas ywnet,steam 1 210.41 kJ> kg gas 2 384.8 kJ> kg gas 1 0.131 kg steam> kg gas 2 1 1331.4 kJ> kg steam 2 Therefore, for each kg of combustion gases produced, the combined plant
will deliver 384.8 kJ of work. The net power output of the plant is determined by multiplying this value by the mass flow rate of the working fluid in
the gasturbine cycle.
(b) The thermal efficiency of the combined cycle is determined from h th wnet
qin 384.8 kJ> kg gas 790.6 kJ> kg gas 0.487 or 48.7% Discussion Note that this combined cycle converts to useful work 48.7 percent of the energy supplied to the gas in the combustion chamber. This value
is considerably higher than the thermal efficiency of the gasturbine cycle
(26.6 percent) or the steamturbine cycle (40.8 percent) operating alone. TOPIC OF SPECIAL INTEREST* Binary Vapor Cycles
With the exception of a few specialized applications, the working fluid predominantly used in vapor power cycles is water. Water is the best working
fluid presently available, but it is far from being the ideal one. The binary
cycle is an attempt to overcome some of the shortcomings of water and to
approach the ideal working fluid by using two fluids. Before we discuss the
binary cycle, let us list the characteristics of a working fluid most suitable
for vapor power cycles:
*This section can be skipped without a loss in continuity. cen84959_ch10.qxd 4/19/05 2:17 PM Page 587 Chapter 10
1. A high critical temperature and a safe maximum pressure. A critical temperature above the metallurgically allowed maximum temperature
(about 620°C) makes it possible to transfer a considerable portion of the
heat isothermally at the maximum temperature as the fluid changes
phase. This makes the cycle approach the Carnot cycle. Very high pressures at the maximum temperature are undesirable because they create
materialstrength problems.
2. Low triplepoint temperature. A triplepoint temperature below the
temperature of the cooling medium prevents any solidification problems.
3. A condenser pressure that is not too low. Condensers usually
operate below atmospheric pressure. Pressures well below the atmospheric pressure create airleakage problems. Therefore, a substance
whose saturation pressure at the ambient temperature is too low is not a
good candidate.
4. A high enthalpy of vaporization (hfg) so that heat transfer to the
working fluid is nearly isothermal and large mass flow rates are not
needed.
5. A saturation dome that resembles an inverted U. This eliminates
the formation of excessive moisture in the turbine and the need for
reheating.
6. Good heat transfer characteristics (high thermal conductivity).
7. Other properties such as being inert, inexpensive, readily available, and nontoxic.
Not surprisingly, no fluid possesses all these characteristics. Water comes
the closest, although it does not fare well with respect to characteristics 1, 3,
and 5. We can cope with its subatmospheric condenser pressure by careful
sealing, and with the inverted Vshaped saturation dome by reheating, but
there is not much we can do about item 1. Water has a low critical temperature (374°C, well below the metallurgical limit) and very high saturation
pressures at high temperatures (16.5 MPa at 350°C).
Well, we cannot change the way water behaves during the hightemperature
part of the cycle, but we certainly can replace it with a more suitable fluid.
The result is a power cycle that is actually a combination of two cycles, one
in the hightemperature region and the other in the lowtemperature region.
Such a cycle is called a binary vapor cycle. In binary vapor cycles, the
condenser of the hightemperature cycle (also called the topping cycle) serves
as the boiler of the lowtemperature cycle (also called the bottoming cycle).
That is, the heat output of the hightemperature cycle is used as the heat input
to the lowtemperature one.
Some working fluids found suitable for the hightemperature cycle are mercury, sodium, potassium, and sodium–potassium mixtures. The schematic and
Ts diagram for a mercury–water binary vapor cycle are shown in Fig. 10–26.
The critical temperature of mercury is 898°C (well above the current metallurgical limit), and its critical pressure is only about 18 MPa. This makes mercury a very suitable working fluid for the topping cycle. Mercury is not
suitable as the sole working fluid for the entire cycle, however, since at a condenser temperature of 32°C its saturation pressure is 0.07 Pa. A power plant
cannot operate at this vacuum because of airleakage problems. At an acceptable condenser pressure of 7 kPa, the saturation temperature of mercury is  587 cen84959_ch10.qxd 4/19/05 2:17 PM Page 588 588  Thermodynamics
T
2 3
Boiler Mercury
pump MERCURY
CYCLE 1 Saturation dome
(mercury) Mercury
turbine Heat exchanger 3
MERCURY
CYCLE 4 Q 7
2
4 6 STEAM
CYCLE Saturation
dome
(steam) 7
Steam
turbine Steam
pump 1 Superheater STEAM
CYCLE 6
5 8 Condenser
5 8
s FIGURE 10–26
Mercury–water binary vapor cycle. 237°C, which is too high as the minimum temperature in the cycle. Therefore,
the use of mercury as a working fluid is limited to the hightemperature
cycles. Other disadvantages of mercury are its toxicity and high cost. The
mass flow rate of mercury in binary vapor cycles is several times that of water
because of its low enthalpy of vaporization.
It is evident from the Ts diagram in Fig. 10–26 that the binary vapor cycle
approximates the Carnot cycle more closely than the steam cycle for the
same temperature limits. Therefore, the thermal efficiency of a power plant
can be increased by switching to binary cycles. The use of mercury–water
binary cycles in the United States dates back to 1928. Several such plants
have been built since then in the New England area, where fuel costs are typically higher. A small (40MW) mercury–steam power plant that was in service in New Hampshire in 1950 had a higher thermal efficiency than most of
the large modern power plants in use at that time.
Studies show that thermal efficiencies of 50 percent or higher are possible
with binary vapor cycles. However, binary vapor cycles are not economically
attractive because of their high initial cost and the competition offered by the
combined gas–steam power plants. cen84959_ch10.qxd 4/19/05 2:17 PM Page 589 Chapter 10  589 SUMMARY
The Carnot cycle is not a suitable model for vapor power
cycles because it cannot be approximated in practice. The
model cycle for vapor power cycles is the Rankine cycle,
which is composed of four internally reversible processes:
constantpressure heat addition in a boiler, isentropic expansion in a turbine, constantpressure heat rejection in a condenser, and isentropic compression in a pump. Steam leaves
the condenser as a saturated liquid at the condenser pressure.
The thermal efficiency of the Rankine cycle can be increased
by increasing the average temperature at which heat is transferred to the working fluid and/or by decreasing the average
temperature at which heat is rejected to the cooling medium.
The average temperature during heat rejection can be
decreased by lowering the turbine exit pressure. Consequently, the condenser pressure of most vapor power plants is
well below the atmospheric pressure. The average temperature during heat addition can be increased by raising the
boiler pressure or by superheating the fluid to high temperatures. There is a limit to the degree of superheating, however,
since the fluid temperature is not allowed to exceed a metallurgically safe value.
Superheating has the added advantage of decreasing the
moisture content of the steam at the turbine exit. Lowering the
exhaust pressure or raising the boiler pressure, however, increases
the moisture content. To take advantage of the improved efficiencies at higher boiler pressures and lower condenser pressures, steam is usually reheated after expanding partially in the
highpressure turbine. This is done by extracting the steam after
partial expansion in the highpressure turbine, sending it back
to the boiler where it is reheated at constant pressure, and
returning it to the lowpressure turbine for complete expansion
to the condenser pressure. The average temperature during the reheat process, and thus the thermal efficiency of the cycle, can
be increased by increasing the number of expansion and reheat
stages. As the number of stages is increased, the expansion and
reheat processes approach an isothermal process at maximum
temperature. Reheating also decreases the moisture content at
the turbine exit.
