Chap IV Exergy Analysis( 火用 )

Transcription

1 Chap IV Exrgy Analyss( 火用 ) Updat on 4// Exrgy analyss s usd to fnd out th nrgy utlzaton ffcncy of an nrgy convrson systm. It s known that any nrgy convrson systm should oby th scond law of thrmodynamcs. owvr, th nrgy convrson systm s usually composd of svral procsss. It s ncssary to know th convrson ffcncy of ach procss such that fforts of mprovmnt could b focusd on th last ffcnt procss. (4.) Exrgy Accordng to th scond law of thrmodynamcs, t s not possbl to totally convrt thrmal nrgy nto work. h nrgy contand nsd any systm could b only partally convrtd nto work thortcally. owvr, du to th rrsbl ffct nsd th systm, th actual work s vn lss than xpctd. Exrgy s th maxmum avalabl work that can b xtractd from a systm whn th systm undrgos a procss from ts ntal stat to th stat n qulbrum wth ts nvronmnt. Equvalnt nams of xrgy ar avalablty, avalabl nrgy, xrgc nrgy, ssrgy, utlzabl nrgy, avalabl work, maxmum work, rsbl work, and dal work. Exrgy s not a thrmodynamc proprty. Its valu dpnds on th stats of th systm as wll as th stat of ts nvronmnt. (4..). Dad Stat Exrgy s a masur of th potntal of a systm to do work as t undrgos a procss from ts orgnal stat to a fnal stat that t achvs qulbrum wth t surroundngs. h surroundngs ar oftn also calld a rfrnc nvronmnt. Aftr th systm and surroundngs rach qulbrum, th systm won't chang or b changd. hs s known as th systm dad stat, and t has an xrgy of zro. Whn a systm s n qulbrum wth ts nvronmnt, t s not possbl to do any work by tslf. All knds of dffrnc btwn a systm and ts nvronmnt can b usd to do work. A dffrnc n tmpratur would caus hat transfr whch could n turn b convrtd to work. A dffrnc n prssur would promot work drctly, and a dffrnc n concntraton would nduc mass transfr whch could also b convrtd to work. Advancd hrmodynamcs NCU ME dpt 頁

2 Q W, th work of coal powr plant u W, th work of wnd powr plant W, th work of hydro powr plant C m W, th work of osmotc powr plant W, th work of dppng brd As dffrnc n potntal vanshs, changs would cas, and no mor work can b drvd. A dad stat s th stat that all th proprts of a systm ar dntcal to thos of th nvronmnt such that no drvng forc xsts btwn th systm and ts nvronmnt, and no work can b drvd.,, C C, u, Assgnmnt 4.: It s stmatd that 3 W of solar nrgy s absorbd by atmosphr. Snc th atmosphr contans hug amount of thrmal nrgy, s t possbl to mak us of ths nrgy and convrt t to work? las plac your own commnt. Novmbr 4, 9 6:5 AM S Norway opns world's frst osmotc powr plant by Rutrs Norway opnd on usday th world's frst osmotc powr plant, whch producs mssons-fr lctrcty by mxng frsh watr and sa watr through a spcal mmbran. Stat-ownd utlty Statkraft's prototyp plant, whch for now wll produc a tny klowatts to 4 klowatts of powr or nough to run a coff machn, wll nabl Statkraft to tst and dvlop th tchnology ndd to drv down producton costs. h plant s drvn by osmoss that naturally draws frsh watr across a mmbran and toward th sawatr sd. hs crats hghr prssur on th sa watr sd, drvng a turbn and producng lctrcty. "Whl salt mght not sav th world alon, w blv osmotc powr wll b an ntrstng part of th rnwabl nrgy mx of th futur," Statkraft Chf Excutv Baard Mkklsn told rportrs. Statkraft, Europ's largst producr of rnwabl nrgy wth xprnc n hydropowr that provds narly all of Norway's lctrcty, ams to bgn buldng commrcal osmotc powr plants by 5. h man ssu s to mprov th ffcncy of th mmbran from around watt pr squar mtr now to som 5 watts, whch Statkraft says would mak osmotc powr costs comparabl to thos from othr rnwabl sourcs. h prototyp, on th Oslo fjord and about 4 mls south of th Norwgan captal, has about, squar mtrs of mmbran. Futur full-scal plants producng 5 mgawatts of lctrcty, nough to provd powr for 3, Europan housholds, Advancd hrmodynamcs NCU ME dpt 頁

