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**Vapor and Combined Power Cycles**

CHAPTER 10 Vapor and Combined Power Cycles

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**10-1 The Carnot Vapor Cycle**

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**FIGURE10-1 T-s diagram of two Carnot vapor cycles.**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE10-1 T-s diagram of two Carnot vapor cycles.

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Operating principles TH TC WNET QH QC (1) (2)

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**10-2 Rankine Cycle: The Ideal Cycle for Vapor Power Cycles**

Operating principles Vapor power plants The ideal Rankine vapor power cycle Efficiency Improved efficiency - superheat

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**The conventional vapor power plant**

QIN QOUT WTURBINE WPUMP

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**The conventional vapor power plant**

QIN QOUT WTURBINE WPUMP High temperature heat addition. Low temperature heat rejection Work input to compress working fluid Turbine to obtain work by expansion of working fluid.

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**FIGURE 10-2 The simple ideal Rankine cycle.**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 10-2 The simple ideal Rankine cycle.

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**A hypothetical vapor power cycle**

Assume a Carnot cycle operating between two fixed temperatures as shown. T s 1 2 3 4

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**The ideal Rankine cycle**

s T 1 2 3 4 3* 4* All processes are internally reversible.

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**The ideal Rankine cycle**

s T 1 2 3 4 3* 4* Reversible constant pressure heat rejection (4 1) Reversible constant pressure heat addition (2 3) Isentropic compression (1 2) Isentropic expansion to produce work (3 4) or (3* 4*) All processes are internally reversible.

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**The ideal Rankine cycle (h-s diagram)**

4 3 2 WOUT QH QC 1 WIN

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**Rankine cycle efficiency**

h s 4 3 2 WOUT QH QC 1 WIN s (3)

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**Ideal Turbine Work s h (4) Isentropic process, s = constant s1 = s2 p1**

All accessible states lie to the right of the process (1 2). (4)

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**Ideal turbine work Steady state. Constant mass flow**

Isentropic Expansion (s = Constant) Adiabatic and reversible No entropy production No changes in KE and PE Usual assumption is to neglect KE and PE effects at inlet and outlet of turbine.

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Ideal turbine work (4) (5)

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Work of Compression (6) (7)

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**Improved Rankine cycle efficiency**

h s 4 3* 2 WOUT QH QC 1 WIN Increased average temperature of heat addition

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**Improved Rankine cycle efficiency**

(8) (9)

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**10-3 Deviation of Actual Vapor Power Cycles from Idealized Ones**

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**Copyright © The McGraw-Hill Companies, Inc**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 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.

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**Raising the average temperature of heat addition**

The Improved Rankine Cycle How Can We Increase the Efficiency of the Rankine Cycle Raising the average temperature of heat addition

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**Copyright © The McGraw-Hill Companies, Inc**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 10-6 The effect of lowering the condenser pressure on the ideal Rankine cycle.

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**Copyright © The McGraw-Hill Companies, Inc**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 10-7 The effect of superheating the steam to higher temperatures on the ideal Rankine cycle.

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**Copyright © The McGraw-Hill Companies, Inc**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 10-8 The effect of increasing the boiler pressure on the ideal Rankine cycle.

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**FIGURE 10-9 A supercritical Rankine cycle.**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE 10-9 A supercritical Rankine cycle.

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**Copyright © The McGraw-Hill Companies, Inc**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE T-s diagrams of the three cycles discussed in Example 9–3.

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**10-5 The Ideal Reheat Rankine Cycle**

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**A hypothetical vapor power cycle**

Assume a Carnot cycle operating between two fixed temperatures as shown. T s 1 2 3 4

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**A hypothetical vapor power cycle with superheat**

Superheating the working fluid raises the average temperature of heat addition. T s 1 2 3 4 TH,2 TH,1

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**A hypothetical vapor power cycle: A Rankine cycle with superheat**

b T a c d s Superheating the working fluid raises the average temperature with a reservoir at a higher temperature.

