CHAPTER 5 ENTROPY GENERATION Instructor: Prof. Dr. Uğur Atikol
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1 CAPER 5 ENROPY GENERAION Istructr: Pr. Dr. Uğur Atkl
2 Chapter 5 Etrpy Geerat (Exergy Destruct Outle st Avalable rk Cycles eat ege cycles Rergerat cycles eat pump cycles Nlw Prcesses teady-flw Prcesses Exergy wheel dagrams
3 st Avalable rk m Atmspherc temperature ad pressure reservr at (,P 2 Atmsphere ystem... P dv P u dv P rk de agast the atmsphere dv m electrcal shear (All mdes wrk traser u P dv magetc Reservr at Reservr at 2 Reservr at
4 st Avalable rk Frst law: de Nte: mh h h m h s kw as methalpy, such that V h 2 2 gz m ystem 2 2 m ecd law: d ms m s
5 st Avalable rk s m ms d h m mh de lst lst s h m s h m E d s h m s h m E d ece hwever we kw that herere erally: ( ( ( hece : zer, s he ersble ( ( ( betwee the tw equats : Elmate Als kw as «exergy destruct des» r «Irersblty»
6 st Avalable rk s always pstve althugh lst (remember lst ad ca be ether pstve r egatve rk prducg devces lst s ve lst s ve rk absrbg devces he ma purpse studyg the lst avalable wrk s t dagse the areas where rersbltes are takg place a prsess s that thermdyamc mprvemets ca be made.
7 st Avalable rk he the system s dg wrk agast the atmsphere that has pressure P the the atmsphere csumes a wrk rate P dv such that : Rate avalable wrk P dv I mst lw systems P dv/ =, therere Ẋ = Ẇ (.e., exergy traser by wrk s smply the wrk tsel d ( E PV m ( h s m ( h s
8 st Avalable rk dv I the ersble lmt : P d ( E PV Maxmum delvery avalable pwer Accumulat lw exergy dφ Exergy taser wth heat traser m ( h s m( h s Itake lw exergy Release lw exergy wth mass lw wth mass lw Ψ m Ψ m Itake lw exergy wth mass lw m Accumulat lw exergy Evrmet (, P dφ Maxmum delvery avalable mechacal pwer Release lw exergy wth mass lw m
9 st Avalable rk st avalable wrk s deed as the derece betwee the maxmum avalable wrk ad the actual wrk. Alteratvely t ca be deed as: ame as Ẇ lst lst ( ame as Ẋ des Evrmet (, P Actual wrk m dφ lst st avalable wrk st exergy Exergy destruct Irersbltes m
10 st Avalable rk Exergy balace the pe system dscussed ca be shw a lw dagram as llws: Exergy lw Exergy lw m dφ lst m
11 st Exergy Cycles Csder as clsed systems that perate a tegral umber cycles. he celg value r avalable pwer (maxmum avalable pwer s ( Exergy ctet heat traser (,, ca be expressed as 2 herere the lst avalable wrk r clsed systems peratg cycles: lst ( ( 2 Clsed system Cycles
12 eat Ege Cycles Frst ad secd laws state lst lst lst temperature Als ca be expressed as : that ca be expressed as llws s assumed t be : Obtaed by applyg the det etrpy t the 2 reservrs. s -ve urce eat Ege k Ẇ
13 eat Ege Cycles emperature -eergy dagram r a heat ege cycle prpsed by Adra Beja Reversble Irersble ta sce lst lst,, ta r ta lst lst ta
14 eat Ege Cycles Cmpars betwee the rst- ad secd-law ececy a heatege cycle gh emperature Reservr at Exergy traser by heat traser E eat Ege eat Ege Destruct Exergy II x E II I = x II w emperature Reservr at where (
15 eat Ege Cycles ecd-law ececy a heat-ege cycle ca als be expressed as llws: ( lst II ( ( ( I I (.e., II II Relatshp betwee rst ad secd law ececes: ad herere, e kw that wrk traser s the same as the exergy traser asscated wth t I II II (
16 Rergerat Cycles hey are clsed systems cmmucat wth tw heat reservrs ( the cld space (at rm whch rergerat lad s extracted (2 the ambet (at t whch heat s rejected Frst ad secd laws state that : lst ere dead state - temperature ambet, whch s. wll be tsel wth a ( ve sg Obtaed by applyg the det etrpy t the 2 reservrs. s -ve lst s the temperature ca be expressed as llws : hs term wll be egatve ( rk put s a egatve umber the Ambet Rergeratr Rergerated space Ẇ Rearragg lst
