CHAPTER 5 – ENTROPY GENERATION

Instructor:

Prof. Dr. Uğur Atikol

Chapter 5 Entropy Generation (Exergy Destruction) Outline

Lost Available Work

Cycles

Heat engine cycles

Refrigeration cycles

Heat pump cycles

Nonflow Processes

Steady-Flow Processes

Exergy wheel diagrams

System

in

out

Reservoir at T1

Reservoir at T2

Reservoir at Tn

...

Atmospheric temperature and pressure reservoir

at ( ,PoTo )

Lost Available Work

inm

outmdt

dVPWWu 0

0Q

1Q 2Q nQ

0P

dt

dVdt

dVP0

(All modes of work transfer)

uW

W

Atmosphere

magneticshearelectrical WWWdt

dVPW

atmosphereeagainst th

doneWork

Lost Available Work

00

out

n

i ini

igen smsm

T

Q

dt

dSS

out

on

i in

o

i hmhmWQdt

dE

0

Note: is known as methalpy, such that

gzV

hho 2

2

oh

inmoutmSystem

T1 T2 Tn

T0

W

0Q

1Q2Q nQ

First law:

Second law:

Lost Available Work

00

out

n

i ini

igen smsm

T

Q

dt

dSS

out

on

i in

o

i hmhmWQdt

dE

0

genlost

revlostgenrev

out

on

i in

o

i

i

rev

gen

gen

n

i out

o

in

o

i

i

STW

WWWSTWW

sThmsThmQT

TSTE

dt

dW

S

STsThmsThmQT

TSTE

dt

dW

Q

0

0

0

1

00

0

0

1

000

0

0

Hence

that know however we

:generally Therefore

)()(1)(

:hence zero, is reversibleWhen

)()(1)(

:equations twoebetween th Eliminate

Also known as «exergy destruction Xdes» or «Irreversibility»

Lost Available Work

Work producing devices

Work absorbing devices

0 revout WW

0 revin WW

ve is lostW

ve is lostW

)(remember

negativeor positiveeither becan and although positive always is

WWW

WWW

revlost

revlost

The main purpose of studying the lost available work is to diagnose the areas where irreversibilities are taking place in a prosess so that thermodynamic improvements can be made.

Lost Available Work

gen

out

o

in

o

i

n

i i

W

STsThmsThm

QT

TSTVPE

dt

d

dt

dVPWX

dtdVP

P

000

1

000

0

workavailable of Rate

0

0

)()(

1)(

:such that of rate

worka consumes atmosphere then the pressure hasthat

atmosphere eagainst th work doing is system When the

In most flow systems P0 dV/dt = 0, therefore ẊW = Ẇ (i.e., exergy transfer

by work is simply the work itself)

out

in

out

flow mass with exergy flow of Release

m

in

flow masswith

exergy flow

of Intake

m dt

dΦ exergy nonflow

ofon Accumulati revWX

power mechanical available

ofdelivery Maximum

Lost Available Work

1QXnQQ XX .......................

2

1T 2T nT

),(t Environmen 00 PT

out outin in

mΨ

out

o

mΨ

in

o

i

n

i i

dtdΦ

revW

revrevW

sThmsThmQT

TSTVPE

dt

dX

dt

dVPWX

flow masswith exergy flow of Release

0

flow masswith exergy flow of Intake

0

ferheat transwith sfer Exergy tan

1

0

exergy nonflow ofon Accumulati

00

power available ofdelivery Maximum

0

)()( 1 )(

:limit reversible In the

out

in

out

m

in

m

dt

dΦ

revWX

Lost Available Work

1QXnQQ XX .......................

2

1T 2T nT

),(t Environmen 00 PT

WX

lostWX

Actual work

Lost available work Lost exergy Exergy destruction Irreversibilities

Lost available work is defined as the difference between the maximum available work Wrev and the actual work W. Alternatively it can be defined as:

WrevWlost XXX )(Same as Ẇlost Same as Ẋdes

Lost Available Work

out

m

n

i

QnX

1

in

m

dt

dΦ

revWX WX

lostWX

Exergy inflow Exergy outflow

Exergy balance of the open system discussed can be shown on a flow diagram as follows:

