Moran M.J., Shapiro H.N. Fundamentals of Engineering Thermodynamics

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For the first pump

5 11 2 y¿ 2 y–21h

2 h

0.7537

174.17 2 173.88

5 0.22 kJ

and for the second pump

5 1h

2 h

5 569.73 2 561.47 5 8.26 kJ

The total heat added is the sum of the energy added by heat transfer during boiling/superheating and reheat-

ing. When expressed on the basis of a unit of mass entering the first turbine, this is

5 1h

2 h

21 11 2 y¿21h

2 h

3348.4 2 882.4

0.8478

3353.3 2 2741.8

5 2984.4 kJ

With the foregoing values, the thermal efficiency is

h 5

1 W

2 W

572.9 1 720.7 2 0.22 2 8.26

2984.4

5 0.431 143.1%2

(b) The mass flow rate entering the first turbine can be determined using the

given value of the net power output. Thus

cycle

1 W

2 W

1100 MW2

3600 s

1285.1 kJ

5 2.8 3 10

➊ Compared to the corresponding values determined for the simple Rankine

cycle of Example 8.1, the thermal efficiency of the present regenerative

cycle is substantially greater and the mass flow rate is considerably less.

If each turbine stage had an isentropic efficiency of 85%, at

which numbered states would the specific enthalpy values change? Ans. 2,

3, 5, and 6.

Ability to…

❑

sketch the T–s diagram of

the reheat–regenerative

vapor power cycle with one

closed and one open

feedwater heater.

❑

fix each of the principal

states and retrieve

necessary property data.

❑

apply mass, energy, and

entropy principles.

❑

calculate performance

parameters for the cycle.

✓

Skills Developed

8.5 Other Vapor Power Cycle Aspects

In this section we consider vapor power cycle aspects related to working fluids, cogen-

eration systems, and carbon capture and storage.

8.5.1

Working Fluids

Demineralized water is used as the working fluid in the vast majority of vapor power

systems because it is plentiful, low cost, nontoxic, chemically stable, and relatively

8.5 Other Vapor Power Cycle Aspects 463

➊

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464 Chapter 8

Vapor Power Systems

noncorrosive. Water also has a large change in specific enthalpy as it vaporizes at

typical steam generator pressures, which tends to limit the mass flow rate for a desired

power output. With water, the pumping power is characteristically low, and the tech-

niques of superheat, reheat, and regeneration are effective for improving power plant

performance.

The high critical pressure of water (22.1 MPa, 3204 lbf/in.

) has posed a challenge

to engineers seeking to improve thermal efficiency by increasing steam generator

pressure and thus average temperature of heat addition. See the discussion of super-

critical cycles in Sec. 8.3.

Although water has some shortcomings as a working fluid, no other single sub-

stance is more satisfactory for large electrical generating plants. Still, vapor cycles

intended for special applications employ working fluids more in tune with the appli-

cation at hand than water.

Organic Rankine cycles employ organic substances as working fluids, including pen-

tane, mixtures of hydrocarbons, commonly used refrigerants, ammonia, and silicon oil.

The organic working fluid is typically selected to meet the requirements of the par-

ticular application. For instance, the relatively low boiling point of these substances

allows the Rankine cycle to produce power from low-temperature sources, including

industrial waste heat, geothermal hot water, and fluids heated by concentrating-solar

collectors.

A binary vapor cycle couples two vapor cycles so the energy discharged by heat

transfer from one cycle is the input for the other. Different working fluids are used

in these cycles, one having advantageous high-temperature characteristics and another

with complementary characteristics at the low-temperature end of the overall operat-

ing range. Depending on the application, these working fluids might include water

and organic substances. The result is a combined cycle having a high average tem-

perature of heat addition and a low average temperature of heat rejection, and thus

a thermal efficiency greater than either cycle has individually.

Figure 8.13 shows the schematic and accompanying T–s diagram of a binary vapor

cycle. In this arrangement, two ideal Rankine cycles are combined using an intercon-

necting heat exchanger that serves as the condenser for the higher-temperature cycle

(topping cycle) and boiler for the lower-temperature cycle (bottoming cycle). Heat

rejected from the topping cycle provides the heat input for the bottoming cycle.

organic cycle

binary cycle

Topping cycle condenser,

bottoming cycle boiler

Topping cycle

boiler

Bottoming cycle superheater

Liquid

Condenser

Vapor

Bottoming cycle:

a–b–c–d–e

Topping cycle:

1–2–3–4–1

Pump Pump

Turbine

Fig. 8.13 Binary vapor cycle.