17 Rergerat Cycles emperature -eergy dagram r a rergerat cycle prpsed by Adra Beja Reversble Irersble lst lst ta sce lst ta lst, r ta ta
18 Rergerat Cycles Eergy cvers vs exergy destruct durg a rergerat cycle gh emperature Reservr at Rergeratr - COP Rergeratr Exergy destruct - II ( Mmum wrk put whe lss r whe ( ( w emperature Reservr at COP ad Ntg that COP II COP II r COP COP COP II
19 eat-pump Cycles Eergy cvers vs exergy destruct durg a heat-pump cycle gh emperature Reservr at eat-pump - COP eat-pump - w emperature Reservr at lst Exergy destruct ( ( r r re - arragg lst
20 eat-pump Cycles he secd - law ececy the heat - pump cycle s calculated by dvdg the mmum wrk requremet by the actual wrk : eat-pump - - II ( ( Exergy destruct COP COP ad II COP Ntg that COP II II COP COP r
21 Nlw Prcesses Geeral equat r avalable wrk : dv P Rate avalable wrk d ( E PV Fr the clsed system shw csder a prcess 2 ad tegrate the abve equat rm t t t t t : A A 2 ( where A E P V Nlw avalablty r a e s P v A s a thermdyamc prperty the system as lg as ad P are xed. 2 m ( h s 2 m ( h s 2 Clsed system Cycles
22 Nlw Prcesses A A 2 ( he the atmsphere s the ly reservr, the max wrk a delvers ca be expressed as : clsed system ( A A hs s kw as the lw exergy Nte that the last tw terms the rgal equat drp. he lw exergy ull : Φ A A E a a e e E ( s ( s P ( V P ( v v V he lw exergy s the ersble wrk delvered by a xed-mass system durg a prcess whch the atmsphere s the ly reservr.
23 teady-lw Prcesses s h b B mb mb s h m s h m PV E d dv P b b ( avalable wrk Rate deed as : he lw avalablty at each prt s ( ( ( ( equat r avalable wrk : Geeral
24 teady-lw Prcesses Csder mult - stream lw thrugh devces where the streams d t mx. he equat btaed the pus slde x b b ( ( ( ca be wrtte as r k r k mb ( mb b h s the we ca dee lw exergy x mb ( mb ( mx ( mx k k where k s the umber streams betwee ad r Mst ppular examples wuld be sgle - stream devces ad tw - stream heat exchagers. ece I the lw avalablty evaluated at stadard evrmetal cs (, P s b as :, such that Remember the lw exergy rm Chp 4 he lw wrk s de agast the lud upstream excess the budary wrk agast the atmsphere such that exergy asscated wth ths lw wrk: x lw = Pv P v = (P P v
25 teady-lw Prcesses Csder a Rake cycle peratg betwee a hgh temperature ad the atmspherc reservr temperature. Usg the equat Bler ( mb mb ( t s pssble t derve the llwg equat : 2 mx 3 m x Ẋ ( m x 2 Pump -Ẋ p ( m x Cd. urb. ( m x ( m x 4 3 Ẋ t Ẇ p Ẇ t 4 II
26 teady-lw Prcesses ( mx m x Bler I the case the bler : m ( x m ( x r m( x 2 Exergy lw 2 m ( x 3 Exergy lw 3, bler, bler Exergy destryed Ẋ ( m x 2 Pump ( m x urb. ( m x 3 I the case r t m ( x 3 Exergy lw m ( x the turbe ( 3 m ( x Exergy lw 4 m ( x 4 t t :, turb, turb Exergy destryed t -Ẋ p Cd. ( m x 4 II Ẋ t
27 teady-lw Prcesses ( mx m x Bler I the case m ( x he ext temperature greater tha I the case p m ( x m ( x 4 2 the cdeser : m ( x ad hece the ext exergy ( x the pump ( m ( x, pump It s s small,t s t shw the dagram, cdeser A sgcat prt stream exergy s destryed due t heat traser rm cdeser t the ambet the cdeser s, whch s 2 p p p m ( x :, pump s te. Ẋ ( m x 2 Pump -Ẋ p ( m x Cd. urb. ( m x ( m x 4 3 II Ẋ t
28 OMEORK Determe (by drawg a exergy wheel dagram the exergy lw wth the asscated exergy destruct cmpets each cmpet a smple vaprcmpress rergerat cycle. rte dw the exergy balace equats r each cmpet ad state ay assumpts made.
29 Mechasms Etrpy Geerat r Exergy Destruct eat raser acrss a Fte emperature Derece Flw wth Frct Mxg
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