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

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the receiver. The heated molten salt or oil provides energy required to vaporize

water flowing in the other stream of the heat exchanger. This steam is provided to

the turbine.

c The geothermal power plant shown in Fig. 8.1d also uses an interconnecting heat

exchanger. In this case hot water and steam from deep below earth’s surface flows

on one side of the heat exchanger. A secondary working fluid having a lower boil-

ing point than the water, such as isobutane or another organic substance, vaporizes

on the other side of the heat exchanger. The secondary working fluid vapor is

provided to the turbine.

Referring again to Fig. 8.1a as representative, let’s consider the other subsystems,

beginning with system B. Regardless of the source of the energy required to vaporize

the working fluid and the type of working fluid, the vapor produced passes through

the turbine, where it expands to lower pressure, developing power. The turbine power

shaft is connected to an electric generator (subsystem C). The vapor exiting the tur-

bine passes through the condenser, where it condenses on the outside of tubes car-

rying cooling water.

The cooling water circuit comprises subsystem D. For the plant shown, cooling water

is sent to a cooling tower, where energy received from steam condensing in the con-

denser is rejected into the atmosphere. Cooling water then returns to the condenser.

Concern for the environment governs what is allowable in the interactions between

subsystem D and its surroundings. One of the major difficulties in finding a site for

a vapor power plant is access to sufficient quantities of condenser cooling water. To

reduce cooling-water needs, harm to aquatic life in the vicinity of the plant, and other

thermal pollution effects, large-scale power plants typically employ cooling towers

(see Energy & Environment, Sec. 2.6.2).

Fuel processing and handling are significant issues for both fossil-fueled and nuclear-

fueled plants because of human-health and environmental-impact considerations.

Fossil-fueled plants must observe increasingly stringent limits on smokestack emissions

and disposal of toxic solid waste. Nuclear-fueled plants are saddled with a significant

radioactive waste–disposal problem. Still, all four of the power plant configurations

considered in Fig. 8.1 have environmental, health, and land-use issues related to vari-

ous stages of their life cycles, including how they are manufactured, installed, operated,

and ultimately disposed.

Rankine cycle

8.2 The Rankine Cycle

Referring to subsystem B of Fig. 8.1a again, observe that each unit of mass of work-

ing fluid periodically undergoes a thermodynamic cycle as it circulates through the

series of interconnected components. This cycle is the Rankine cycle.

Important concepts introduced in previous chapters for thermodynamic power

cycles generally also apply to the Rankine cycle:

c The first law of thermodynamics requires that the net work developed by a system

undergoing a power cycle must equal the net energy added by heat transfer to the

system (Sec. 2.6.2).

c The second law of thermodynamics requires that the thermal efficiency of a power

cycle to be less than 100% (Sec. 5.6.1).

It is recommended that you review this material as needed.

Discussions in previous chapters also have shown that improved thermodynamic per-

formance accompanies the reduction of irreversibilities and losses. The extent to which

irreversibilities and losses can be reduced in vapor power plants depends on several

factors, however, including limits imposed by thermodynamics and by economics.

8.2 The Rankine Cycle 433

Power_Cycle

A.9 – All Tabs

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434 Chapter 8

Vapor Power Systems

TAKE NOTE...

When analyzing vapor power

cycles, we take energy trans-

fers as positive in the direc-

tions of arrows on system

schematics and write energy

balances accordingly.

8.2.1

Modeling the Rankine Cycle

The processes taking place in a vapor power plant are sufficiently complicated that

idealizations are required to develop thermodynamic models of plant components and

the overall plant. Depending on the objective, models can range from highly detailed

computer models to very simple models requiring a hand calculator at most.

Study of such models, even simplified ones, can lead to valuable conclusions about

the performance of the corresponding actual plants. Thermodynamic models allow at

least qualitative deductions about how changes in major operating parameters affect

actual performance. They also provide uncomplicated settings in which to investigate

the functions and benefits of features intended to improve overall performance.