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8.5.2

Cogeneration

Our society can use fuel more effectively through greater use of cogeneration systems,

also known as combined heat and power systems. Cogeneration systems are inte-

grated systems that simultaneously yield two valuable products, electricity and steam

(or hot water), from a single fuel input. Cogeneration systems typically provide cost

savings relative to producing power and steam (or hot water) in separate systems.

Costing of cogeneration systems is introduced in Sec. 7.7.3.

Cogeneration systems are widely deployed in industrial plants, refineries, paper

mills, food processing plants, and other facilities requiring process steam, hot water,

and electricity for machines, lighting, and other purposes.

District heating is another

important cogeneration application. District heating plants are located within com-

munities to provide steam or hot water for space heating and other thermal needs

together with electricity for domestic, commercial, and industrial use. For instance, in

New York City, district heating plants provide heating to Manhattan buildings while

also generating electricity for various uses.

Cogeneration systems can be based on vapor power plants, gas turbine power plants,

reciprocating internal combustion engines, and fuel cells. In this section, we consider

vapor power–based cogeneration and, for simplicity, only district heating plants. The

particular district heating systems considered have been selected because they are well

suited for introducing the subject. Gas turbine–based cogeneration is considered in

Sec. 9.9.2. The possibility of fuel cell–based cogeneration is considered in Sec. 13.4.

BACK-PRESSURE PLANTS. A back-pressure district heating plant is shown in

Fig. 8.14a. The plant resembles the simple Rankine cycle plant considered in Sec. 8.2

but with an important difference: In this case, energy released when the cycle work-

ing fluid condenses during flow through the condenser is harnessed to produce steam

for export to the nearby community for various uses. The steam comes at the expense

of the potential for power, however.

The power generated by the plant is linked to the district heating need for steam

and is determined by the pressure at which the cycle working fluid condenses, called

the back pressure. For instance, if steam as saturated vapor at 1008C is needed by the

community, the cycle working fluid, assumed here to be demineralized water, must

condense at a temperature greater than 1008C and thus at a back pressure greater

than 1 atm. Accordingly, for fixed turbine inlet conditions and mass flow rate, the

power produced in district heating is necessarily less than when condensation occurs

well below 1 atm as it does in a plant fully dedicated to power generation.

EXTRACTION PLANTS. An extraction district heating plant is shown in Fig. 8.14b.

The figure is labeled (in parentheses) with fractions of the total flow entering the tur-

bine remaining at various locations; in this respect the plant resembles the regenerative

vapor power cycles considered in Sec. 8.4. Steam extracted from the turbine is used to

service the district heating need. Differing heating needs can be flexibly met by varying

the fraction of the steam extracted, denoted by y. For fixed turbine inlet conditions and

mass flow rate, an increase in the fraction y to meet a greater district heating need is

met by a reduction in power generated. When there is no demand for district heating,

the full amount of steam generated in the boiler expands through the turbine, produc-

ing greatest power under the specified conditions. The plant then resembles the simple

Rankine cycle of Sec. 8.2.

8.5.3

Carbon Capture and Storage

The concentration of carbon dioxide in the atmosphere has increased significantly

since preindustrial times. Some of the increase is traceable to burning fossil fuels.

Coal-fired vapor power plants are major sources. Evidence is mounting that excessive

8.5 Other Vapor Power Cycle Aspects 465

cogeneration

district heating

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466 Chapter 8

Vapor Power Systems

Steam

Condensate

(1)

(y)

)

Fuel

–

(b) Extraction plant.

To cooling tower

Condensate

Cooling tower

(1 – y)

Fig. 8.14 Vapor cycle district heating plants.

Turbine

Pump

Steam

Condensate

Fuel

Boiler

–

(a) Back-pressure plant.

in the atmosphere contributes to global climate change, and there is growing

agreement that measures must be taken to reduce such emissions.