Another way of increasing the thermal efficiency of the
Rankine cycle is regeneration. During a regeneration process,
liquid water (feedwater) leaving the pump is heated by steam
bled off the turbine at some intermediate pressure in devices
called feedwater heaters. The two streams are mixed in open
feedwater heaters, and the mixture leaves as a saturated liquid
at the heater pressure. In closed feedwater heaters, heat is
transferred from the steam to the feedwater without mixing.
The production of more than one useful form of energy
(such as process heat and electric power) from the same
energy source is called cogeneration. Cogeneration plants produce electric power while meeting the process heat requirements of certain industrial processes. This way, more of the
energy transferred to the fluid in the boiler is utilized for a
useful purpose. The fraction of energy that is used for either
process heat or power generation is called the utilization factor of the cogeneration plant.
The overall thermal efficiency of a power plant can be
increased by using a combined cycle. The most common
combined cycle is the gas–steam combined cycle where a
gasturbine cycle operates at the hightemperature range and
a steamturbine cycle at the lowtemperature range. Steam is
heated by the hightemperature exhaust gases leaving the gas
turbine. Combined cycles have a higher thermal efficiency
than the steam or gasturbine cycles operating alone. REFERENCES AND SUGGESTED READINGS
1. R. L. Bannister and G. J. Silvestri. “The Evolution of
Central Station Steam Turbines.” Mechanical Engineering, February 1989, pp. 70–78.
2. R. L. Bannister, G. J. Silvestri, A. Hizume, and T. Fujikawa. “High Temperature Supercritical Steam Turbines.”
Mechanical Engineering, February 1987, pp. 60–65.
3. M. M. ElWakil. Powerplant Technology. New York:
McGrawHill, 1984.
4. K. W. Li and A. P. Priddy. Power Plant System Design.
New York: John Wiley & Sons, 1985.
5. H. Sorensen. Energy Conversion Systems. New York: John
Wiley & Sons, 1983. 6. Steam, Its Generation and Use. 39th ed. New York:
Babcock and Wilcox Co., 1978.
7. Turbomachinery 28, no. 2 (March/April 1987). Norwalk,
CT: Business Journals, Inc.
8. K. Wark and D. E. Richards. Thermodynamics. 6th ed.
New York: McGrawHill, 1999.
9. J. Weisman and R. Eckart. Modern Power Plant Engineering. Englewood Cliffs, NJ: PrenticeHall, 1985. cen84959_ch10.qxd 4/19/05 2:17 PM Page 590 590  Thermodynamics PROBLEMS*
Carnot Vapor Cycle
10–1C Why is excessive moisture in steam undesirable in
steam turbines? What is the highest moisture content
allowed?
10–2C Why is the Carnot cycle not a realistic model for
steam power plants?
10–3E Water enters the boiler of a steadyflow Carnot
engine as a saturated liquid at 180 psia and leaves with a
quality of 0.90. Steam leaves the turbine at a pressure of 14.7
psia. Show the cycle on a Ts diagram relative to the saturation lines, and determine (a) the thermal efficiency, (b) the
quality at the end of the isothermal heatrejection process,
and (c) the net work output. Answers: (a) 19.3 percent,
(b) 0.153, (c) 148 Btu/lbm 10–4 A steadyflow 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°C. Heat rejection takes place at a pressure of 20 kPa. Show the cycle on
a Ts diagram relative to the saturation lines, and determine
(a) the thermal efficiency, (b) the amount of heat rejected, in
kJ/kg, and (c) the net work output.
10–5 Repeat Prob. 10–4 for a heat rejection pressure of
10 kPa.
10–6 Consider a steadyflow Carnot cycle with water as the
working fluid. The maximum and minimum temperatures in
the cycle are 350 and 60°C. The quality of water is 0.891 at
the beginning of the heatrejection process and 0.1 at the end.
Show the cycle on a Ts 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.
Answers: (a) 0.465, (b) 1.40 MPa, (c) 1623 kJ/kg The Simple Rankine Cycle
10–7C What four processes make up the simple ideal Rankine cycle?
10–8C Consider a simple ideal Rankine cycle with fixed
turbine inlet conditions. What is the effect of lowering the
condenser pressure on *Problems designated by a “C” are concept questions, and students
are encouraged to answer them all. Problems designated by an “E”
are in English units, and the SI users can ignore them. Problems
with a CDEES icon
are solved using EES, and complete solutions
together with parametric studies are included on the enclosed DVD.
Problems with a computerEES icon
are comprehensive in nature,
and are intended to be solved with a computer, preferably using the
EES software that accompanies this text. Pump work input: (a) increases, (b) decreases,
(c) remains the same
Turbine work
(a) increases, (b) decreases,
output:
(c) remains the same
Heat supplied:
(a) increases, (b) decreases,
(c) remains the same
Heat rejected:
(a) increases, (b) decreases,
(c) remains the same
Cycle efficiency:
(a) increases, (b) decreases,
(c) remains the same
Moisture content (a) increases, (b) decreases,
at turbine exit: (c) remains the same 10–9C Consider a simple ideal Rankine cycle with fixed
turbine inlet temperature and condenser pressure. What is the
effect of increasing the boiler pressure on
Pump work input: (a) increases, (b) decreases,
(c) remains the same
Turbine work
(a) increases, (b) decreases,
output:
(c) remains the same
Heat supplied:
(a) increases, (b) decreases,
(c) remains the same
Heat rejected:
(a) increases, (b) decreases,
(c) remains the same
Cycle efficiency:
(a) increases, (b) decreases,
(c) remains the same
Moisture content (a) increases, (b) decreases,
at turbine exit: (c) remains the same 10–10C 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
Pump work input: (a) increases, (b) decreases,
(c) remains the same
Turbine work
(a) increases, (b) decreases,
output:
(c) remains the same
Heat supplied:
(a) increases, (b) decreases,
(c) remains the same
Heat rejected:
(a) increases, (b) decreases,
(c) remains the same
Cycle efficiency:
(a) increases, (b) decreases,
(c) remains the same
Moisture content (a) increases, (b) decreases,
at turbine exit: (c) remains the same 10–11C How do actual vapor power cycles differ from idealized ones? cen84959_ch10.qxd 4/19/05 2:17 PM Page 591 Chapter 10
10–12C Compare the pressures at the inlet and the exit of
the boiler for (a) actual and (b) ideal cycles.
10–13C 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?
10–14C Is it possible to maintain a pressure of 10 kPa in a
condenser that is being cooled by river water entering at
20°C?
10–15 A steam power plant operates on a simple ideal
Rankine cycle between the pressure limits of 3 MPa and
50 kPa. The temperature of the steam at the turbine inlet is
300°C, and the mass flow rate of steam through the cycle is
35 kg/s. Show the cycle on a Ts diagram with respect to saturation lines, and determine (a) the thermal efficiency of the
cycle and (b) the net power output of the power plant.
10–16 Consider a 210MW steam power plant that operates
on a simple ideal Rankine cycle. Steam enters the turbine at
10 MPa and 500°C and is cooled in the condenser at a pressure of 10 kPa. Show the cycle on a Ts 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. Answers: (a) 0.793,
(b) 40.2 percent, (c) 165 kg/s 10–17 Repeat Prob. 10–16 assuming an isentropic efficiency of 85 percent for both the turbine and the pump.