Whether the aim is a detailed or simplified model of a vapor power plant adhering

to the Rankine cycle, all of the fundamentals required for thermodynamic analysis

have been introduced in previous chapters. They include the conservation of mass

and conservation of energy principles, the second law of thermodynamics, and use of

thermodynamic data. These principles apply to individual plant components such as

turbines, pumps, and heat exchangers as well as to the overall cycle.

Let us now turn to the thermodynamic modeling of subsystem B of Fig. 8.1a. The

development begins by considering, in turn, the four principal components: turbine,

condenser, pump, and boiler. Then we consider important performance parameters.

Since the vast majority of large-scale vapor power plants use water as the working

fluid, water is featured in the following discussions. For ease of presentation, we also

focus on fossil-fuel plants, recognizing that major findings apply to the other types of

power plants shown in Fig. 8.1.

The principal work and heat transfers of subsystem B are illustrated in Fig. 8.2. In

subsequent discussions, these energy transfers are taken to be positive in the directions

of the arrows. The unavoidable stray heat transfer that takes place between the plant

components and their surroundings is neglected here for simplicity. Kinetic and poten-

tial energy changes are also ignored. Each component is regarded as operating at steady

state. Using the conservation of mass and conservation of energy principles together

with these idealizations, we develop expressions for the energy transfers shown on

Fig. 8.2 beginning at state 1 and proceeding through each component in turn.

Turbine

Vapor from the boiler at state 1, having an elevated temperature and pressure, expands

through the turbine to produce work and then is discharged to the condenser at state

2 with relatively low pressure. Neglecting heat transfer with the surroundings, the

mass and energy rate balances for a control volume around the turbine reduce at

steady state to give

0 5 Q

2 W

1 m

2 h

2 V

1 g1z

2 z

5 h

2 h

(8.1)

where m

denotes the mass flow rate of the cycle working fluid, and

is the rate at which work is developed per unit of mass of vapor

passing through the turbine. As noted above, kinetic and potential

energy changes are ignored.

Condenser

In the condenser there is heat transfer from the working fluid to cool-

ing water flowing in a separate stream. The working fluid condenses

and the temperature of the cooling water increases. At steady state,

Boiler

Cooling wate

Turbine

Pump

Condenser

out

Fig. 8.2 Principal work and heat transfers

of subsystem B.

Turbine

A.19 – Tabs a, b & c

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mass and energy rate balances for a control volume enclosing the condensing side of the

heat exchanger give

out

5 h

2 h

(8.2)

where Q

out

is the rate at which energy is transferred by heat from the working fluid

to the cooling water per unit mass of working fluid passing through the condenser.

This energy transfer is positive in the direction of the arrow on Fig. 8.2.

Pump

The liquid condensate leaving the condenser at 3 is pumped from the condenser into

the higher pressure boiler. Taking a control volume around the pump and assuming

no heat transfer with the surroundings, mass and energy rate balances give

5 h

2 h

(8.3)

where W

is the rate of power input per unit of mass passing through the pump.

This energy transfer is positive in the direction of the arrow on Fig. 8.2.

Boiler

The working fluid completes a cycle as the liquid leaving the pump at 4, called the

boiler feedwater, is heated to saturation and evaporated in the boiler. Taking a control

volume enclosing the boiler tubes and drums carrying the feedwater from state 4 to

state 1, mass and energy rate balances give

5 h

2 h

(8.4)

where Q

is the rate of heat transfer from the energy source into the working fluid

per unit mass passing through the boiler.

Performance Parameters

The thermal efficiency gauges the extent to which the energy input to the working

fluid passing through the boiler is converted to the net work output. Using the quantities

and expressions just introduced, the thermal efficiency of the power cycle of Fig. 8.2 is

h 5

2 W

2 h

22 1h

2 h

(8.5a)

The net work output equals the net heat input. Thus, the thermal efficiency can be

expressed alternatively as

h 5

2 Q

out

5 1 2

out

5 1 2

2 h

(8.5b)

The heat rate is the amount of energy added by heat transfer to the cycle, usually in

Btu, to produce a unit of net work output, usually in kW ? h. Accordingly, the heat

rate, which is inversely proportional to the thermal efficiency, has units of Btu/kW ? h.