Carbon dioxide emissions can be reduced by using fossil fuels more efficiently and

avoiding wasteful practices. Moreover, if utilities use fewer fossil-fueled plants and

more wind, hydropower, and solar plants, less carbon dioxide will come from this

sector. Practicing greater efficiency, eliminating wasteful practices, and using more

renewable energy are important pathways for controlling CO

. Yet these strategies

are insufficient.

Since fossil fuels will be plentiful for several decades, they will continue to be used

for generating electricity and meeting industrial needs. Accordingly, reducing CO

emissions at the plant level is imperative. One option is greater use of low-carbon

fuels—more natural gas and less coal, for example. Another option involves removal

of carbon dioxide from the exhaust gas of power plants, oil and gas refineries, and

other industrial sources followed by storage (sequestration) of captured CO

Figure 8.15 illustrates a type of carbon dioxide storage method actively under

consideration today. Captured CO

is injected into depleted oil and gas reservoirs,

unminable coal seams, deep salty aquifers, and other geological structures. Storage in

oceans by injecting CO

to great depths from offshore pumping stations is another

method under consideration.

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Deployment of CO

capture and storage technology faces major hurdles, including

uncertainty over how long injected gas will remain stored and possible collateral

environmental impact when so much gas is stored in nature. Another technical chal-

lenge is the development of effective means for separating CO

from voluminous

power plant and industrial gas streams.

Expenditures of energy resources and money required to capture CO

, transport

it to storage sites, and place it into storage will be significant. Yet with our current

knowledge, carbon capture and storage is the principal strategy available today for

reducing carbon dioxide emissions at the plant level. This area clearly is ripe for

innovation. For more, see the following Horizons.

Electric power

capture facility

Exhaust

gas

injection, typically at a distance

stored in salty aquifer

stored in unminable

coal seams

stored in depleted

oil and gas reservoirs

Power plant

Fossil fuel

Fig. 8.15 Carbon capture and storage: power plant application.

The race is on to find alternatives to storage of

carbon dioxide captured from power plant exhaust gas

streams and other sources. Analysts say there may be

no better alternative, but storage does not have to be the fate

of all of the captured CO

if there are commercial applications

for some of it.

One use of carbon dioxide is for enhanced oil recovery—namely,

to increase the amount of oil extractable from oil fields. By injecting

at high pressure into an oil-bearing underground layer, difficult-

to-extract oil is forced to the surface. Proponents contend that

widespread application of captured carbon dioxide for oil recovery

will provide a source of income instead of cost, which is the case

when the CO

is simply stored underground. Some envision a lively

commerce involving export of liquefied carbon dioxide by ship from

industrialized, oil-importing nations to oil-producing nations.

Another possible commercial use proposed for captured car-

bon dioxide is to produce algae, a tiny single-cell plant. When

supplied with carbon dioxide, algae held in bioreactors absorb the

carbon dioxide via photosynthesis, spurring algae growth. Carbon-

enriched algae can be processed into transportation fuels, provid-

ing substitutes for gasoline and a source of income.

Researchers are also working on other ways to turn captured

carbon dioxide into fuel. One approach attempts to mimic pro-

cesses occurring in living things, whereby carbon atoms,

extracted from carbon dioxide, and hydrogen atoms, extracted

from water, are combined to create hydrocarbon molecules.

Another approach uses solar radiation to split carbon dioxide

into carbon monoxide and oxygen, and split water into hydro-

gen and oxygen. These building blocks can be combined into

liquid fuels, researchers say.

Algae growth and fuel production using carbon dioxide are

each in early stages of development. Still, such concepts sug-

gest potential commercial uses for captured carbon dioxide and

inspire hope of others yet to be imagined.

What to Do About That CO

8.5 Other Vapor Power Cycle Aspects 467

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468 Chapter 8 Vapor Power Systems

8.6 Case Study: Exergy Accounting

of a Vapor Power Plant

The discussions to this point show that a useful picture of power plant performance

can be obtained with the conservation of mass and conservation of energy principles.