Answers: (a) 0.874, (b) 34.1 percent, (c) 194 kg/s 10–18E A steam power plant operates on a simple ideal
Rankine cycle between the pressure limits of 1250 and
2 psia. The mass flow rate of steam through the cycle is
75 lbm/s. The moisture content of the steam at the turbine exit
is not to exceed 10 percent. Show the cycle on a Ts diagram
with respect to saturation lines, and determine (a) the minimum turbine inlet temperature, (b) the rate of heat input in
the boiler, and (c) the thermal efficiency of the cycle.
10–19E Repeat Prob. 10–18E assuming an isentropic efficiency of 85 percent for both the turbine and the pump.
10–20 Consider a coalfired steam power plant that produces 300 MW of electric power. The power plant operates
on a simple ideal Rankine cycle with turbine inlet conditions
of 5 MPa and 450°C and a condenser pressure of 25 kPa. The
coal has a heating value (energy released when the fuel is
burned) of 29,300 kJ/kg. Assuming that 75 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. Answers: (a) 24.5 percent, (b) 150 t/h  591 10–21 Consider a solarpond power plant that operates on a
simple ideal Rankine cycle with refrigerant134a 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 kg/s. Show the cycle on a Ts diagram
with respect to saturation lines, and determine (a) the thermal
efficiency of the cycle and (b) the power output of this plant.
10–22 Consider a steam power plant that operates on a simple ideal Rankine cycle and has a net power output of
45 MW. Steam enters the turbine at 7 MPa and 500°C and is
cooled in the condenser at a pressure of 10 kPa by running
cooling water from a lake through the tubes of the condenser
at a rate of 2000 kg/s. Show the cycle on a Ts diagram with
respect to saturation lines, and determine (a) the thermal efficiency of the cycle, (b) the mass flow rate of the steam, and
(c) the temperature rise of the cooling water. Answers:
(a) 38.9 percent, (b) 36 kg/s, (c) 8.4°C 10–23 Repeat Prob. 10–22 assuming an isentropic efficiency of 87 percent for both the turbine and the pump.
Answers: (a) 33.8 percent, (b) 41.4 kg/s, (c) 10.5°C 10–24 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 10 MPa as a saturated
vapor, and the condenser pressure is 20 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 Ts diagrams for both cycles.
10–25 A binary geothermal power plant uses geothermal
water at 160°C as the heat source. The cycle 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°C at a rate of 555.9 kg/s
and leaves at 90°C. Isobutane enters the turbine at 3.25 MPa
and 147°C at a rate of 305.6 kg/s, and leaves at 79.5°C and
Aircooled
condenser 4 1 Turbine
Pump
3 2
Heat exchanger Geothermal
water in Geothermal
water out FIGURE P10–25 cen84959_ch10.qxd 4/19/05 2:17 PM Page 592 592  Thermodynamics 410 kPa. Isobutane is condensed in an aircooled 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 cycle.
10–26 The schematic of a singleflash geothermal power
plant with state numbers is given in Fig. P10–26. Geothermal
resource exists as saturated liquid at 230°C. The geothermal
liquid is withdrawn from the production well at a rate of 230
kg/s, and is flashed to a pressure of 500 kPa by an essentially
isenthalpic flashing process where the resulting vapor is separated from the liquid in a separator and directed to the turbine. The steam leaves the turbine at 10 kPa with a moisture
content of 10 percent and enters the condenser where it is
condensed and routed to a reinjection well along with the liquid coming off the separator. Determine (a) the mass flow
rate of steam through the turbine, (b) the isentropic efficiency
of the turbine, (c) the power output of the turbine, and (d ) the
thermal efficiency of the plant (the ratio of the turbine work
output to the energy of the geothermal fluid relative to standard ambient conditions). Answers: (a) 38.2 kg/s, (b) 0.686,
(c) 15.4 MW, (d) 7.6 percent 3 Steam
turbine
Separator 4 2
Condenser
Flash
chamber 3
Steam
turbine 8
Separator
I 4 2
6
Flash
chamber Condenser 7 Separator
II Flash
chamber 5
9 1
Production
well Reinjection
well FIGURE P10–27
10–28 Reconsider Prob. 10–26. Now, it is proposed that the
liquid water coming out of the separator be used as the heat
source in a binary cycle with isobutane as the working fluid.
Geothermal liquid water leaves the heat exchanger at 90°C
while isobutane enters the turbine at 3.25 MPa and 145°C
and leaves at 80°C and 400 kPa. Isobutane is condensed in an
aircooled condenser and then pumped to the heat exchanger
pressure. Assuming an isentropic efficiency of 90 percent for
the pump, determine (a) the mass flow rate of isobutane in
the binary cycle, (b) the net power outputs of both the flashing and the binary sections of the plant, and (c) the thermal
efficiencies of the binary cycle and the combined plant.
Answers: (a) 105.5 kg/s, (b) 15.4 MW, 6.14 MW, (c) 12.2 percent,
10.6 percent 6
5
3 Steam
turbine Separator 1
Production
well 9 FIGURE P10–26
2 10–27 Reconsider Prob. 10–26. Now, it is proposed that the
liquid water coming out of the separator be routed through
another flash chamber maintained at 150 kPa, and the steam
produced be directed to a lower stage of the same turbine.
Both streams of steam leave the turbine at the same state of
10 kPa and 90 percent quality. Determine (a) the temperature
of steam at the outlet of the second flash chamber, (b) the
power produced by the lower stage of the turbine, and (c) the
thermal efficiency of the plant. 6 Condenser 4 Reinjection
well
Isobutane
turbine Aircooled
condenser BINARY
CYCLE 5 10 8
Heat exchanger
Flash
chamber 7 Pump 11 1
Production
well Reinjection
well FIGURE P10–28 cen84959_ch10.qxd 4/19/05 2:17 PM Page 593 Chapter 10
The Reheat Rankine Cycle
10–29C 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.
Pump work input: (a)
(c)
Turbine work
(a)
output:
(c)
Heat supplied:
(a)
(c)
Heat rejected:
(a)
(c)
Moisture content (a)
at turbine exit: (c) increases, (b) decreases,
remains the same
increases, (b) decreases,
remains the same
increases, (b) decreases,
remains the same
increases, (b) decreases,
remains the same
increases, (b) decreases,
remains the same 10–30C Show the ideal Rankine cycle with three stages of
reheating on a Ts diagram. Assume the turbine inlet temperature is the same for all stages. How does the cycle efficiency
vary with the number of reheat stages?
10–31C Consider a simple Rankine cycle and an ideal
Rankine cycle with three reheat stages. Both cycles operate
between the same pressure limits. The maximum temperature
is 700°C in the simple cycle and 450°C in the reheat cycle.
Which cycle do you think will have a higher thermal
efficiency?
10–32 A steam power plant operates on the ideal
reheat Rankine cycle. Steam enters the highpressure turbine at 8 MPa and 500°C and leaves at 3 MPa.
Steam is then reheated at constant pressure to 500°C before it
expands to 20 kPa in the lowpressure turbine. Determine the
turbine work output, in kJ/kg, and the thermal efficiency of
the cycle. Also, show the cycle on a Ts diagram with respect
to saturation lines.  10–35 Repeat Prob. 10–34 assuming both the pump and the
turbine are isentropic. Answers: (a) 0.949, (b) 41.3 percent,
(c) 50.0 kg/s 10–36E Steam enters the highpressure turbine of a steam
power plant that operates on the ideal reheat Rankine cycle at
800 psia and 900°F and leaves as saturated vapor. Steam is
then reheated to 800°F before it expands to a pressure of
1 psia. Heat is transferred to the steam in the boiler at a rate of
6 104 Btu/s. Steam is cooled in the condenser by the cooling
water from a nearby river, which enters the condenser at 45°F.