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**The Rankine cycle with reheat**

The extra expansion via reheating to state “d” allows a greater enthalpy to be released between states “c” to “e”. s T f a b c p1 p2 d e

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**The reheat cycle QOUT WIN a b e f QH WOUT QC c d**

Single stage reheat. Work produced in both turbines.

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**Reheat Cycle Efficiency**

(1)

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**FIGURE 10-11 The ideal reheat Rankine cycle.**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE The ideal reheat Rankine cycle.

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Example 1

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**Example - 1: A Carnot cycle**

To begin our analysis of Rankine cycle operations, consider a steady Carnot cycle (a-b-c-d-a) with water as the working fluid operating between to given temperature limits as shown. The given data are that the boiler pressure is 500 psi (pa = 500 psi) and the condenser temperature is 70o F (Tc = 70o F). Determine the work output, thermal efficiency, irreversibility, and work ratio. T s a b c d T1 T2 p1 p2 b c d a T1 T2

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Example 1 - Given data

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**Example 1 - Computed data**

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**Example 1 - Process quantities**

D H BTU/lbm d W Q S BTU/ lbm-R Q/T BTU/lbm- R s a-b 755 0.8147 b-c -430 430 c-d -432 d-a 107 -107 Net 323 To get the above process quantities, the First Law for open systems has been used assuming KE and PE effects are negligible. The entropy production was obtained from an entropy balance for an open system. Note that the cyclic heat equals the cyclic work as required by the First Law and that entropy production is zero as required by the Clausius Equality.

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**Example 1 - Thermal efficiency and back work ratio**

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Example 2

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**Example 2 - A Rankine cycle without superheat**

A Rankine cycle with water as the working fluid operates between the same limits as in Example l, pa = 500 psi and a condensing temperature of 70o F. Assuming all processes to be internally reversible, determine the work output, efficiency, entropy production, work ratio. T s a b c d T1 T2 pa pd

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**Example 2 - Computed data**

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**Example 2 - Process quantities**

Work output = BTU/lbm Thermal efficiency = 36.8% Work ratio = Entropy production = 0

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Example 3

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**Example 3 - Effect of irreversibility in the turbine and pump**

A Rankine cycle operates between the same limits as above and has pump and turbine efficiencies of 80%. Determine the work output, efficiency, work ratio, and entropy production. Assume the condensing and ambient temperatures to be the same. T1 T2 s a b c d pa pd c’ a’ T

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**Example 3 - Computed data**

The states at a’ and c’ are determined via the First Law for an open system and the definition of isentropic efficiency for turbines and pumps as appropriate.

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**Example 3 - Process quantities**

Isentropic processes are determined prior to actual processes where irreversibility is involved. Work output = 342 BTU/lbm Thermal efficiency = 29.4% Work ratio = Entropy production = BTU/lbm-R

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Example 3 - Comparison

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Example 4

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Example 4 - Superheat An internally reversible Rankine cycle is determined by specifying a maximum temperature of 800o F, a quality at the turbine discharge of 0.9, and a minimum condensing temperature of 70oF. Compare the thermal efficiency with that of a Carnot cycle operating between the same temperature limits. b a c d pd pa T s

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**Example 4 - Given and computed data**

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**Example 4 - Thermal efficiency**

The Carnot efficiency

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Example 5

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**Example 5 - The reheat cycle**

f a b c pa pc s d e T

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**Example 5 - Given and computed data**

The state at “c” has the same as the pressure specified in Example 4. This determines state “b”. State “a” is determined via the usual approximation for an incompressible liquid under going process f-a.

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**Example 5 - Process quantities**

Work output = 701 BTU/lbm Thermal efficiency = 701/( ) = 0.424 Carnot efficiency = 1-(530/1260) = 0.579

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Example 6

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**Variation of the (First Law) cycle efficiency with a variation**

of the pressure of heat addition in a basic Rankine cycle with no super heat. The condenser pressure was assumed to be 14 psia.