3 would b as larg as a football stadum and rqur som 5 mllon squar mtrs of mmbran, Statkraft sad. Onc nw mmbran "archtctur" s solvd, Statkraft blvs th global producton capacty for osmotc nrgy could amount to,6 to,7 trawatt hours annually, or about half of th Europan Unon's total lctrcty dmand. Europ's osmotc powr potntal s sn at 8 trawatts, or about 5 prcnt of total consumpton, whch could hlp th bloc rach rnwabl nrgy goals st to curb mssons of hat-trappng gass and lmt global warmng. Osmotc powr, whch can b locatd anywhr whr clan frsh watr runs nto th sa, s sn as mor rlabl than mor varabl wnd or solar nrgy. r s th company's llustraton of how th plant works. (Crdt: Statkraft) Advancd hrmodynamcs NCU ME dpt 頁 3

4 (4.). Rvrsbl Work and Avalablty Rvrsbl work s th maxmum work that can b xtractd from a systm f th systm movd from th currnt stat to th dad stat. A B C It s notd that th amount of work that a systm may dlvr dpnds on th procss that th systm undrgos from th frst stat to th scond stat. owvr, thr xsts a maxmum valu of work that no othr procss may produc mor work than ths valu. h valuaton of xrgy s basd on th prncpl of ncras of ntropy. If a systm procds from ts orgnal stat to a fnal stat n qulbrum wth t surroundngs, no mattr what that procss s, th nt ntropy chang of th systm as wll as ts nvronmnt would nvr b ngatv. Snt Ssys Snv In an solatd systm, th ntropy always ncrass all th tm. S In a closd systm, th ncras of ntropy can b attrbutd to th xtrnal rrsblty and th ntrnal rrsblty. S S S Q( ) nt sys v In an opn systm, th nt ncras can b attrbutd to th xtrnal rrsblty and th ntrnal rrsblty. ds Q j dt nt j j Advancd hrmodynamcs NCU ME dpt 頁 4

5 (4..). Rvrsbl Work for a Non-ractng closd Systm Stat Stat Q W a If a systm undrgos a procss from stat to stat, and rcvs an amount of hat Q from a hgh tmpratur rsrvor at durng th procss, th work output and th nt ntropy chang ar Q S, Snt S Ssys S S W Q ( U U ) a Q Snc th tmpratur of th rsrvor ( ) must b hghr than that of th systm ( ), thr s a fnt dffrnc of tmpratur ( = - )btwn th rsrvor and th systm. Entropy s producd durng th hat transfr procss from th rsrvor to th systm. In ordr to rduc th ntropy ncras du to th fnt tmpratur dffrnc hat transfr, a nw approach should b conductd. A Carnot ngn should b opratd btwn th rsrvor and th systm n ordr to avod th fnt tmpratur dffrnc hat transfr. owvr, as th sam amount of hat (Q ) s transfrrd from th rsrvor to th Carnot ngn, part of t wll b convrtd to work (W E = Q -Q L ), and only th rst of hat (Q L ) wll b transfrrd to th systm. As a rsult, th amount of hat transfrrd to th systm s lss than Q, and th systm wll not undrgo th procss from stat to stat bcaus th hat transfr amount s not adquat. In ordr to gt suffcnt amount of hat to complt th procss, A Carnot rfrgrator has to b opratd btwn th systm and th nvronmnt to supply th Advancd hrmodynamcs NCU ME dpt 頁 5

6 shortag of hat (Q -Q L ). If th hat absorbd from th nvronmnt by th Carnot rfrgrator s Q, th work nput to th rfrgrator should b W R = Q -QL- Q. Q W E = Q -Q Stat Stat Q L W a Q -Q L W R = Q -QL-Q Q Snc n th nw approach, ntropy ncras s rducd to zro, a ntropy balanc could b conductd as follows. Q Q S nt S S h hat transfr from th nvronmnt to th Carnot rfrgrator (Q ) should b Q Q ( S S) h work dlvrd by th Carnot ngn s W Q Q E L h work dlvrd to th Carnot rfrgrator s W Q Q Q R L Advancd hrmodynamcs NCU ME dpt 頁 6