Another parameter used to describe power plant performance is the

back work ratio,

or bwr, defined as the ratio of the pump work input to the work developed by the

turbine. With Eqs. 8.1 and 8.3, the back work ratio for the power cycle of Fig. 8.2 is

bwr 5

2 h

(8.6)

feedwater

thermal efficiency

heat rate

back work ratio

8.2 The Rankine Cycle 435

Pump

A.21 – Tabs a, b, & c

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436 Chapter 8

Vapor Power Systems

Examples to follow illustrate that the change in specific enthalpy for the expansion

of vapor through the turbine is normally many times greater than the increase in

enthalpy for the liquid passing through the pump. Hence, the back work ratio is

characteristically quite low for vapor power plants.

Provided states 1 through 4 are fixed, Eqs. 8.1 through 8.6 can be applied to determine

the thermodynamic performance of a simple vapor power plant. Since these equations

have been developed from mass and energy rate balances, they apply equally for actual

performance when irreversibilities are present and for idealized performance in the

absence of such effects. It might be surmised that the irreversibilities of the various

power plant components can affect overall performance, and this is the case. Accordingly,

it is instructive to consider an idealized cycle in which irreversibilities are assumed

absent, for such a cycle establishes an upper limit on the performance of the Rankine

cycle. The ideal cycle also provides a simple setting in which to study various aspects of

vapor power plant performance. The ideal Rankine cycle is the subject of Sec. 8.2.2.

ENERGY & ENVIRONMENT The United States currently relies on relatively

abundant coal supplies to generate half of its electricity (Table 8.1). A large fleet of

coal-burning vapor power plants reliably provides comparatively inexpensive electricity

to homes, businesses, and industry. Yet this good news is eroded by human-health and environmental-

impact problems linked to coal combustion. Impacts accompany coal extraction, power generation,

and waste disposal. Analysts say the cost of coal-derived electricity would be much higher if the

full costs related to these adverse aspects of coal use were included.

Coal extraction practices such as mountaintop mining, where tops of mountains are sheared

off to get at underlying coal, are a particular concern when removed rock, soil, and mining debris

are discarded into streams and valleys below, marring natural beauty, affecting water quality, and

devastating CO

-trapping forests. Moreover, fatalities and critical injuries of coal miners while

working to extract coal are widely seen as deplorable.

Gases formed in coal combustion include sulfur dioxide and oxides of nitrogen, which contribute

to acid rain and smog. Fine particles and mercury, which more directly affect human health, are other

unwanted outcomes of coal use. Coal combustion is also a major contributor to global climate change,

primarily through carbon dioxide emissions. At the national level, controls are required for sulfur

dioxide, nitric oxides, and fine particles but not currently required for mercury and carbon dioxide.

Solid waste is another major problem area. Solid waste from coal combustion is one of the

largest waste streams produced in the United States. Solid waste includes sludge from smoke-

stack scrubbers and fly ash, a by-product of pulverized coal combustion. While some of this waste

is diverted to make commercial products, including cement, road de-icer, and synthetic gypsum

used for drywall and as a fertilizer, vast amounts of waste are stored in landfills and pools contain-

ing watery slurries. Leakage from these impoundments can contaminate drinking water supplies.

Watery waste accidentally released from holding pools causes widespread devastation and ele-

vated levels of dangerous substances in surrounding areas. Some observers contend much more

should be done to regulate health- and environment-endangering gas emissions and solid waste

from coal-fired power plants and other industrial sites.

The more efficiently each ton of coal is utilized to generate power, the less CO

, other combus-

tion gases, and solid waste will be produced. Accordingly, improving efficiency is a well-timed

pathway for continued coal use in the twenty-first century. Gradual replacement of existing power

plants, beginning with those several decades old, by more efficient plants will reduce to some

extent gas emissions and solid waste related to coal use.