However, these principles provide only the quantities of energy transferred to and

from the plant and do not consider the utility of the different types of energy trans-

fer. For example, with the conservation principles alone, a unit of energy exiting as

generated electricity is regarded as equivalent to a unit of energy exiting in relatively

low-temperature cooling water, even though the electricity has greater utility and

economic value. Also, nothing can be learned with the conservation principles alone

about the relative significance of the irreversibilities present in the various plant com-

ponents and the losses associated with those components. The method of exergy anal-

ysis introduced in Chap. 7 allows issues such as these to be dealt with quantitatively.

Exergy Accounting

In this section we account for the exergy entering a power plant with the fuel. (Means

for evaluating the fuel exergy are introduced in Sec. 13.6.) A portion of the fuel

exergy is ultimately returned to the plant surroundings as the net work developed.

However, the largest part is either destroyed by irreversibilities within the various

plant components or carried from the plant by cooling water, stack gases, and unavoid-

able heat transfers with the surroundings. These considerations are illustrated in the

present section by three solved examples, treating respectively the boiler, turbine and

pump, and condenser of a simple vapor power plant.

The irreversibilities present in each power plant component exact a tariff on the

exergy supplied to the plant, as measured by the exergy destroyed in that component.

The component levying the greatest tariff is the boiler, for a significant portion of the

exergy entering the plant with the fuel is destroyed by irreversibilities within it. There

are two main sources of irreversibility in the boiler: (1) the irreversible heat transfer

occurring between the hot combustion gases and the working fluid of the vapor power

cycle flowing through the boiler tubes, and (2) the combustion process itself. To sim-

plify the present discussion, the boiler is considered to consist of a combustor unit in

which fuel and air are burned to produce hot combustion gases, followed by a heat

exchanger unit where the cycle working fluid is vaporized as the hot gases cool. This

idealization is illustrated in Fig. 8.16.

TAKE NOTE...

Chapter 7 is a prerequisite

for the study of this

section.

Fig. 8.16 Power plant

schematic for the exergy

analysis case study.

Hot combustion

products

Combustor

unit

Fuel

Air

Cycle working

fluid

Condenser

Cooling

water in

Cooling

water out

Pump

Net power out

Turbine

Heat exchanger unit

Exiting stack gases

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For purposes of illustration, let us assume that 30% of the exergy entering the com-

bustion unit with the fuel is destroyed by the combustion irreversibility and 1% of the

fuel exergy exits the heat exchanger unit with the stack gases. The corresponding values

for an actual power plant might differ from these nominal values. However, they provide

characteristic values for discussion. (Means for evaluating the combustion exergy destruc-

tion and the exergy accompanying the exiting stack gases are introduced in Chap. 13.)

Using the foregoing values for the combustion exergy destruction and stack gas loss,

it follows that a maximum of 69% of the fuel exergy remains for transfer from the hot

combustion gases to the cycle working fluid. It is from this portion of the fuel exergy

that the net work developed by the plant is obtained. In Examples 8.7 through 8.9, we

account for the exergy supplied by the hot combustion gases passing through the heat

exchanger unit. The principal results of this series of examples are reported in Table 8.4.

Carefully note that the values of Table 8.4 are keyed to the vapor power plant of Exam-

ple 8.2 and thus have only qualitative significance for vapor power plants in general.

Case Study Conclusions

The entries of Table 8.4 suggest some general observations about vapor power plant

performance. First, the table shows that the exergy destructions are more significant than

the plant losses. The largest portion of the exergy entering the plant with the fuel is

destroyed, with exergy destruction in the boiler overshadowing all others. By contrast,

the loss associated with heat transfer to the cooling water is relatively unimportant. The

cycle thermal efficiency (calculated in the solution to Example 8.2) is 31.4%, so over

two-thirds (68.6%) of the energy supplied to the cycle working fluid is subsequently

carried out by the condenser cooling water. By comparison, the amount of exergy carried

out is virtually negligible because the temperature of the cooling water is raised only a

few degrees over that of the surroundings and thus has limited utility. The loss amounts

to only 1% of the exergy entering the plant with the fuel. Similarly, losses accompanying

unavoidable heat transfer with the surroundings and the exiting stack gases typically

amount only to a few percent of the exergy entering the plant with the fuel and are

generally overstated when considered from the perspective of energy alone.

