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Exergy Analysis
ME 210 AdvancedThermodynamics
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Definitions
Exergy (also called Availability or Work otential!" themaxim#m #sef#l $ork that can be obtained from a system ata given state in a given environment% in other $ords& the most$ork yo# can get o#t of a system
'#rro#ndings" o#tside the system bo#ndaries Environment" the area of the s#rro#ndings not affected by the
rocess at any oint ()or examle& if yo# have a hot t#rbine&the air next to the t#rbine is $arm* The environment is thearea of the s#rro#ndings far eno#gh a$ay that the
temerat#re isn+t affected*! Dead 'tate" $hen a system is in thermodynamic e,#ilibri#m
$ith the environment& denoted by a s#bscrit -ero% at thisoint no more $ork can be done
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Examle
A coal.fired f#rnace is #sed in a o$er lant* /t delivers000 kW at 1000 * The environment is at 00 * Whatis the exergy of the added heat3 4o# can #se t$o stes
to solve this roblem* Determine the maxim#m ercentage of the heat that can beconverted to $ork*
5sing yo#r ans$er from the first art& determine the maxim#m$ork ossible*
This is the maxim#m $ork o#t#t ossible bet$een thegiven state and the dead state& i*e*& the heat+s exergy* /nthis case& 06 of the 000 kW is unavailable energy7itcan+t be converted to $ork*
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Why 't#dy Exergy3
/n the last several decades& exergy analysis has
beg#n to be #sed for system otimi-ation*
8y analy-ing the exergy destroyed by eachcomonent in a rocess& $e can see $here $e
sho#ld be foc#sing o#r efforts to imrove system
efficiency*
/t can also be #sed to comare comonents orsystems to hel make informed design decisions*
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9eversible Work
Wrev(reversible $ork!" the maxim#m amo#nt of$ork it+s ossible to rod#ce (or minim#mnecessary to in#t! in a rocess bet$een giveninitial and final states* :ote that this is differentfrom an isentroic rocess $here $e $ere givenan inlet state and solved for the exit state #sings2;s1* 'ince the exit and inlet states are both
fixed& the rocess is not necessarily isentroic* What t$o conditions $ill ca#se a rocess to beisentroic3
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/rreversibilities
/rreversibility& /" exergy destroyed% $asted
$ork otential* /t reresents energy that
co#ld have been converted into $ork b#t$as instead $asted
What are some so#rces of /3
To have high system efficiency& $e $ant /to be as small as ossible*
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/& cont*
/;Wrev& o#t
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'#rro#ndings Work& Ws#rr
>ere some $ork is
#sed to #sh the
atmosheric air (thes#rro#ndings! o#t of
the $ay% that $ork
can+t be #sed forother #roses*
( ) positive1200 == VVPdVPWsurr
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'#rro#ndings Work& Ws#rr& cont* >ere atm hels #sh the
iston in% this is gained
$ork* /n a rocess $here
the iston goes in and o#t
contin#ally& the s#rro#nding
$ork val#es cancel o#t*
What is Ws#rrfor a control
vol#me3
( ) negative120 VVPWsurr =
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'econd ?a$ Efficiency& //
Thermal efficiency tells #s $hat $e get o#t
comared to $hat $e #t in*
The second la$ efficiency tells #s ho$
m#ch $e get o#t comared to the
maxim#m ossible $e co#ld get o#t& given
the inlet and exit conditions*
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'econd ?a$ Efficiency& cont*
th&max;1.T?@T>;1.00@00;0*B 'ay th;0*C//;0*C@0*B2;0*2 We $ant a high th and //Another $ay to look at this" for
a $ork o#t#t device
//;W#@Wrev
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'econd ?a$ Efficiency& cont*
A general definition"
suppliedexergy
(I)destroyedexergy1
beginning)at theavailables(what'suppliedexergyprocess)after theavailables(what'recoveredexergy
=
=II
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Three Efficiency Definitions
The second t$o are defined for $ork
=5T5T devices
rev
uII
isentropic
actual
in
net
W
W
W
W
Q
W
=
=
=
Law2
Isentropic
Theral
nd
s
th
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Examle
A free-er is maintained at 20) by
removing heat from it at a rate of
8t#@min* The o$er in#t to the free-er is0*0 h& and the s#rro#nding air is )*
Determine a! the reversible o$er& b! the
irreversibility& an c! the second.la$efficiency of this free-er*
9ef" Fengel G 8oles& Thermodynamics& An Engineering Aroach& Cth edition& Mc.Hra$ >ill& 2002*!"
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Exergy
We can calc#late the exergy& I ($ork otential! at a givenstate* The $ork otential is a f#nction of the total energy of thesystem*
(remember that in a control mass& there $ill be no flo$ $ork!
IE(exergy d#e to kinetic energy!" J2
@2 (on a er #nit massbasis IE" gK
Iinternalenergy" #.#oLo(v.vo!.To(s.s0!