Show the cycle on a Ts 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.
10–37 A steam power plant operates on an ideal reheat Rankine cycle between the pressure limits of 15 MPa and 10 kPa.
The mass flow rate of steam through the cycle is 12 kg/s. Steam
enters both stages of the turbine at 500°C. If the moisture content of the steam at the exit of the lowpressure turbine is not to
exceed 10 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 Ts diagram with respect to saturation lines.
10–38 A steam power plant operates on the reheat Rankine
cycle. Steam enters the highpressure turbine at 12.5 MPa
and 550°C at a rate of 7.7 kg/s and leaves at 2 MPa. Steam is
then reheated at constant pressure to 450°C before it expands
in the lowpressure 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.
Answers: (a) 9.73 kPa, (b) 10.2 MW, (c) 36.9 percent 10–33 Reconsider Prob. 10–32. Using EES (or other)
software, solve this problem by the diagram
window data entry feature of EES. Include the effects of the
turbine and pump efficiencies and also show the effects of
reheat on the steam quality at the lowpressure turbine exit.
Plot the cycle on a Ts diagram with respect to the saturation
lines. Discuss the results of your parametric studies. 10–34 Consider a steam power plant that operates on a
reheat Rankine cycle and has a net power output of 80 MW.
Steam enters the highpressure turbine at 10 MPa and 500°C
and the lowpressure turbine at 1 MPa and 500°C. Steam
leaves the condenser as a saturated liquid at a pressure of
10 kPa. The isentropic efficiency of the turbine is 80 percent,
and that of the pump is 95 percent. Show the cycle on a Ts
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. Answers: (a) 88.1°C,
(b) 34.1 percent, (c) 62.7 kg/s 593 3 Turbine Boiler
4 6
5
Condenser 2 Pump
1 FIGURE P10–38 cen84959_ch10.qxd 4/19/05 2:17 PM Page 594 594  Thermodynamics Regenerative Rankine Cycle thermal efficiency of the cycle. Answers: (a) 30.5 MW, 10–39C 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. (b) 47.1 percent Turbine work
output:
Heat supplied:
Heat rejected:
Moisture content
at turbine exit: (a)
(c)
(a)
(c)
(a)
(c)
(a)
(c) increases, (b) decreases,
remains the same
increases, (b) decreases,
remains the same
increases, (b) decreases,
remains the same
increases, (b) decreases,
remains the same 10–40C 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?
10–41C How do open feedwater heaters differ from closed
feedwater heaters? 10–47 Consider an ideal steam regenerative Rankine
cycle with two feedwater heaters, one closed
and one open. Steam enters the turbine at 12.5 MPa and
550°C and exhausts to the condenser at 10 kPa. Steam is
extracted from the turbine at 0.8 MPa for the closed feedwater heater and at 0.3 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 Ts diagram with respect to saturation lines, and determine (a) the mass flow rate of steam through the boiler for a
net power output of 250 MW and (b) the thermal efficiency
of the cycle.
8
Turbine
Boiler 10–42C 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? 10–45 Repeat Prob. 10–44 by replacing 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.
10–46 A steam power plant operates on an ideal regenerative Rankine cycle with two open feedwater heaters. Steam
enters the turbine at 10 MPa and 600°C and exhausts to the
condenser at 5 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 22 kg/s. Show the cycle on a Ts diagram, and determine (a) the net power output of the power plant and (b) the y
z Closed
FWH 4
Open
FWH 3 5
6 11 10 P II 10–43C Devise an ideal regenerative Rankine cycle that has
the same thermal efficiency as the Carnot cycle. Show the
cycle on a Ts diagram.
10–44 A steam power plant operates on an ideal regenerative Rankine cycle. Steam enters the turbine at 6 MPa and
450°C and is condensed in the condenser at 20 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 Ts diagram, and
determine (a) the net work output per kilogram of steam
flowing through the boiler and (b) the thermal efficiency of
the cycle. Answers: (a) 1017 kJ/kg, (b) 37.8 percent 9 7 1–y –z Condenser
2
1
PI FIGURE P10–47
10–48 Reconsider Prob. 10–47. Using EES (or other)
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 Ts diagram for
turbine and pump efficiencies of 85 percent. 10–49 A steam power plant operates on an ideal reheat–
regenerative Rankine cycle and has a net power output of 80
MW. Steam enters the highpressure turbine at 10 MPa and
550°C and leaves at 0.8 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°C and is expanded in
the lowpressure turbine to the condenser pressure of 10 kPa.
Show the cycle on a Ts 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.
Answers: (a) 54.5 kg/s, (b) 44.4 percent 10–50 Repeat Prob. 10–49, but replace the open feedwater
heater with a closed feedwater heater. Assume that the feed cen84959_ch10.qxd 4/19/05 2:17 PM Page 595 Chapter 10
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. 5
HighP
turbine Boiler
1–y
Mixing
chamber
4 LowP
turbine 6
7 y 8 Closed
FWH 9 10–52 A steam power plant operates on the reheatregenerative Rankine cycle with a closed feedwater heater.
Steam enters the turbine at 12.5 MPa and 550°C at a rate of
24 kg/s and is condensed in the condenser at a pressure of
20 kPa. Steam is reheated at 5 MPa to 550°C. Some steam is
extracted from the lowpressure turbine at 1.0 MPa, is completely condensed in the closed feedwater heater, and pumped
to 12.5 MPa before it mixes with the feedwater at the same
pressure. Assuming an isentropic efficiency of 88 percent for
both the turbine and the pump, determine (a) the temperature
of the steam at the inlet of the closed feedwater heater,
(b) the mass flow rate of the steam extracted from the turbine
for the closed feedwater heater, (c) the net power output, and
(d ) the thermal efficiency. Answers: (a) 328°C, (b) 4.29 kg/s, Condenser 5 3
PI P II 1 HighP
turbine Boiler 10–51E A steam power plant operates on an ideal
reheat–regenerative Rankine cycle with one reheater and two
open feedwater heaters. Steam enters the highpressure turbine at 1500 psia and 1100°F and leaves the lowpressure turbine at 1 psia. Steam is extracted from the turbine at 250 and
40 psia, and it is reheated to 1000°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
105 Btu/s. Show the cycle on a Ts 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. HighP
turbine
8
y LowP
turbine
9 z
1–y–z 1–y
y
Open
FWH
II 6 Open
FWH
I
4 12 z
Condenser
2
1 3 5
P III 11 10 P II FIGURE P10–51E PI 9
1–y 7
4 Mixing
chamber Closed
FWH
10 11
P II 8 Condenser 2
3 y PI
1 FIGURE P10–52
SecondLaw Analysis of Vapor Power Cycles
10–53C How can the secondlaw efficiency of a simple
ideal Rankine cycle be improved?
10–54 Determine the exergy destruction associated with
each of the processes of the Rankine cycle described in Prob.
10–15, assuming a source temperature of 1500 K and a sink
temperature of 290 K. 7
Reheater LowP
turbine 6 FIGURE P10–50 Boiler 595 (c) 28.6 MW, (d) 39.3 percent 2
10  10–55 Determine the exergy destruction associated with
each of the processes of the Rankine cycle described in Prob.