An exergy analysis allows the sites where destructions or losses occur to be identified

and rank ordered for significance. This knowledge is useful in directing attention to

aspects of plant performance that offer the greatest opportunities for improvement

through the application of practical engineering measures. However, the decision to adopt

Vapor Power Plant Exergy Accounting

Outputs

Net power out

30%

Losses

Condenser cooling water

Stack gases (assumed) 1%

Exergy destruction

Boiler

Combustion unit (assumed) 30%

Heat exchanger unit

30%

Turbine

Pump

—

Condenser

Total 100%

TABLE 8.4

All values are expressed as a percentage of

the exergy carried into the plant with the

fuel. Values are rounded to the nearest full

percent. Exergy losses associated with stray

heat transfer from plant components are

ignored.

Example 8.8

Example 8.9.

Example 8.7.

Example 8.8.

Example 8.9.

8.6 Case Study: Exergy Accounting of a Vapor Power Plant 469

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470 Chapter 8 Vapor Power Systems

any particular modification is governed by economic considerations that take into account

both economies in fuel use and the costs incurred to achieve those economies.

The calculations presented in the following examples illustrate the application of

exergy principles through the analysis of a simple vapor power plant. There are no

fundamental difficulties, however, in applying the methodology to actual power plants,

including consideration of the combustion process. The same procedures also can be

used for exergy accounting of the gas turbine power plants considered in Chap. 9 and

other types of thermal systems.

The following example illustrates the exergy analysis of the heat exchanger unit

of the boiler of the case study vapor power plant.

Vapor Cycle Exergy Analysis—Heat Exchanger Unit

c c c c EXAMPLE 8.7 c

The heat exchanger unit of the boiler of Example 8.2 has a stream of water entering as a liquid at 8.0 MPa and

exiting as a saturated vapor at 8.0 MPa. In a separate stream, gaseous products of combustion cool at a constant

pressure of 1 atm from 1107 to 5478C. The gaseous stream can be modeled as air as an ideal gas. Let T

5 228C,

5 1 atm. Determine (a) the net rate at which exergy is carried into the heat exchanger unit by the gas stream,

in MW, (b) the net rate at which exergy is carried from the heat exchanger by the water stream, in MW, (c) the

rate of exergy destruction, in MW, (d) the exergetic efficiency given by Eq. 7.27.

SOLUTION

Known:

A heat exchanger at steady state has a water stream entering and exiting at known states and a separate

gas stream entering and exiting at known states.

Find: Determine the net rate at which exergy is carried into the heat exchanger by the gas stream, in MW, the

net rate at which exergy is carried from the heat exchanger by the water stream, in MW, the rate of exergy

destruction, in MW, and the exergetic efficiency.

Schematic and Given Data:

Engineering Model:

The control volume shown in the accompanying figure

operates at steady state with Q

5 W

5 0.

2. Kinetic and potential energy effects can be ignored.

3. The gaseous combustion products are modeled as air

as an ideal gas.

4. The air and the water each pass through the steam

generator at constant pressure.

5. Only 69% of the exergy entering the plant with the

fuel remains after accounting for the stack loss and

combustion exergy destruction.

6. T

5 228C, p

5 1 atm.

Analysis: The analysis begins by evaluating the mass flow rate of the air in terms of the mass flow rate of the

water. The air and water pass through the boiler in separate streams. Hence, at steady state the conservation of

mass principle requires

5 m



1air2

5 m



water

Using these relations, an energy rate balance for the overall control volume reduces at steady state to

0 5 Q

2 W

1 m

2 h

21 m

2 h

1107°C,

1 atm

Air

547°C,

1 atm

Steam

saturated vapor,

8.0 MPa

Liquid,

8.0 MPa

Fig. E8.7

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where Q

5 W

5 0 by assumption 1, and the kinetic and potential energy terms are dropped by assumption 2.