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T s 1 2 3 5 6 4 p2 pmiddle

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**The variation of cycle efficiency of a Rankine cycle with one**

stage of reheat as a function of the pressure at which reheat is done. Pup is the pressure of high temperature heat addition.

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**Rankine cycle with reheat Rankine cycle with regeneration**

Key terms and concepts Cycle efficiency Rankine cycle with reheat Rankine cycle with regeneration Work ratio

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**10-6 The Ideal Regenerative Rankine cycle**

Another technique to raise the average temperature of the heat addition process.

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**Review - The reheat cylce The Rankine Cycle with regeneration Example**

Overview Review - The reheat cylce The Rankine Cycle with regeneration Open and closed feedwater heaters Example

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The Reheat Cycle Reheating the expanding fluid with primary heat source is made at inter-mediate points in the expansion process. Net effect is to raise the average expansion temperature of the turbine without raising the temperature of the heat source.

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**The Reheat Cycle s p1 The extra expansion allows a greater enthapy**

to be released between states 3 to 4. Here one additional reheat process has been added. T s 1 2 3 5 6 4 p2 p1 The Objective of Reheating: Increase work output The reheat process takes place form State 5 to 6. The expansion from States 6 to 4 takes place with no moisture in the turbine as shown here. The second stage of expansion is entirely in the superheat region. Without the reheat process, a single exzpansion would have produced a two-pahse (x < 1) mixture when the temperture dropped blow the saturation temperature at State 5. With reheat, the total work output of the cycle is larger than it would have been with a single expansion process. If State 4 yet lies in the vapor-liquid region (x < 1), at least additional work was extracted and the existense of the two-phase mixture at presumably a high quality (x near unity) would not be too detrimental to the low pressure turbine. As discussedin your text (Moran and Shapiro, pp ), the condsensing process is designed to operate at the lowest possible temeperature, usually the ambinetn. A lower condenser pressure allows the cycle to produce work with the largest possible pressure range and, hence, extract more work. In such systems, the condenser is sealed, and the entire system operates (ideally) in a closed loop.

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T s 1 2 3 5 6 4 p2 p1

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**The Rankine cycle with regeneration**

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**Copyright © The McGraw-Hill Companies, Inc**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE The first part of the heat-addition process in the boiler takes place at relatively low temperatures.

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**Principle of the regenerative cycle**

b f WOUT WIN QH QC A higher feed water inlet temperature as a result of heating from States a - b. e d

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Impacted processes Heating of some of the compressed liquid is done to raise the average temperature of heat addition. Heat is supplied after the liquid is compressed to a high pressure at State a.

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**The T-s diagram for the regenerative cycle**

b c s Internal heat transfer to feed water heater. e d a

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**Practical considerations...**

Turbines cannot be designed economically with internal heat exchangers. Condensation could occur in the turbine. Not practical!

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**The practical regenerative cycle**

5 Q2-3 = 0 1 2 3 W2,out WIN,1 QH 6 WIN,2 7 QC 4 W1,out Feedwater heater The Practical Regnerative Cycle Configuration A feedwazter heater is inserted between the stages of expansion. The expansion in each turbine is carried out isentropically. Note that after a fraction of mass flow is drawn off at State 6 for the feewater heater, the reminaing fraction passes through states 7 to 2. A unit mass of the working fluid is returned to the high tempeaure source at State 4 for heat addition. The net work of the cycle is obtained in the two stages of expansion less the work input to the two feewater pumps. The feedwater heater (Stated 2 - 3) as depicted here is “closed” feedwater heater. No additional liquid is provided, i.e., makup water is not used. Thus mass conservation is easily determined when a mass balance is made for the device. Idally, the feedwater heater accomplished its purpose adiabatically, i.e., Q2-3 = 0.