10–16, assuming a source temperature of 1500 K and a sink
temperature of 290 K. Answers: 0, 1112 kJ/kg, 0, 172.3 kJ/kg
10–56 Determine the exergy destruction associated with the
heat rejection process in Prob. 10–22. Assume a source temperature of 1500 K and a sink temperature of 290 K. Also,
determine the exergy of the steam at the boiler exit. Take P0
100 kPa.
10–57 Determine the exergy destruction associated with
each of the processes of the reheat Rankine cycle described
in Prob. 10–32. Assume a source temperature of 1800 K and
a sink temperature of 300 K. cen84959_ch10.qxd 4/27/05 5:49 PM Page 596 596  Thermodynamics 10–58 Reconsider Prob. 10–57. Using EES (or other)
software, solve this problem by the diagram
window data entry feature of EES. Include the effects of the
turbine and pump efficiencies to evaluate the irreversibilities
associated with each of the processes. Plot the cycle on a Ts
diagram with respect to the saturation lines. Discuss the
results of your parametric studies. chamber, and the exergy destructions and the secondlaw
(exergetic) efficiencies for (c) the flash chamber, (d) the turbine, and (e) the entire plant. Answers: (a) 10.8 MW, 0.053, 10–59 Determine the exergy destruction associated with the
heat addition process and the expansion process in Prob.
10–34. Assume a source temperature of 1600 K and a sink
temperature of 285 K. Also, determine the exergy of the
100 kPa. Answers: 1289
steam at the boiler exit. Take P0 10–63C How is the utilization factor Pu for cogeneration
plants defined? Could Pu be unity for a cogeneration plant
that does not produce any power? (b) 17.3 MW, (c) 5.1 MW, 0.898, (d) 10.9 MW, 0.500,
(e) 39.0 MW, 0.218 Cogeneration kJ/kg, 247.9 kJ/kg, 1495 kJ/kg 10–64C Consider a cogeneration plant for which the utilization factor is 1. Is the irreversibility associated with this
cycle necessarily zero? Explain. 10–60 Determine the exergy destruction associated with the
regenerative cycle described in Prob. 10–44. Assume a source
temperature of 1500 K and a sink temperature of 290 K. 10–65C 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? Answer: 1155 kJ/kg 10–66C What is the difference between cogeneration and
regeneration? 10–61 Determine the exergy destruction associated with the
reheating and regeneration processes described in Prob.
10–49. Assume a source temperature of 1800 K and a sink
temperature of 290 K.
10–62 The schematic of a singleflash geothermal power
plant with state numbers is given in Fig. P10–62. Geothermal
resource exists as saturated liquid at 230°C. The geothermal
liquid is withdrawn from the production well at a rate of 230
kg/s and is flashed to a pressure of 500 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 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 10–67 Steam enters the turbine of a cogeneration plant at
7 MPa and 500°C. Onefourth of the steam is extracted from
the turbine at 600kPa pressure for process heating. The
remaining steam continues to expand to 10 kPa. The
extracted steam is then condensed and mixed with feedwater
at constant pressure and the mixture is pumped to the boiler
pressure of 7 MPa. The mass flow rate of steam through the
boiler is 30 kg/s. Disregarding any pressure drops and heat
losses in the piping, and assuming the turbine and the pump
to be isentropic, determine the net power produced and the
utilization factor of the plant.
6 Boiler Turbine ·
Q process 3 7
Steam
turbine 8
Process
heater Separator
4 5 Condenser 3 2
1
Flash
chamber Condenser 6 P II
4 2 PI 5 FIGURE P10–67
1
Production
well Reinjection
well FIGURE P10–62 10–68E A large foodprocessing plant requires 2 lbm/s of
saturated or slightly superheated steam at 80 psia, which is
extracted from the turbine of a cogeneration plant. The boiler
generates steam at 1000 psia and 1000°F at a rate of 5 lbm/s, cen84959_ch10.qxd 4/19/05 2:17 PM Page 597 Chapter 10
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 86 percent, determine (a) the
rate of heat transfer to the boiler and (b) the power output of
the cogeneration plant. Answers: (a) 6667 Btu/s, (b) 2026 kW
10–69 Steam is generated in the boiler of a cogeneration
plant at 10 MPa and 450°C at a steady rate of 5 kg/s. In
normal operation, steam expands in a turbine to a pressure of
0.5 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 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.
10–70 Consider a cogeneration power plant modified with
regeneration. Steam enters the turbine at 6 MPa and 450°C
and expands to a pressure of 0.4 MPa. At this pressure, 60
percent of the steam is extracted from the turbine, and the
remainder expands to 10 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 0.4 MPa. It
is subsequently mixed with the feedwater leaving the feedwater heater, and the mixture is pumped to the boiler pressure.
6  Assuming the turbines and the pumps to be isentropic, show
the cycle on a Ts diagram with respect to saturation lines,
and determine the mass flow rate of steam through the boiler
for a net power output of 15 MW. Answer: 17.7 kg/s
10–71 Reconsider Prob. 10–70. Using EES (or other)
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. 10–72E Steam is generated in the boiler of a cogeneration
plant at 600 psia and 800°F at a rate of 18 lbm/s. The plant is
to produce power while meeting the process steam requirements for a certain industrial application. Onethird 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°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.
10–73 A cogeneration plant is to generate power and 8600
kJ/s of process heat. Consider an ideal cogeneration steam
plant. Steam enters the turbine from the boiler at 7 MPa and
500°C. Onefourth of the steam is extracted from the turbine
at 600kPa pressure for process heating. The remainder of the
steam continues to expand and exhausts to the condenser at
10 kPa. The steam extracted for the process heater is condensed in the heater and mixed with the feedwater at 600
kPa. The mixture is pumped to the boiler pressure of 7 MPa.
Show the cycle on a Ts 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. 6 Turbine
Boiler
7 Turbine Boiler
Process
heater
5 Condenser FWH
4 Process
heater 8 PI 8 7 5 9 Condenser 3 3
4 2
1 2 1 P II
PI PI FIGURE P10–70 597 FIGURE P10–73 cen84959_ch10.qxd 4/19/05 2:17 PM Page 598 598  Thermodynamics Combined Gas–Vapor Power Cycles
10–74C In combined gas–steam cycles, what is the energy
source for the steam?
10–75C Why is the combined gas–steam cycle more efficient than either of the cycles operated alone?
10–76 The gasturbine portion of a combined gas–steam
power plant has a pressure ratio of 16. Air enters the compressor at 300 K at a rate of 14 kg/s and is heated to 1500 K
in the combustion chamber. The combustion gases leaving
the gas turbine are used to heat the steam to 400°C at 10
MPa in a heat exchanger. The combustion gases leave the
heat exchanger at 420 K. The steam leaving the turbine is
condensed at 15 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. Answers: reheat Rankine cycle between the pressure limits of 6 MPa
and 10 kPa. Steam is heated in a heat exchanger at a rate of
1.15 kg/s by the exhaust gases leaving the gas turbine and the
exhaust gases leave the heat exchanger at 200°C. Steam
leaves the highpressure turbine at 1.0 MPa and is reheated to
400°C in the heat exchanger before it expands in the lowpressure turbine. Assuming 80 percent isentropic efficiency
for all pumps and turbine, determine (a) the moisture content
at the exit of the lowpressure turbine, (b) the steam temperature at the inlet of the highpressure turbine, (c) the net power
output and the thermal efficiency of the combined plant.