7 h total work of th procss s th sum of thr trms. W Wa WE WR Q ( U U) Q QL ( Q QL Q) Q Q ( U U) Q Q ( U U) ( S S) ( U U) ( S S) Q ( ) ( U S) ( US) Q ( ) w ( u u) ( s s) ( v v) q ( ) I W Wa Wcarnot Snt Scond law ffcncy: th rato of actual work to rsbl work. Wa nd for postv work W W nd for ngatv work Wa Exampl: An ron block of kg at 3 s coold down naturally n an atmosphr of 5. Calculat th rsbl work and th rrsblty of th procss. h hat capacty of ron s 45 J/kg-K. Exampl: An ron block of kg at 3 s mmrsd nto a basn of watr at 5. h volum of watr s ltrs. Assumng th atmosphrc tmpratur s 5, calculat th rsbl work and th rrsblty of th procss. mc A va.447 = 4.47 kj mc B vb 4.86 = 48.6 kj av = 7.9 S macvaln mbcvbln A = =.747 kj/k B ( W ) S U Q S =35.6 kj I W Wa =35.6 kj, Wa nd = W Advancd hrmodynamcs NCU ME dpt 頁 7

8 Exampl An nsulatd rgd chambr s dvdd nto two qual parts wth a daphragm. h daphragm nthr movs nor conducts hat. h lft part s flld wth ar at 3 bars and 5, and th rght part s kpt at vacuum. If th daphragm rupturs and th whol chambr s flld wth ar, calculat th rsbl work and th rrsblty of th procss assumng th atmosphrc tmpratur s 5. 3 bars Vacuum 5.5 bars 5.5 bars 5 (K) (bar) V (L) Q L =U 3 -U V Advancd hrmodynamcs NCU ME dpt 頁 8

9 Assgnmnt 4. wo ron blocks ar of th sam wght and at dffrnt tmpratur. On s at 3 and th othr on s at 3. A Carnot ngn uss ths two blocks as thrmal rsrvor and convrts hat to work. ow much work can b convrtd at most? 3 3 W=? Assgnmnt 4.3: An nsulatd rgd chambr s dvdd nto two parts wth a daphragm. h daphragm s hat conductv and can mov wthout frcton. h lft part s flld wth ar of kg at 3 bars and 5, and th rght part s flld wth ar at 3 and.5 bars wth a volum of 4 ltrs. Now lt th daphragm mov frly untl th prssur and th tmpratur on both sds ar qual. Calculat th rsbl work and th rrsblty of th procss assumng th atmosphrc tmpratur s 5. If th systm undrgos a procss to th dad stat, th avalabl work s w ( u u) ( s s) q ( ) Snc th nvronmnt s at th prssur of,xpanson of th systm would xpl th ar and do work to ts nvronmnt, and th avalabl work would b rducd f th work to th nvronmnt s countd. waval w ( v v) ( u u) ( s s) ( v v) q ( ) hs s th maxmum work that s avalabl f th systm undrgos a procss to th dad stat. W dfn th avalablty of th systm as uu ( ss) ( vv) q ( ) And th maxmum work that s avalabl f th systm undrgos a procss from stat to stat could b obtand as Advancd hrmodynamcs NCU ME dpt 頁 9

10 w ( u u ) ( s s ) ( v v ) q ( ) q ( ) aval If If, th procss rqurs work n., thr s a postv work, whch mans that th procss would do work out. (4..). Rvrsbl Work for a Non-ractng opn Systm V V w ( h gz) ( h gz) ( s s) q ( ) If kntc nrgy and gravtatonal potntal nrgy can b nglctd, th rsbl work s w h h( s s) q ( ) If th hat transfr s towards th nvronmnt, =, thn th rsbl work s w h h ( s s ) If th systm undrgos a procss to th dad stat, th avalabl work s w ( h h) ( s s) q ( ) [ hs] [ h s] q ( ) h xrgy of th systm s dfnd as h s such that th avalabl work f th systm undrgos a procss to th dad stat can b obtand as w q ( ) s th potntal of th systm to dlvr work. hus th rsbl work of a systm gong from stat to stat s w h h( s s) q ( ) q ( ) Exampl: Ar at 3 ka and 5 flows through a throttl valv and drops to th prssur of ka at a rat of kg/sc. Calculat th rsbl work of th procss. Advancd hrmodynamcs NCU ME dpt 頁