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**The h-s diagram for the regenerative cycle**

1 3 4 2 WOUT,1 QH QC WIN,1 5 6 7 WOUT,2 WIN,2 (1 kg) (y kg) (1-y kg)

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**Energy balances and thermal efficiency**

1 3 4 2 WOUT,1 QH QC WIN,1 5 6 7 WOUT,2 WIN,2 (1 kg) (y kg) (1-y kg)

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**Open and Closed Feedwater Heaters**

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**Regeneration with an open feedwater heater**

QH y 1-y WIN,1 WIN,2 WOUT Regeneration with an open feedwater heater at the mass fraction rate of “y” per unit mass of primary the flow rate. QC

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**The open feedwater heater**

y From the outlet of the condenser and first feedwater pump. (1-y kg.) From the turbine. (y kg.) To the second feedwater pump. (1 kg.) 1-y

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**Regenerative cycle with a closed feedwater heater**

5 1 2 3 4 6 7 8 y 1-y QH QC WT Closed feedwater heater Trap Condenser

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**T-s diagram for a regenerative cycle with a closed feedwater heater**

1 2 3 4 5 6 7 8 s T

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**Copyright © The McGraw-Hill Companies, Inc**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE The ideal regenerative Rankine cycle with an open feedwater heater.

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**Copyright © The McGraw-Hill Companies, Inc**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE The ideal regenerative Rankine cycle with a closed feedwater heater.

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**Copyright © The McGraw-Hill Companies, Inc**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE A steam power plant with one open and three closed feedwater heaters.

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**Example - Regeneration with a single extraction and an open feedwater heater**

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**Example A regenerative Rankine cycle with a single extraction**

provides saturated steam at 500 psi a the turbine inlet. Condensation takes place at 70o F. One open regenerative feedwater heater is included, using extracted steam at a temperature midway between the limits of the cycle. All processes are assumed to be internally reversible except that in the regenerative heater. Neglect KE and PE effects, and determine the thermal efficiency, the internal irreversibility, and the extraction pressure. Assume steady operation.

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**Example - Plant diagram**

WOUT QC a d e c b QH y 1-y WIN,1 WIN,2 g f

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Example - T-s diagram a b c d e f g y 1-y 1 T s

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**Example - Mass fraction at State “c”**

The mass fraction of fluid extracted at State c is obtained from the energy balance for an open system applied to the feedwater heater. Assume adiabatic mixing. a b c d e f g y 1-y 1 T s

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**Example - Entropy balance for the feedwater heater**

Apply the entropy balance for an open system to the feedwater heater.

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Example - Given data

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**Example - Computed data**

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**Example - Process quantities**

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**Example - Process quantities**

Note the positive entropy production in the feedwater heater.

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**Example - Thermal efficiency**

Note that regeneration has increased thermal efficiency above that of the previous example at the expense of some work output per lbm of steam.

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**Commercial steam-power plants**

Reheat (multiple stages) Regeneration (multiple extractions) Nearly ideal heat addition Constant temperature boiling for water

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**Commercial steam-power plants**

Heat transfer characteristics of steam and water permit external combustion systems Compression of condensed liquid produces a favorable work ratio.

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**Commercial steam-power plants**

The Rankine cycle with reheat and regeneration is advantageous for large plants. Small plants do not have economies of scale Internal combustion for heat addition. A different thermodynamic cycle

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**10-7 Second-Law Analysis of Vapor Power Cycles**

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10-8 Cogeneration

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**FIGURE 10-20 A simple process-heating plant.**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE A simple process-heating plant.

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**FIGURE 10-21 An ideal cogeneration plant.**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE An ideal cogeneration plant.

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**FIGURE 10-22 A cogeneration plant with adjustable loads.**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE A cogeneration plant with adjustable loads.

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**10-9 Combined /gas-Vapor Power Cycles**

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**FIGURE 10-24 Combined gas–steam power plant.**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE Combined gas–steam power plant.

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**FIGURE 10-26 Mercury–water binary vapor cycle.**

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. FIGURE Mercury–water binary vapor cycle.

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