Lost Exergy in Cycles

W

X

i

n

i

Qlost

Q

i

n

i i

revW

XXW

T

TQX

TTQ

QT

TX

revW

)(

1

0

0

1

0

)(

:cyclesin operating systems closed

for work availablelost theTherefore

1

as expressed becan ) , ,(fer heat trans ofcontent Exergy

1)(

is power) available (maximumpower availablefor valueceiling The

cycles. ofnumber integralan in operate that systems closed asConsider

Tn T2 T1

Q1 Q2 Qn Closed system

Cycles

W T0

Heat Engine Cycles

Heat Engine

Sink TL

Ẇ

HQ

LQ

genLlost

H

LHWQlost

L

lost

H

H

L

Lgen

LH

STW

WT

TQXXW

TT

W

T

Q

T

QS

WQQ

H

:as expressed becan Also

1

be toassumed is etemperatur

if follows as expressed becan

0

0

: thatstate laws second andFirst

0

Source TH Obtained by applying the

definition of entropy to the 2 reservoirs. QH is -ve

Heat Engine Cycles

revLQ , revW

HQ

HT

LT

HT

LQ W

HQ

LT

0 0

lostW

Temperature -energy diagram for a heat engine cycle proposed by Adrian Bejan

lostW

genS1tan

gengen

genLlost

L

lost

SS

STW

T

W

1tanor tan

, since

tan

Reversible Irreversible

Heat Engine Cycles

HeatEngine

EQH

II x EQH

De

stru

ction of Exergy

Comparison between the first- and second-law efficiency of a heat-engine cycle

XQH

II XQH

Exergy transfer by heat transfer

H

LHrevWQ

Q

WII

T

TQXX

X

X

H

H

1)( where

HeatEngine

High Temperature Reservoir at TH

Low Temperature Reservoir at TL

QH

QL

W x Q = HI

Heat Engine Cycles Second-law efficiency of a heat-engine cycle can also be expressed as follows:

revW

genL

revW

lostrevW

revW

WII

X

ST

X

WX

X

X

)(1

)(

)(

)(

H

LIII

H

X

HLHII

H

QII

I

W

Q

WII

H

I

T

T

Q

TTQ

Q

X

XW

X

X

Q

W

HQ

H

H

1

)1(

Therefore, ) (i.e.,

it with associatednsfer exergy tra theas same theis transfer that workknow We

and

Relationship between first and second law efficiencies:

Ambient TH

They are closed systems in communication with two heat reservoirs

(1) the cold space (at TL) from which refrigeration load QL is extracted

(2) the ambient (at TH) to which heat QH is rejected

Refrigeration Cycles

Refrigerator

Refrigerated space TL

Ẇ

HQ

LQ

lost

L

HL

L

HL

W

W

T

TQ

Qlost

lostH

H

H

L

Lgen

HL

WT

TQW

WT

TQXXW

WT

T

T

Q

T

QS

WQQ

L

HL

L

1 gRearrangin

)(1

:follows as expressed becan . is which ambient,

theof re temperatu theis etemperatur-state dead Here

0

0

: thatstate laws second andFirst

numbernegative a is

input Work

negative be will termThissign ve)(

a with itself be will

1

0

Obtained by applying the definition of entropy to the

2 reservoirs. QL is -ve

Refrigeration Cycles Temperature -energy diagram for a refrigeration cycle proposed by Adrian Bejan

LQrevW

HQ

HT

LT

HT

LQ W

HQ

LT

0 0

lostW lostW

genS1tan

gengen

genHlost

L

lost

SS

STW

T

W

1tanor tan

, since

tan

Reversible Irreversible

Refrigeration Cycles Energy conversion vs exergy destruction during a refrigeration cycle

Refr

ige

rato

r

High Temperature Reservoir at TH

Low Temperature Reservoir at TL

QH

QL

W

W

QCOP L

revWLQ

loss

L

L

XXW

genHQ

Q

W

revWII

STX

X

X

X

)(or when 0when

input work Minimum

)(

)(

1or 1

1

1 that Noting

and II

LH

II

L

HII

LH

rev

rev

L

TTCOP

T

TCOP

TTCOP

COP

COP

W

QCOP

Refrigerator

-XW

-XQL

Ex

ergy

de

structio

n

Heat-Pump Cycles Energy conversion vs exergy destruction during a heat-pump cycle

W

QCOP H

Heat-

pu

mp

High Temperature Reservoir at TH

Low Temperature Reservoir at TL

QH

QL

W

Heat-pump

-XW

-XQH

WXW

H

H

LQ Q

T

TX

H

1

)()(1

or ndestructio

Exergy

WQT

TW

HQrevgenL

XW

H

H

L

ST

lost

lostH

H

L WQT

TW

1 arranging-reor

Heat-Pump Cycles

Heat-pump

-XW

-XQH

WXW

H

H

LQ Q

T

TX

H

1

ndestructioExergy

II)(

)(

: workactual by thet requiremen work minimum thedividingby calculated is cycle pump-heat theof efficiency law-second The