Various advanced technologies also aim to foster coal use—but used more responsibly. They

include supercritical vapor power plants (Sec. 8.3), carbon capture and storage (Sec. 8.5.3), and

integrated gasification combined cycle (IGCC) power plants (Sec. 9.10). Owing to our large coal

reserves and the critical importance of electricity to our society, major governmental and private-sector

initiatives are in progress to develop additional technologies that promote responsible coal use.

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8.2.2

Ideal Rankine Cycle

If the working fluid passes through the various components of the simple vapor power

cycle without irreversibilities, frictional pressure drops would be absent from the boiler

and condenser, and the working fluid would flow through these components at con-

stant pressure. Also, in the absence of irreversibilities and heat transfer with the sur-

roundings, the processes through the turbine and pump would be isentropic. A cycle

adhering to these idealizations is the

ideal Rankine cycle shown in Fig. 8.3.

Referring to Fig. 8.3, we see that the working fluid undergoes the following series

of internally reversible processes:

Process 1–2: Isentropic expansion of the working fluid through the turbine from

saturated vapor at state 1 to the condenser pressure.

Process 2–3: Heat transfer from the working fluid as it flows at constant pressure

through the condenser with saturated liquid at state 3.

Process 3–4: Isentropic compression in the pump to state 4 in the compressed

liquid region.

Process 4–1: Heat transfer to the working fluid as it flows at constant

pressure through the boiler to complete the cycle.

The ideal Rankine cycle also includes the possibility of superheating the

vapor, as in cycle 19–29–3–4–19. The importance of superheating is dis-

cussed in Sec. 8.3.

Since the ideal Rankine cycle consists of internally reversible processes,

areas under the process lines of Fig. 8.3 can be interpreted as heat transfers

per unit of mass flowing. Applying Eq. 6.49, area 1–b–c–4–a–1 represents

the heat transfer to the working fluid passing through the boiler and area

2–b–c–3–2 is the heat transfer from the working fluid passing through the

condenser, each per unit of mass flowing. The enclosed area 1–2–3–4–a–1

can be interpreted as the net heat input or, equivalently, the net work

output, each per unit of mass flowing.

Because the pump is idealized as operating without irreversibilities, Eq.

6.51b can be invoked as an alternative to Eq. 8.3 for evaluating the pump work. That is

int

rev

y dp

(8.7a)

where the minus sign has been dropped for consistency with the positive value for

pump work in Eq. 8.3. The subscript “int rev” signals that this expression is restricted

to an internally reversible process through the pump. An “int rev” designation is not

required by Eq. 8.3, however, because it is obtained with the conservation of mass

and energy principles and thus is generally applicable.

Evaluation of the integral of Eq. 8.7a requires a relationship between the specific

volume and pressure for Process 3–4. Because the specific volume of the liquid nor-

mally varies only slightly as the liquid flows from the inlet to the exit of the pump,

a plausible approximation to the value of the integral can be had by taking the spe-

cific volume at the pump inlet, y

, as constant for the process. Then

< y

2 p

(8.7b)

where the subscript s signals the isentropic—internally reversible and adiabatic—process

of the liquid flowing through the pump.

The next example illustrates the analysis of an ideal Rankine cycle.

ideal Rankine cycle

TAKE NOTE...

For cycles, we modify the

problem-solving methodol-

ogy: The Analysis begins

with a systematic evalua-

tion of required property

data at each numbered

state. This reinforces what

we know about the compo-

nents, since given informa-

tion and assumptions are

required to fix the states.

22′

1′

Fig. 8.3 Temperature–entropy diagram

of the ideal Rankine cycle.

8.2 The Rankine Cycle 437

Rankine_Cycle

A.26 – Tabs a & b

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438 Chapter 8 Vapor Power Systems

Analyzing an Ideal Rankine Cycle

c c c c EXAMPLE 8.1 c

Steam is the working fluid in an ideal Rankine cycle. Saturated vapor enters the turbine at 8.0 MPa and satu-

rated liquid exits the condenser at a pressure of 0.008 MPa. The net power output of the cycle is 100 MW.