Combustion
chamber
9 8 Gas
turbine Compressor (a) 1.275 kg/s, (b) 7819 kW, (c) 66.4 percent 10–77 Consider a combined gas–steam power plant
that has a net power output of 450 MW. The
pressure ratio of the gasturbine cycle is 14. Air enters the
compressor at 300 K and the turbine at 1400 K. The combustion gases leaving the gas turbine are used to heat the steam
at 8 MPa to 400°C in a heat exchanger. The combustion
gases leave the heat exchanger at 460 K. An open feedwater
heater incorporated with the steam cycle operates at a pressure of 0.6 MPa. The condenser pressure is 20 kPa. Assuming
all the compression and expansion processes to be isentropic,
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.
Reconsider Prob. 10–77. Using EES (or other)
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. 7 10 11
Heat
exchanger 3
Steam
turbine
4
6 5 2 Condenser 10–78 10–79 Repeat Prob. 10–77 assuming isentropic efficiencies
of 100 percent for the pump, 82 percent for the compressor,
and 86 percent for the gas and steam turbines.
10–80 Reconsider Prob. 10–79. Using EES (or other)
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. 10–81 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°C at a rate of 10
kg/s and the gas turbine at 950°C. The bottoming cycle is a Pump
1 FIGURE P10–81
Special Topic: Binary Vapor Cycles
10–82C What is a binary power cycle? What is its purpose?
10–83C 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.
10–84C Why is steam not an ideal working fluid for vapor
power cycles?
10–85C Why is mercury a suitable working fluid for the
topping portion of a binary vapor cycle but not for the bottoming cycle?
10–86C What is the difference between the binary vapor
power cycle and the combined gas–steam power cycle? cen84959_ch10.qxd 4/19/05 2:17 PM Page 599 Chapter 10
Review Problems
10–87 Show that the thermal efficiency of a combined
gas–steam power plant hcc can be expressed as
hcc hg hs hghs hcc hg hs 599 rejection from the working fluid to the air in the condenser,
(c) the mass flow rate of the geothermal water at the preheater, and (d ) the thermal efficiency of the Level I cycle of
this geothermal power plant. Answers: (a) 267.4°F, (b) 29.7
MBtu/h, (c) 187,120 lbm/h, (d ) 10.8 percent Wg /Qin and hs
Ws /Qg,out are the thermal effiwhere hg
ciencies of the gas and steam cycles, respectively. Using this
relation, determine the thermal efficiency of a combined
power cycle that consists of a topping gasturbine cycle with
an efficiency of 40 percent and a bottoming steamturbine
cycle with an efficiency of 30 percent.
10–88 It can be shown that the thermal efficiency of a combined gas–steam power plant hcc can be expressed in terms of
the thermal efficiencies of the gas and the steamturbine
cycles as  Vapor
Condenser
9 8
Air 4 Generator 5
Fluid pump Turbine hghs
3 Prove that the value of hcc is greater than either of hg or hs.
That is, the combined cycle is more efficient than either of
the gasturbine or steamturbine cycles alone.
10–89 Consider a steam power plant operating on the ideal
Rankine cycle with reheat between the pressure limits of 25
MPa and 10 kPa with a maximum cycle temperature of
600°C and a moisture content of 8 percent at the turbine exit.
For a reheat temperature of 600°C, determine the reheat pressures of the cycle for the cases of (a) single and (b) double
reheat.
10–90E The Stillwater geothermal power plant in Nevada,
which started full commercial operation in 1986, is designed
to operate with seven identical units. Each of these seven
units consists of a pair of power cycles, labeled Level I and
Level II, operating on the simple Rankine cycle using an
organic fluid as the working fluid.
The heat source for the plant is geothermal water (brine)
entering the vaporizer (boiler) of Level I of each unit at
325°F at a rate of 384,286 lbm/h and delivering 22.79
MBtu/h (“M” stands for “million”). The organic fluid that
enters the vaporizer at 202.2°F at a rate of 157,895 lbm/h
leaves it at 282.4°F and 225.8 psia as saturated vapor. This
saturated vapor expands in the turbine to 95.8°F and 19.0
psia and produces 1271 kW of electric power. About 200 kW
of this power is used by the pumps, the auxiliaries, and the
six fans of the condenser. Subsequently, the organic working
fluid is condensed in an aircooled condenser by air that
enters the condenser at 55°F at a rate of 4,195,100 lbm/h and
leaves at 84.5°F. The working fluid is pumped and then preheated in a preheater to 202.2°F by absorbing 11.14 MBtu/h
of heat from the geothermal water (coming from the vaporizer of Level II) entering the preheater at 211.8°F and leaving
at 154.0°F.
Taking the average specific heat of the geothermal water to
be 1.03 Btu/lbm · °F, determine (a) the exit temperature of
the geothermal water from the vaporizer, (b) the rate of heat 6 Preheater
mgeo Vaporizer
Vapor
Electricity
7
Working fluid
1
Land surface 2
Injection
pump Production pump Cooler geothermal brine
Hot geothermal brine FIGURE P10–90E
Schematic of a binary geothermal power plant.
Courtesy of ORMAT Energy Systems, Inc. 10–91 Steam enters the turbine of a steam power plant that
operates on a simple ideal Rankine cycle at a pressure of 6
MPa, and it leaves as a saturated vapor at 7.5 kPa. Heat is
transferred to the steam in the boiler at a rate of 40,000 kJ/s.
Steam is cooled in the condenser by the cooling water from a
nearby river, which enters the condenser at 15°C. Show the
cycle on a Ts 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.
10–92 A steam power plant operates on an ideal Rankine
cycle with two stages of reheat and has a net power output of cen84959_ch10.qxd 4/19/05 2:17 PM Page 600 600  Thermodynamics 120 MW. Steam enters all three stages of the turbine at
500°C. The maximum pressure in the cycle is 15 MPa, and
the minimum pressure is 5 kPa. Steam is reheated at 5 MPa
the first time and at 1 MPa the second time. Show the
cycle on a Ts diagram with respect to saturation lines, and
determine (a) the thermal efficiency of the cycle and (b) the
mass flow rate of the steam. Answers: (a) 45.5 percent,
(b) 64.4 kg/s 10–93 Consider a steam power plant that operates on a
regenerative Rankine cycle and has a net power output of 150
MW. Steam enters the turbine at 10 MPa and 500°C and the
condenser at 10 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 Ts 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 K and a sink
temperature of 303 K. 10–96 Repeat Prob. 10–95 assuming an isentropic efficiency of 84 percent for the turbines and 100 percent for the
pumps.
10–97 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
highpressure turbine at 15 MPa and 600°C and the lowpressure turbine at 1 MPa and 500°C. The condenser pressure
is 5 kPa. Steam is extracted from the turbine at 0.6 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 Ts 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 kg/s through the
boiler.
8 5
Boiler HighP
Turbine Reheater LowP
Turbine Turbine Boiler 9
y 7 Open
FWH 4 1–y–z 10 1– y 6 11
3 Condenser P II y z Open
FWH 12 Condenser 13 5
Closed
FWH 4 3 2 2
PI Pump II
1 FIGURE P10–93 1 6
7 Pump I FIGURE P10–97
10–94 Repeat Prob. 10–93 assuming both the pump and the
turbine are isentropic.
10–95 Consider an ideal reheat–regenerative Rankine cycle
with one open feedwater heater. The boiler pressure is 10
MPa, the condenser pressure is 15 kPa, the reheater pressure
is 1 MPa, and the feedwater pressure is 0.6 MPa. Steam
enters both the high and lowpressure turbines at 500°C.