11 Exampl: A stram of hot ar flow at 3 s coold down to 5 at a rat of kg/sc. Calculat th rsbl work of th procss. Exampl: ot ar at 3 ka and 3 flows through a turbn at a rat of kg/sc, and drops to a prssur of ka. If th ffcncy of th turbn s 85%, calculat th rsbl work of th procss and th scond law ffcncy. Assgnmnt 4.4: Ar s coold by watr n a hat xchangr. Ar flows nto th hat xchangr at wth th flow rat s kg/sc. Watr flows nto th hat xchangr at 3 wth th flow rat 5 kg/sc. If ar s to b coold to 4, calculat th ntropy gnraton nsd th hat xchangr, and th rsbl work of ths procss. Advancd hrmodynamcs NCU ME dpt 頁

12 Assgnmnt 4.5 Ar s coold by watr n a hat xchangr. Ar flows nto th hat xchangr at wth th flow rat s kg/sc. Watr flows nto th hat xchangr at wth th flow rat kg/sc. ow much work can b obtand f Carnot ngns ar placd btwn th ar flow and th watr flow. W mc ( ) mc ( ) W a p a a w w w w mc a p w w ( a a) mc w w a w S macpln mwcwln a w mc a p mc w w W a a w w mc w w a a w w mc a p mc a a p a a ln ln ( ) mc w w a mc w ww a.45 a a ln ln ( ) Advancd hrmodynamcs NCU ME dpt 頁

13 a a.ln ln a a mc a.8, 98.4 a p a, w w ( a a) 373 mc w w W m c ( ) m c ( ) a p a a w w w w Advancd hrmodynamcs NCU ME dpt 頁 3

14 (4..3). Global Exrgy Rsrvors, Flux, and Anthropognc Dstructon h cascadng flow of xrgy from prmary rsrvors nto scondary rsrvors and on to ts vntual natural or anthropognc dstructon can b summarzd as a systm of xrgy rsrvors and flows. h major xrgy flux s suppld by drct sun lght whch s about 6 tra-watts. h amount of xrgy from sun lght n a yar s about 5 ZJ. It s notd that th global nrgy consumpton at th yar of 5 s 46 QBtu, whch s quvalnt to.487 ZJ. hat s, th amount of xrgy from sun lght n a yar can b usd to supply 485 yars of nrgy consumpton at th lvl of 5. owvr, only a vry small porton of th xrgy flux s utlzd by human and consumd n anthropognc actvts. Most of th xrgy flux has bn dstructd and dsspatd n th natur. ug amount of xrgy s stord undr ground as th form of crustal thrmal nrgy whch s quvalnt of 935 tms of th amount of xrgy from sun lght n a yar. An vn gratr amount of xrgy s stord nsd th nuclus of dutrum whch s th sotop of hydrogn. Advancd hrmodynamcs NCU ME dpt 頁 4

15 (4.3). Rvrsbl work of procss (4.3.). Closd systm comprsson procss In a closd systm, th rsbl work s as th followng. w ( u u) ( s s) ( v v) q ( ) (4.3..). Adabatc procss q w ( u u ) ( s s ) ( v v ) If th procss s sntropc V s s cv ln( ) Rln( ) V k V s V w u u ( v v ) c ( ) ( v v ) s v s owvr, f th procss s not sntropc V s s cv ln( ) Rln( ) V k V V wa u u( v v) cv( ) ( v v) w wa k v c v ( v v) w v nd w c ( ) ( v v ) a v Exampl:Calculat th rsbl work of an nsulatd pston to comprss kg of ar at ka and 5 to a volum of. m 3. = ka, = 98 K,v =.8553 m 3 /kg,v =. m 3 /kg s s w w a I Advancd hrmodynamcs NCU ME dpt 頁 5