To see a derivation of this last e,#ation& see the aendices on
the $eb site* The oN stands for the dead state (atmoshericconditions!* /f a iston is at atmosheric ress#re andtemerat#re (the dead state!& it can+t do any $ork*
!" #" internal energy flow wor$ X X X X X= + + +
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Exergy of a Flosed 'ystem
Exergy of a closed system& er #nit mass , can befo#nd be adding all the terms
This gives #s the maxim#m $ork $e co#ld ossibly geto#t of a system*
5s#ally $e $ill be more interested in the change in
exergy from the beginning to end of a rocess* )or a closed system&
( ) ( ) ( )
2
2o o o o oV
u u P v v T s s gZ = + + +
2 1 % = =
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)or a control vol#me
Icv;IclosedLIflo$$ork;Icv@m (exergy er #nit mass! Iflo$ $ork;Wflo$.Wagainstatmos(here;v.ov
:o$ combine terms" #Lv;h% #oLovo;ho
( ) ( ) oooooooocv vPPvgzV
ssTvPvPuu ++++=2
2
( ) ( ) gzV
ssThh ooocv ++= 2
2
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Fhange in exergy
/f $e only have one fl#id stream
/f $e have m#ltile streams
( ) ( ) ( )122
12
2121212
2zzg
VVssThh o +
+==
++
++=
1
21
1112
22
222
22
gzV
sThmgzV
sThm oo
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Exergy 8alance We $ill #se these e,#ations in an exergy balance to
solve for s#ch ,#antities as reversible $ork or exergydestroyed*
Iin.Io#t.Idestroyed;Isys
Idestroyed is otential $ork that $as destroyed d#e toirreversibilities like friction*
Exergy can be transferred (Iin.Io#t! by heat& $ork& andmass flo$
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Exergy Transfer by >eat Transfer
As $e add heat to a system& $e
increase its ability to do $ork*
'ee Aendix 8 on $eb for adisc#ssion of ho$ to deal $ith cold
sinks*
===H
oHHheatT
TQQXW 1axax
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Exergy Transfer by Work and Mass
)lo$ /f $e do $ork on a system& $e increase its
ability to do $ork*
I$ork;W.Ws#rr for bo#ndary $ork I$ork;W for all other kinds of $ork
9emember
Imass;m
( )120 VVPWsurr =
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Idestroyed
Idestroyed;/;To'gen
'ee Aendix F on the $eb for a
derivation*
9evie$ from ME 2O
'sys;'in.'o#tL'gen
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Entroy Henerated& 'gen
)or a steady.state control vol#me& this leads #s to
)or a control mass& this becomes
>ere Tkis the temerat#re of the heat so#rce or heatsink (not the system temerat#re!*
=k
k
in
ii
out
eegenT
QsmsmS
=k
kgen
T
QSSS 12
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)inal E,#ation for Isys for control
mass
( )[ ] 12121 XXSTVVPWQT
Tgenook
k
o =
P Terms in Q R are W.Ws#rr;W#
P /f $e $ant to find Wrev& then To'gen;0 and
W#;Wrev
P :ote that if heat transfer is to@from the
s#rro#ndings& the S term dros o#t*
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Examle
A 12.ftrigid tank contains 9.1Ca at 0 sia
and C06 ,#ality* >eat is transferred no$ to the
refrigerant from a so#rce at 120) #ntil theress#re rises to B0 sia* Ass#ming the
s#rro#ndings to be at )& determine a! the
amo#nt of heat transfer bet$een the so#rce and
the refrigerant and b! the exergy destroyedd#ring the rocess*
9ef" Fengel and 8oles
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)inal E,#ation for Isys for control
vol#me
( )[ ] 12121 XXmmSTVVPWQ
T
Teeiigenook
k
o =+
( ) 01 =+
eigenok
k
o
mSTWQT
T
)or m#ltile fl#id streams& #nsteady flo$"
)or one fl#id streams& steady flo$"
To find Wrev& set 'gen;0* /f adiabatic& S;0*
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'et # the follo$ing roblems*
1* 9efrigerant at T1 and 1is throttled to a ress#re of 2*)ind the reversible $ork and exergy destroyed d#ringthis rocess* The atmoshere has a temerat#re of To*
2* Air at T1and 1$ith a velocity of J1enters a no--le andexits at 2and T2$ith a velocity of J2* There is a heatloss S from the no--le to the s#rro#ndings at To* )indthe exergy destroyed d#ring this rocess*
* Air enters a comressor at ambient conditions (Toand
o! and leaves at 2and T2* The comressor isdeliberately cooled& and there is a rate of heat loss of Sto the s#rro#ndings* The o$er in#t to the comressoris W9* )ind the rate of irreversibility& /& for this rocess*
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Examle
'ee hando#t
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Exergy Analysis for a Fycle& 1 fl#id
stream& steady flo$
( )
=
+
+
+
=
+++=
=
=
ink
in
outk
outo
lake
incond
o
turbine
chambercomb
boiler
o
pump
condgenturbinegenboilergenpumpgengen
kiegen
geno
T
Q
T
QmTI
T
Qss
T
Qss
T
Qss
T
Qssm
SSSSS
T
QssmS
STI
&&
&1
212
&&&&
*coponentafor
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'econd ?a$ Efficiency for a Fycle
IW
W
W
W
actualnet
actualnet
reversiblenet
actualnet
II
+==
&
&
&
&