Show the cycle on a Ts diagram with respect to saturation
lines, and determine (a) the fraction of steam extracted for
regeneration and (b) the thermal efficiency of the cycle.
Answers: (a) 0.144, (b) 42.1 percent 10–98 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 highpressure turbine
at 8 MPa and 500°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°C and expanded in the lowpressure turbine
to the condenser pressure of 15 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 com cen84959_ch10.qxd 4/19/05 2:17 PM Page 601 Chapter 10
pressed liquid at 120°C. The mixture is then pumped to the
boiler pressure. Assuming the turbine to be isentropic, show
the cycle on a Ts 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. 6
3 MW
LowP
Turbine HighP
Turbine Boiler
7 8
9 Process
heater 7 MW 5
Condenser 3 601 10–102 Steam is to be supplied from a boiler to a highpressure turbine whose isentropic efficiency is 75 percent
at conditions to be determined. The steam is to leave the
highpressure turbine as a saturated vapor at 1.4 MPa, and the
turbine is to produce 1 MW of power. Steam at the turbine
exit is extracted at a rate of 1000 kg/min and routed to a
process heater while the rest of the steam is supplied to a
lowpressure turbine whose isentropic efficiency is 60 percent. The lowpressure turbine allows the steam to expand to
10 kPa pressure and produces 0.8 MW of power. Determine
the temperature, pressure, and the flow rate of steam at the
inlet of the highpressure turbine.
10–103 A textile plant requires 4 kg/s of saturated steam at
2 MPa, which is extracted from the turbine of a cogeneration
plant. Steam enters the turbine at 8 MPa and 500°C at a rate
of 11 kg/s and leaves at 20 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. Answers: (a) 8.56 MW,
(b) 8.60 MW, (c) 53.8 percent P II 6 1 4  2 PI FIGURE P10–98 Turbine
Boiler 10–99 The gasturbine cycle of a combined gas–steam
power plant has a pressure ratio of 8. Air enters the compressor at 290 K and the turbine at 1400 K. The combustion
gases leaving the gas turbine are used to heat the steam at 15
MPa to 450°C in a heat exchanger. The combustion gases
leave the heat exchanger at 247°C. Steam expands in a highpressure turbine to a pressure of 3 MPa and is reheated in the
combustion chamber to 500°C before it expands in a lowpressure turbine to 10 kPa. The mass flow rate of steam is 30
kg/s. Assuming all the compression and expansion processes
to be isentropic, determine (a) the mass flow rate of air in the
gasturbine cycle, (b) the rate of total heat input, and (c) the
thermal efficiency of the combined cycle.
Answers: (a) 263 kg/s, (b) 2.80 105 kJ/s, (c) 55.6 percent 10–100 Repeat Prob. 10–99 assuming isentropic efficiencies of 100 percent for the pump, 80 percent for the compressor, and 85 percent for the gas and steam turbines.
10–101 Starting with Eq. 10–20, show that the exergy
destruction associated with a simple ideal Rankine cycle can
be expressed as i
qin(hth,Carnot
hth), where hth is efficiency of the Rankine cycle and hth,Carnot is the efficiency of
the Carnot cycle operating between the same temperature
limits. 7 8 Process
heater 5 Condenser 3
P II
4 2 PI
1 FIGURE P10–103
10–104 Using EES (or other) 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 5 MPa and 500°C
while the condenser pressure is varied from 5 to 100 kPa.
Determine the thermal efficiency of the cycle and plot it
against the condenser pressure, and discuss the results. 10–105 Using EES (or other) software, investigate the
effect of the boiler pressure on the performance of a simple ideal Rankine cycle. Steam enters the turbine at 500°C and exits at 10 kPa. The boiler pressure is cen84959_ch10.qxd 4/19/05 2:17 PM Page 602 602  Thermodynamics 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.
10–106 Using EES (or other) 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 kPa. The turbine inlet temperature is
varied from 250 to 1100°C. Determine the thermal efficiency
of the cycle and plot it against the turbine inlet temperature,
and discuss the results. 10–107 Using EES (or other) 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 MPa and 10 kPa, respectively, and
steam enters both stages of the turbine at 500°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. 10–108 Using EES (or other) software, investigate the
effect of number of reheat stages on the performance of an ideal Rankine cycle. The maximum and minimum pressures in the cycle are 15 MPa and 10 kPa,
respectively, and steam enters all stages of the turbine at
500°C. For each case, maintain roughly the same pressure
ratio across each turbine stage. Determine the thermal efficiency of the cycle and plot it against the number of reheat
stages 1, 2, 4, and 8, and discuss the results. 10–109 Using EES (or other) software, investigate the
effect of extraction pressure on the performance of an ideal regenerative Rankine cycle with one open
feedwater heater. Steam enters the turbine at 15 MPa and
600°C and the condenser at 10 kPa. Determine the thermal
efficiency of the cycle, and plot it against extraction pressures
of 12.5, 10, 7, 5, 2, 1, 0.5, 0.1, and 0.05 MPa, and discuss the
results. 10–110 Using EES (or other) software, investigate the
effect of the number of regeneration stages on
the performance of an ideal regenerative Rankine cycle.
Steam enters the turbine at 15 MPa and 600°C and the condenser at 5 kPa. For each case, maintain about the same temperature difference between any two regeneration stages.
Determine the thermal efficiency of the cycle, and plot it
against the number of regeneration stages for 1, 2, 3, 4, 5, 6,
8, and 10 regeneration stages. Fundamentals of Engineering (FE) Exam Problems
10–111 Consider a steadyflow Carnot cycle with water as
the working fluid executed under the saturation dome
between the pressure limits of 8 MPa and 20 kPa. Water
changes from saturated liquid to saturated vapor during the
heat addition process. The net work output of this cycle is
(a) 494 kJ/kg
(d ) 845 kJ/kg (b) 975 kJ/kg
(e) 1148 kJ/kg (c) 596 kJ/kg 10–112 A simple ideal Rankine cycle operates between the
pressure limits of 10 kPa and 3 MPa, with a turbine inlet
temperature of 600°C. Disregarding the pump work, the cycle
efficiency is
(a) 24 percent
(d ) 63 percent (b) 37 percent
(e) 71 percent (c) 52 percent 10–113 A simple ideal Rankine cycle operates between the
pressure limits of 10 kPa and 5 MPa, with a turbine inlet
temperature of 600°C. The mass fraction of steam that condenses at the turbine exit is
(a) 6 percent
(d ) 15 percent (b) 9 percent
(e) 18 percent (c) 12 percent 10–114 A steam power plant operates on the simple ideal
Rankine cycle between the pressure limits of 10 kPa and 10
MPa, with a turbine inlet temperature of 600°C. The rate of
heat transfer in the boiler is 800 kJ/s. Disregarding the pump
work, the power output of this plant is
(a) 243 kW
(d ) 335 kW (b) 284 kW
(e) 800 kW (c) 508 kW 10–115 Consider a combined gassteam power plant. Water
for the steam cycle is heated in a wellinsulated heat
exchanger by the exhaust gases that enter at 800 K at a rate
of 60 kg/s and leave at 400 K. Water enters the heat
exchanger at 200°C and 8 MPa and leaves at 350°C and 8
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 kg/s
(d ) 53 kg/s (b) 24 kg/s
(e) 60 kg/s (c) 46 kg/s 10–116 An ideal reheat Rankine cycle operates between the
pressure limits of 10 kPa and 8 MPa, with reheat occurring at
4 MPa. The temperature of steam at the inlets of both turbines is 500°C, and the enthalpy of steam is 3185 kJ/kg at the
exit of the highpressure turbine, and 2247 kJ/kg at the exit
of the lowpressure turbine. Disregarding the pump work, the
cycle efficiency is
(a) 29 percent
(d ) 41 percent (b) 32 percent
(e) 49 percent (c) 36 percent 10–117 Pressurized feedwater in a steam power plant is to
be heated in an ideal open feedwater heater that operates at a
pressure of 0.5 MPa with steam extracted from the turbine. If
the enthalpy of feedwater is 252 kJ/kg and the enthalpy of
extracted steam is 2665 kJ/kg, the mass fraction of steam
extracted from the turbine is
(a) 4 percent
(d ) 27 percent (b) 10 percent
(e) 12 percent (c) 16 percent 10–118 Consider a steam power plant that operates on the
regenerative Rankine cycle with one open feedwater heater.