16 Not: h xtra nrgy to comprss ar s usd to ovrcom th frcton forc, and wll dsspat as hat to ar. As a rsult, th fnal tmpratur s gttng hghr (4.3..). Comprsson wth hat transfr ston comprsson procss wth hat transfr to or from th cylndr wall: w u u( s s) ( v v) q( ) w wu u( v v) q u u( s s) q( ) w w nd wa u uq Exampl:Calculat th rsbl work to comprss kg of ar at ka and 5 to a volum of.5 m 3 n a polytropc procss wth n=.3. h atmosphrc tmpratur s 5, and th atmosphrc prssur s ka. = ka, = 98 K,v =.8553 m 3 /kg = (v / v ).3 =.94 ka = (v / v ).3 = 35. K Δs sys = kj/kg-k q= kj/kg Δs n =.479 kj/kg-k Δs nt =.336 kj/kg-k waval ( u u) ( s s) ( v v) q ( ) = (35.-98) ( ) = kj Wa ( V V ) ( VV ) =-4.7 kj n I W Wa =.966 kj W nd =.93 Wa Not: at transfr occurs btwn comprssd ar and cylndr wall. h wall tmpratur s not ncssary dntcal to that of atmosphrc tmpratur. owvr, fnally th hat transfr wll go to th atmosphr at all. Advancd hrmodynamcs NCU ME dpt 頁 6

17 Assgnmnt 4.4: Calculat th rsbl work to comprss m 3 of ar at ka and 5 to a prssur of Ma n a polytropc procss wth n=.5. h atmosphrc tmpratur s 5, and th atmosphrc prssur s ka (4.3..3). Isothrmal comprsson Durng th comprsson procss, th tmpratur s kpt at. w u u s s v v q ( ) ( ) ( ) w v Rln ( v v) v wu u ( v v ) q( v v ) q nd v Rln ( v v) w v w q( v v ) a In an actual sothrmal comprsson procss, th hat that should b rmovd out of th systm s hghr than that of a rsbl sothrmal comprsson procss. h xtra hat transfr s convrtd from th frcton work Exampl:Calculat th rsbl work to comprss kg of ar at ka and 5 to a volum of.5 m 3 sothrmally. = ka, = 98 K,v =.8553 m 3 /kg = (v / v ) = 7.6 ka w a = R ln( ) =-45.9 kj/kg Δs sys =- Rln( ) =-.54 kj/kg-k q= kj/kg W = Δs sys =-45.9 kj/kg Advancd hrmodynamcs NCU ME dpt 頁 7

18 h actual work s mor than 45.9 kj/kg to ar at ka and 5 to a volum of.5 m 3 sothrmally. Onc th actual work s masurd, th scond law ffcncy can thn b obtand (4.3.). Opn systm comprsson procss V V w ( h gz ) ( h gz ) ( s s ) q ( ) (4.3..). Adabatc axal typ comprssor w h h ( s s ) a w h h qh h For sntropc comprsson s ws hs h w s, w w a, c, nd w h h w a For comprssor wth ffcncy lss than. s s, w w a, nd, c a c ws w a s =sntropc work/adabatc work c k k k k s s cpln( ) Rln( ) cpln Rln( ) c k k k k w h h( s s) c p cpln Rln( ) c c Advancd hrmodynamcs NCU ME dpt 頁 8

19 Advancd hrmodynamcs NCU ME dpt 頁 9 k k a p c w h h c ln ln( ) k k a p c I w w c R ln ln( ) k k p c nd k a k p c c R w w c For a comprssor wth gvn ffcncy, ts scond law ffcncy can b calculatd f th prssur rato and th nvronmntal tmpratur ar known Exampl:Calculat th rsbl work of an nsulatd comprssor to comprss kg of ar at ka and 5 to a prssur of bars f th comprssor ffcncy s.85. h atmosphrc tmpratur s 5. = ka, = 98 K,v =.8553 m 3 /kg,v =.5 m 3 /kg k k c =64.3 K w a = kj/kg Δs sys =.8 kj/kg-k I = 4.44 kj/kg W = kj/kg nd

20 Assgnmnt 4.5: Calculat th rsbl work to comprss m 3 of ar at ka and 5 to a prssur of Ma n a polytropc procss wth n=.5. h atmosphrc tmpratur s 5, and th atmosphrc prssur s ka (4.3..). Adabatc axal typ comprssor wth hat transfr w h h s s q w h h q a ( ) ( ) w I w wa ( s s) q w nd h h s s q w w h h q a ( ) ( ) w = rsbl work/actual work Exampl:Calculat th rsbl work to comprss kg of ar at ka and 5 to a volum of.5 m 3.n a polytropc procss wth n=.3. = ka, = 98 K,v =.8553 m 3 /kg = (v / v ).3 =.94 ka = (v / v ).3 = 35. K n w a = ( V V ) = kj/kg n Δs sys = kj/kg-k q= kj/kg W = kj/kg I =.3 kj/kg nd.9853 Advancd hrmodynamcs NCU ME dpt 頁