genLQ

Q

W

revW

STX

X

X

X

H

H

HL

II

H

LII

HL

rev

rev

H

TTCOP

T

TCOP

TTCOP

COP

COP

W

QCOP

1or 1

1

1 that Noting

and II

fixed. are and as long as

system theofproperty amic thermodyna is

tyavailabili Nonflow or

where

)(

: to from

equation above theintegrate and 2 1 process

aconsider shown system closed For the

)()(1)(

: workavailablefor equation General

00

00

00

1

021

21

000

1

000

0

workavailable of Rate

PT

A

vPsTea

VPSTEA

STXAAX

tttt

STsThmsThmQT

TSTVPE

dt

d

dt

dVPWX

n

i

geniQW

gen

out

o

in

o

i

n

i i

W

Nonflow Processes

Tn T2 T1

Q1 Q2 Qn Closed system

Cycles W T0

Nonflow Processes

)()(

)()(

:fullin exergy nonflow The

out. dropequation original in the termslast two that theNote

)(

:as expressed becan delivers

system closed amax work thereservoir,only theis atmosphere When the

)(

000000

000000

exergy nonflow theasknown is This

0

1

021

vvPssTeeaa

VVPSSTEEAAΦ

AAX

STXAAX

revW

n

i

geniQW

The nonflow exergy is the reversible work delivered by a fixed-mass system during a process in which the atmosphere is the only reservoir.

Steady-flow Processes

sThb

STHB

STbmbmX

STsThmsThmQT

TSTVPE

dt

d

dt

dVPWX

o

o

gen

outin

n

i

iQ

gen

outb

o

inb

on

i

X

i

i

W

iQ

0

0

0

1

000

1

)(

000

0

workavailable of Rate

:as defined isport each at ty availabili flow The

)(

)()(1)(

: workavailablefor equation General

Steady-flow Processes

gen

r

kkoutfinf

n

i

iQW

f

f

o

gen

r

kkoutin

n

i

iQW

gen

outin

n

i

iQW

STxmxmXX

bbx

x

sThb

bPT

rk

STbmbmXX

STbmbmXX

0

11

0

0000

000

0

11

0

1

)()()(

Hence

:as exergy flow definecan then we

such that , is ),( conditions talenvironmen standardat evaluatedty availabili flow theIf

.exchangersheat stream- twoand devices stream-single be wouldexamplespopular Most

and 1between streams ofnumber theis where

)()()(

as written becan

)(

slide previous in the obtained

equation The mix.not do streams the wheredevices through flow stream-multiConsider

Remember the flow exergy from Chp 4 The flow work is done against the fluid upstream in excess of the boundary work against the atmosphere such that exergy associated with this flow work:

xflow = Pv – P0v = (P – P0)v

Steady-flow Processes

gen

out

f

in

f

n

i

iQW

gen

outin

n

i

iQW

H

STxmxmXX

STbmbmXX

T

T

0

1

0

1

0

)(

:equation following thederive topossible isit

)(

equation the Using. etemperaturreservoir catmospheri

theand raturehigh tempe abetween operating cycle Rankine aConsider

Ẇt Ẇp

TH

T0

LQ

HQ

1

2 3

4

ẊQH

Boiler

1)( fxm

3)( fxm

2)( fxm

4)( fxmẊWt

-ẊWp

Pump

Cond.

Turb.

HQII X

Steady-flow Processes gen

out

f

in

f

n

i

iQW STxmxmXX 0

1

)(

ẊQH

Boiler

1)( fxm

3)( fxm

2)( fxm

4)( fxmẊWt

-ẊWp

Pump

Cond.

Turb.

HQII X

destroyedExergy

,0

outflowExergy

4

inflowExergy

3

,043

destroyedExergy

,0

outflowExergy

3

inflowExergy

2

,032

)()(

or

)()(0

:)( turbine theof case In the

)()(

or

)()(0

:boiler theof case In the

turbgenfWf

turbgenffW

tW

boilergenffQ

boilergenffQ

STxmXxm

STxmxmX

WX

STxmxmX

STxmxmX

t

t

t

H

H

Steady-flow Processes

gen

out

f

in

f

n

i

iQW STxmxmXX 0

1

)(

ẊQH

Boiler

1)( fxm

3)( fxm

2)( fxm

4)( fxmẊWt

-ẊWp

Pump

Cond.

Turb.

HQII X

)()(

)()(0

:)( pump theof case In the

finite. is )(exergy exit thehence and an greater th

is which , iscondenser theof ratureexit tempe The

)()(0

:condenser theof case In the

diagram theonshown not isit small, so isIt

,02

,021

10

1

ambient thetocondenser fromfer heat trans

todue destroyed isexergy stream of

portiont significanA

,014

fWpumpgenf

pumpgenffW

pW

f

condensergenff

xmXSTxm

STxmxmX

WX

xT

T

STxmxm

p

p

p

HOMEWORK Determine (by drawing an exergy wheel diagram) the

exergy flow with the associated exergy destruction components of each component of a simple vapor-compression refrigeration cycle. Write down the exergy balance equations for each component and state any assumptions made.

Mechanisms of Entropy Generation or Exergy Destruction

Heat Transfer across a Finite Temperature Difference

Flow with Friction

Mixing