Determine for the cycle (a) the thermal efficiency, (b) the back work ratio, (c) the mass flow rate of the steam,

in kg/h, (d) the rate of heat transfer, Q

, into the working fluid as it passes through the boiler, in MW, (e) the

rate of heat transfer,

out

, from the condensing steam as it passes through the condenser, in MW, (f) the mass

flow rate of the condenser cooling water, in kg/h, if cooling water enters the condenser at 158C and exits at

358C.

SOLUTION

Known:

An ideal Rankine cycle operates with steam as the working fluid. The boiler and condenser pressures

are specified, and the net power output is given.

Find: Determine the thermal efficiency, the back work ratio, the mass flow rate of the steam, in kg/h, the rate

of heat transfer to the working fluid as it passes through the boiler, in MW, the rate of heat transfer from the

condensing steam as it passes through the condenser, in MW, the mass flow rate of the condenser cooling water,

which enters at 158C and exits at 358C.

Schematic and Given Data:

Boiler

Saturated

vapor

8.0 MPa

Cooling

water

Turbine

Condenser

Saturated

liquid at 0.008 MPa

out

Pump

0.008 MPa

8.0 MPa

Fig. E8.1

Engineering Model:

Each component of the cycle is analyzed as a control volume at steady state. The control volumes are shown

on the accompanying sketch by dashed lines.

2. All processes of the working fluid are internally reversible.

3. The turbine and pump operate adiabatically.

4. Kinetic and potential energy effects are negligible.

5. Saturated vapor enters the turbine. Condensate exits the condenser as saturated liquid.

Analysis: To begin the analysis, we fix each of the principal states located on the accompanying schematic

and T–s diagrams. Starting at the inlet to the turbine, the pressure is 8.0 MPa and the steam is a saturated

vapor, so from Table A-3, h

5 2758.0 kJ/kg and s

5 5.7432 kJ/kg ? K.

➊

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State 2 is fixed by p

5 0.008 MPa and the fact that the specific entropy is constant for the adiabatic, internally

reversible expansion through the turbine. Using saturated liquid and saturated vapor data from Table A-3, we

find that the quality at state 2 is

2 s

5.7432 2 0.5926

7.6361

5 0.6745

The enthalpy is then

5 h

1 x

5 173.88 1 10.674522403.1

5 1794.8 kJ

State 3 is saturated liquid at 0.008 MPa, so h

5 173.88 kJ/kg.

State 4 is fixed by the boiler pressure p

and the specific entropy s

5 s

. The specific enthalpy h

can be found

by interpolation in the compressed liquid tables. However, because compressed liquid data are relatively sparse,

it is more convenient to solve Eq. 8.3 for h

, using Eq. 8.7b to approximate the pump work. With this approach

5 h

1 W

5 h

1 y

2 p

By inserting property values from Table A-3

5 173.88 kJ

kg 1 11.0084 3 10

kg218.0 2 0.0082MPa `

1 MPa

1 kJ

N ? m

5 173.88 1 8.06 5 181.94 kJ

(a) The net power developed by the cycle is

cycle

5 W

2 W

Mass and energy rate balances for control volumes around the turbine and pump give, respectively,

5 h

2 h





and



5 h

2 h

where m

is the mass flow rate of the steam. The rate of heat transfer to the working fluid as it passes through

the boiler is determined using mass and energy rate balances as

5 h

2 h

The thermal efficiency is then

h 5

2 W

2 h

22 1h

2 h

312758.0 2 1794.822 1181.94 2 173.8824

12758.0 2 181.942 kJ

5 0.371 137.1%2

(b) The back work ratio is

bwr 5

2 h

1181.94 2 173.882

12758.0 2 1794.82 kJ

8.06

963.2

5 8.37 3 10

10.84%2

cycle

2 h

22 1h

2 h

1100 MW2

3600 s

1963.2 2 8.062 kJ

5 3.77 3 10

➋

8.2 The Rankine Cycle 439

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440 Chapter 8 Vapor Power Systems

(d) With the expression for Q

from part (a) and previously determined specific enthalpy values

5 m

2 h

13.77 3 10

h212758.0 2 181.942 kJ

3600 s

5 269.77 MW

(e) Mass and energy rate balances applied to a control volume enclosing the steam side of the condenser give

out

5 m

2 h

13.77 3 10

h211794.8 2 173.882 kJ

3600 s

5 169.75 MW

➌ Note that the ratio of Q

out

to Q

is 0.629 (62.9%).