In this equation m

and

denote, respectively, the mass flow rates of the air and water. On solving

2 h

The solution to Example 8.2 gives h

5 2758 kJ/kg and h

5 183.36 kJ/kg. From Table A-22, h

5 1491.44 kJ/kg

and h

5 843.98 kJ/kg. Hence

2758 2 18

3.36

1491.44 2 843.98

5 3.977

kg 1ai

kg 1steam2

From Example 8.2, m

5 4.449 3 10

h. Thus, m

5 17.694 3 10

(a) The net rate at which exergy is carried into the heat exchanger unit by the gaseous stream can be evaluated

using Eq. 7.18

net rate at which exergy

is carried in by the

gaseous stream

§5 m

2 e

5 m

2 h

2 T

2 s

Since the gas pressure remains constant, Eq. 6.20a giving the change in specific entropy of an ideal gas reduces

to s

2 s

5 s

82s

8. Thus, with h and s8 values from Table A-22

2 e

25 117.694 3 10

h2311491.44 2 843.982 kJ

kg 2 1295 K213.34474 2 2.745042 kJ

kg ? K4

8.326 3 10

3600 s

1 MW

`5 231.28 MW

(b) The net rate at which exergy is carried out of the boiler by the water stream is determined similarly

net rate at which exergy

is carried out by the

water stream

§5 m

2 e

5 m

2 h

2 T

2 s

From Table A-3, s

5 5.7432 kJ/kg ? K. Double interpolation in Table A-5 at 8.0 MPa and h

5 183.36 kJ/kg gives

5 0.5957 kJ/kg ? K. Substituting known values

2 e

25 14.449 3 10

2312758 2 183.3622 29515.7432 2 0.595724

➊

4.699 3 10

3600 s

1 MW

`5 130.53 MW

5 m

2 e

21 m

2 e

2➋

With the results of parts (a) and (b)

➌ E

5 231.28 MW 2 130.53 MW 5 100.75 MW

(d) The exergetic efficiency given by Eq. 7.27 is

e 5

2 e

130.53

231.28 MW

5 0.564 156.4%2

This calculation indicates that 43.6% of the exergy supplied to the heat exchanger unit by the cooling com-

bustion products is destroyed. However, since only 69% of the exergy entering the plant with the fuel is assumed

to remain after the stack loss and combustion exergy destruction are accounted for (assumption 5), it can be

concluded that 0.69 3 43.6% 5 30% of the exergy entering the plant with the fuel is destroyed within the heat

exchanger. This is the value listed in Table 8.4.

8.6 Case Study: Exergy Accounting of a Vapor Power Plant 471

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472 Chapter 8 Vapor Power Systems

In the next example, we determine the exergy destruction rates in the turbine and

pump of the case study vapor power plant.

➊ Since energy is conserved, the rate at which energy is transferred to the water as it flows through the heat

exchanger equals the rate at which energy is transferred from the gas passing through the heat exchanger.

By contrast, the rate at which exergy is transferred to the water is less than the rate at which exergy is trans-

ferred from the gas by the rate at which exergy is destroyed within the heat exchanger.

➋ The rate of exergy destruction can be determined alternatively by evaluating

the rate of entropy production, s

, from an entropy rate balance and mul-

tiplying by T

to obtain E

5 T

➌ Underlying the assumption that each stream passes through the heat

exchanger at constant pressure is the neglect of friction as an irreversibility.

Thus, the only contributor to exergy destruction in this case is heat transfer

from the higher-temperature combustion products to the vaporizing water.

If the gaseous products of combustion are cooled to 5178C (h

810.99 kJ/kg), what is the mass flow rate of the gaseous products, in

kg/h? Ans. 16.83 3 10

kg/h.

Vapor Cycle Exergy Analysis—Turbine and Pump

c c c c EXAMPLE 8.8 c

Reconsider the turbine and pump of Example 8.2. Determine for each of these components the rate at which

exergy is destroyed, in MW. Express each result, and the net power output of the plant, as a percentage of the

exergy entering the plant with the fuel. Let T

5 228C, p

=1 atm.

SOLUTION

Known:

A vapor power cycle operates with steam as the working fluid. The turbine and pump each have an

isentropic efficiency of 85%.

Find: For the turbine and the pump individually, determine the rate at which exergy is destroyed, in MW. Express

each result, and the net power output, as a percentage of the exergy entering the plant with the fuel.

Schematic and Given Data:

Condenser

0.008 MPa

8.0 MPa

Pump

Cooling

water

Saturated

vapor

8.0 MPa

Saturated

liquid at

0.008 MPa

Turbine

out

Boiler

2s 23

Fig. E8.8

Ability to…

❑

perform exergy analysis of a

power plant steam generator.

✓

Skills Developed

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