The enthalpy of the steam is 3374 kJ/kg at the turbine inlet,
2797 kJ/kg at the location of bleeding, and 2346 kJ/kg at the cen84959_ch10.qxd 4/28/05 10:24 AM Page 603 Chapter 10  603 turbine exit. The net power output of the plant is 120 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 is cooled and condensed by the cooling water from a
nearby river, which enters the adiabatic condenser at a rate of
463 kg/s. (a) 117 kg/s
(d ) 268 kg/s (a) 17.0 MW
(d ) 20.0 MW (b) 126 kg/s
(e) 679 kg/s (c) 219 kg/s 10–119 Consider a simple ideal Rankine cycle. If the condenser pressure is lowered while keeping 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.
10–120 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.
10–121 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.
10–122 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.
10–123 Consider a cogeneration power plant modified with
regeneration. Steam enters the turbine at 6 MPa and 450°C at
a rate of 20 kg/s and expands to a pressure of 0.4 MPa. At
this pressure, 60 percent of the steam is extracted from the
turbine, and the remainder expands to a pressure of 10 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 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 1. The total power output of the turbine is
(b) 8.4 MW
(e) 3.4 MW (c) 12.2 MW 2. The temperature rise of the cooling water from the river in
the condenser is
(a) 8.0°C
(d ) 12.9°C (b) 5.2°C
(e) 16.2°C (c) 9.6°C 3. The mass flow rate of steam through the process heater is
(a) 1.6 kg/s
(d ) 7.6 kg/s (b) 3.8 kg/s
(e) 10.4 kg/s (c) 5.2 kg/s 4. The rate of heat supply from the process heater per unit
mass of steam passing through it is
(a) 246 kJ/kg
(d ) 1891 kJ/kg (b) 893 kJ/kg
(e) 2060 kJ/kg (c) 1344 kJ/kg 5. The rate of heat transfer to the steam in the boiler is
(a) 26.0 MJ/s
(d ) 62.8 MJ/s (b) 53.8 MJ/s
(e) 125.4 MJ/s
h6 (c) 39.5 MJ/s 3302.9 kJ/kg 6 h7 Boiler h8 h10 20 kg/s 8 7
h11
11 10 Process
heater
5
h5 Turbine 2665.6 kJ/kg 2128.8 9
610.73
Condenser
Condenser
P II
4
h3 3
h4 h9 ∆T FWH
2 463 kg/s
PI 604.66
h2 1
h1 191.81 192.20 FIGURE P10–123 Design and Essay Problems
10–124 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 cen84959_ch10.qxd 4/19/05 2:17 PM Page 604 604  Thermodynamics 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 Ts diagrams with labeled states and
temperature, pressure, enthalpy, and entropy information
for your design.
(c) Sample calculations.
10–125 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.
10–126 Several geothermal power plants are in operation in
the United States and more are being built since the heat
source of a geothermal plant is hot geothermal water, which
is “free energy.” An 8MW geothermal power plant is being
considered at a location where geothermal water at 160°C is
available. Geothermal water is to serve as the heat source for
a closed Rankine power cycle with refrigerant134a as the
working fluid. Specify suitable temperatures and pressures
for the cycle, and determine the thermal efficiency of the
cycle. Justify your selections.
10–127 A 10MW geothermal power plant is being considered at a site where geothermal water at 230°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 kPa and 8 kPa, respectively. Highpressure flash chambers yield a small amount of
steam with high exergy whereas lowerpressure flash chambers yield considerably more steam but at a lower exergy. By
trying several pressures, determine the optimum pressure of Turbine Flash
chamber 230°C
Geothermal
water FIGURE P10–127 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.
10–128 A natural gas–fired furnace in a textile plant is used
to provide steam at 130°C. At times of high demand, the furnace supplies heat to the steam at a rate of 30 MJ/s. The plant
also uses up to 6 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 processheat 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.
10–129E A photographic equipment manufacturer uses a
flow of 64,500 lbm/h of steam in its manufacturing process.
Presently the spent steam at 3.8 psig and 224°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 h/yr and its value
is $0.05/kWh. If the energy is used for space heating, the
value is also $0.05/kWh, but it can only be used about 3000
h/yr (only during the “heating season”). If the steam is condensed and the liquid H2O is recycled through the process, its
value is $0.50/100 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).
10–130 Design the condenser of a steam power plant that
has a thermal efficiency of 40 percent and generates 10 MW
of net electric power. Steam enters the condenser as saturated
vapor at 10 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°C,
and the velocity of the cooling water in the pipes is limited to
6 m/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 W/m2. Specify the
pipe diameter, total pipe length, and the arrangement of the
pipes to minimize the condenser volume.
10–131 Watercooled steam condensers are commonly used
in steam power plants. Obtain information about watercooled
steam condensers by doing a literature search on the topic and cen84959_ch10.qxd 4/19/05 2:17 PM Page 605 Chapter 10
also by contacting some condenser manufacturers. In a report,
describe the various types, the way they are designed, the limitation on each type, and the selection criteria.
10–132 Steam boilers have long been used to provide
process heat as well as to generate power. Write an
essay on the history of steam boilers and the evolution of
modern supercritical steam power plants. What was the role
of the American Society of Mechanical Engineers in this
development?
10–133 The technology for power generation using geothermal energy is well established, and numerous geothermal
power plants throughout the world are currently generating
electricity economically. Binary geothermal plants utilize a
volatile secondary fluid such as isobutane, npentane, and
R114 in a closed loop. Consider a binary geothermal plant  605 with R114 as the working fluid that is flowing at a rate of 600
kg/s. The R114 is vaporized in a boiler at 115°C by the geothermal fluid that enters at 165°C, and is condensed at 30°C
outside the tubes by cooling water that enters the tubes at
18°C. Based on prior experience, the average heat flux based
on the outer surface of the tubes can be taken to be 4600
W/m2. The enthalpy of vaporization of R114 at 30°C is hfg
121.5 kJ/kg.
Specify (a) the length, diameter, and number of tubes and
their arrangement in the condenser to minimize overall volume of the condenser; (b) the mass flow rate of cooling
water; and (c) the flow rate of makeup water needed if a
cooling tower is used to reject the waste heat from the cooling water. The liquid velocity is to remain under 6 m/s and
the length of the tubes is limited to 8 m. cen84959_ch10.qxd 4/19/05 2:17 PM Page 606 ...
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This note was uploaded on 03/07/2011 for the course MATH 1350 taught by Professor Cho during the Spring '08 term at Texas Tech.
 Spring '08
 CHO
 Calculus

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