Alternatively, Q

out

can be determined from an energy rate balance on the overall vapor power plant. At steady

state, the net power developed equals the net rate of heat transfer to the plant

cycle

5 Q

2 Q

out

Rearranging this expression and inserting values

out

5 Q

2 W

cycle

5 269.77 MW 2 100 MW 5 169.77 MW

The slight difference from the above value is due to round-off.

(f) Taking a control volume around the condenser, the mass and energy rate balances give at steady state

0 5 Q

2 W

1 m

cw, in

2 h

cw, out

21 m

2 h

where m

is the mass flow rate of the cooling water. Solving for m

2 h

cw, out

2 h

cw,in

The numerator in this expression is evaluated in part (e). For the cooling water, h < h

, so with saturated

liquid enthalpy values from Table A-2 at the entering and exiting temperatures of the cooling water

1169.75 MW2010

MW 003600 s

h 0

1146.68 2 62.992 kJ

5 7.3 3 10

➊ Note that a slightly revised problem-solving methodology is used in this

example problem: We begin with a systematic evaluation of the specific

enthalpy at each numbered state.

➋ Note that the back work ratio is relatively low for the Rankine cycle. In the

present case, the work required to operate the pump is less than 1% of the

turbine output.

➌ In this example, 62.9% of the energy added to the working fluid by heat

transfer is subsequently discharged to the cooling water. Although consider-

able energy is carried away by the cooling water, its exergy is small because

the water exits at a temperature only a few degrees greater than that of the

surroundings. See Sec. 8.6 for further discussion.

Ability to…

❑

sketch the T–s diagram of

the basic Rankine cycle.

❑

fix each of the principal

states and retrieve

necessary property data.

❑

apply mass and energy

balances.

❑

calculate performance

parameters for the cycle.

✓

Skills Developed

If the mass flow rate of steam were 150 kg/s, what would be the

net power, in MW, and the thermal efficiency? Ans. 143.2 MW, 37.1%.

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8.2.3

Effects of Boiler and Condenser Pressures

on the Rankine Cycle

In discussing Fig. 5.12 (Sec. 5.9.1), we observed that the thermal efficiency of power

cycles tends to increase as the average temperature at which energy is added by

heat transfer increases and/or the average temperature at which energy is rejected

by heat transfer decreases. (For elaboration, see box.) Let us apply this idea to

study the effects on performance of the ideal Rankine cycle of changes in the

boiler and condenser pressures. Although these findings are obtained with refer-

ence to the ideal Rankine cycle, they also hold qualitatively for actual vapor power

plants.

Figure 8.4a shows two ideal cycles having the same condenser pressure but differ-

ent boiler pressures. By inspection, the average temperature of heat addition is seen

to be greater for the higher-pressure cycle 19–29–39–49–19 than for cycle 1–2–3–4–1. It

follows that increasing the boiler pressure of the ideal Rankine cycle tends to increase

the thermal efficiency.

Considering the Effect of Temperature on Thermal Efficiency

Since the ideal Rankine cycle consists entirely of internally reversible processes, an

expression for thermal efficiency can be obtained in terms of average temperatures

during the heat interaction processes. Let us begin the development of this expression

by recalling that areas under the process lines of Fig. 8.3 can be interpreted as the heat

transfer per unit of mass flowing through the respective components. For example, the

total area 1–b–c–4–a–1 represents the heat transfer into the working fluid per unit of

mass passing through the boiler. In symbols,

int

T ds 5 area 1–b–c–4–a–1

The integral can be written in terms of an average temperature of heat addition,

, as

follows:

int

rev

5 T

2 s

where the overbar denotes average. Similarly, area 2–b–c–3–2 represents the heat trans-

fer from the condensing steam per unit of mass passing through the condenser

out

int

rev

5 T

out

2 s

25 area 22b2c2322

5 T

out

2 s

where T

out

denotes the temperature on the steam side of the condenser of the ideal

Rankine cycle pictured in Fig. 8.3. The thermal efficiency of the ideal Rankine cycle can

be expressed in terms of these heat transfers as

ideal

5 1 2

out

int

rev

5 1 2

out

(8.8)

By the study of Eq. 8.8, we conclude that the thermal efficiency of the ideal cycle tends

to increase as the average temperature at which energy is added by heat transfer

increases and/or the temperature at which energy is rejected decreases. With similar

reasoning, these conclusions can be shown to apply to the other ideal cycles considered

in this chapter and the next.

8.2 The Rankine Cycle 441

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442 Chapter 8

Vapor Power Systems

Figure 8.4b shows two cycles with the same boiler pressure but two different con-

denser pressures. One condenser operates at atmospheric pressure and the other at

less than atmospheric pressure. The temperature of heat rejection for cycle 1–2–3–4–1

condensing at atmospheric pressure is 1008C (2128F). The temperature of heat rejec-

tion for the lower-pressure cycle 1–20–30–40–1 is correspondingly lower, so this cycle

has the greater thermal efficiency. It follows that decreasing the condenser pressure

tends to increase the thermal efficiency.

The lowest feasible condenser pressure is the saturation pressure corresponding to

the ambient temperature, for this is the lowest possible temperature for heat rejection

to the surroundings. The goal of maintaining the lowest practical turbine exhaust

(condenser) pressure is a primary reason for including the condenser in a power plant.

Liquid water at atmospheric pressure could be drawn into the boiler by a pump, and

steam could be discharged directly to the atmosphere at the turbine exit. However,

by including a condenser in which the steam side is operated at a pressure below

atmospheric, the turbine has a lower-pressure region in which to discharge, resulting

in a significant increase in net work and thermal efficiency. The addition of a con-

denser also allows the working fluid to flow in a closed loop. This arrangement per-

mits continual circulation of the working fluid, so purified water that is less corrosive

than tap water can be used economically.

Comparison with Carnot Cycle

Referring to Fig. 8.5, the ideal Rankine cycle 1–2–3–4–49–1 has a lower

thermal efficiency than the Carnot cycle 1–2–39–49–1 having the same

maximum temperature T

and minimum temperature T

because the

average temperature between 4 and 49 is less than T

. Despite the

greater thermal efficiency of the Carnot cycle, it has shortcomings as

a model for the simple fossil-fueled vapor power cycle. First, heat

transfer to the working fluid of such vapor power plants is obtained

from hot products of combustion cooling at approximately constant

pressure. To exploit fully the energy released on combustion, the hot

products should be cooled as much as possible. The first portion of the

heating process of the Rankine cycle shown in Fig. 8.5, Process 4–49,

is achieved by cooling the combustion products below the maximum

temperature T

. With the Carnot cycle, however, the combustion

products would be cooled at the most to T

. Thus, a smaller portion

of the energy released on combustion would be used. Another short-

coming of the Carnot vapor power cycle involves the pumping pro-

cess. Note that state 39 of Fig. 8.5 is a two-phase liquid–vapor mixture.

Significant practical problems are encountered in developing pumps

that handle two-phase mixtures, as would be required by Carnot cycle

Fixed boiler pressure

Ambient temperature

Decreased

condenser pressure

2″

atm

p < p

atm

3″

″

Increased

boiler pressure

4′

322′

′

100° C

(212° F)

)

(a)

Fixed

condenser pressure

Fig. 8.4 Effects of varying operating pressures on the ideal Rankine cycle. (a) Effect of boiler

pressure. (b) Effect of condenser pressure.

Cooling curve for the

products of combustion

4′

3′3

p ≈

constant

Fig. 8.5 Illustration used to compare the ideal

Rankine cycle with the Carnot cycle.

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