21 (4.3.3). Adabatc xpanson procss Exampl: gas turbn w h h ( s s ) For xpanson wth ffcncy lss than., s s, w w a, nd c wa w s s k k k k s s cpln( ) Rln( ) cpln Rln( ) I w w ( s s ) a nd h h h h ( s s ) Exampl:Calculat th rsbl work of an nsulatd turbn to xpand kg of ar at ka and 8 to ka f th turbn ffcncy s.85. = ka, = 73 K, = ka = K,w a = 44.6 kj/kg Δs sys =.3 kj/kg-k I = kj/kg W = kj/kg nd.985 Advancd hrmodynamcs NCU ME dpt 頁

22 Assgnmnt 4.6: In a gas turbn ngn, ar s comprssd from 5 and ka to th prssur of Ma, and thn hatd to K n th combustor. h nlt ar flow rat s m 3 /sc. If th comprssor ffcncy s 85%, th turbn ffcncy s 9%, calculat th powr of ngn and th rsbl work. (4.3.4). Unconstrand xpanson procss Exampl: throttl valv, xpanson valv, flash chambr V V qh gz h gz w q, w h h w h h ( s s ) ( s s ) For dal gas wth constant hat capacty, s s c R R p ln( ) ln( ) ln( ) w R ln( ) wa I R ln( ) Snc thr s no work output for unconstrand xpanson procss, th rsbl work s th xrgy lost du to th unconstrand xpanson Exampl:Calculat th rsbl work of ar flowng through a throttl valv wth Advancd hrmodynamcs NCU ME dpt 頁

23 th upstram prssur of ka and th downstram prssur of 5 ka. w I R =59.8 kj/kg ln( ) Exampl:Calculat th rsbl work of mthan at 8 Ma and K xpandng to th prssur of ka. = 8 Ma, = K,h =88.54,s =7.69 =.3 ka,h = x*5.33 x =.7349,s = *4.576 = 8.95 Δs sys =.856 kj/kg-k W = 33.5 kj/kg I = 33.5 kj/kg (4.3.5). Sparaton procss Exampl: flash chambr, sparaton of vapor and lqud. V V qh gz h gz w Advancd hrmodynamcs NCU ME dpt 頁 3

24 q, w h h xh ( x) h h xh g f f fg It s notd that h s th nthalpy of condnsd flud aftr condnsr and c f s th hat capacty of flud. h h c ( ) xh f f fg cf ( ) x h fg s xsg ( x) s f w h h ( s s ) ( xs ( x) s s ) ( xs s s ) g f fg f s s c f f ln cs w ( ( ) c ln ) c ( ln ) c ( ln ) s f fg f f f hfg s ln c f s ln( )... c f Usually th tmpratur dffrnc s lss than th tmpratur aftr xpanson. s c f Accordng to th Clapyron Equaton, th saturaton prssur and saturaton Advancd hrmodynamcs NCU ME dpt 頁 4

25 tmpratur durng phas transton s rlatd as th followng. hfg hfg h fg ln ( ) R R R R ln h fg s R R ln ln ln cf hfg hfg Exampl:Calculat th rsbl work of comprssd watr at Ma and 8 undrgong an xpanson procss to ka n a flash chambr. = ka, = 8,h =767.84,s =.75 = ka,h = x*58 x =.445,s =.36* *.445 =.778 Δs sys =.53 kj/kg-k W = 4.99 kj/kg I = 4.99 kj/kg Assgnmnt 4.7: A rfrgraton systm works wth R34a as th rfrgrant. coolng load s tons at th tmpratur of -4 and th comprssor ffcncy s 9%. Fnd out th CO of th systm, th rfrgrant rat, and th ntropy ncras n ach procss. It s known that =5. (). A sngl stag systm s usd wth th followng stats: =.564 bar, =-4, =9. bar, 3 =3 (). A two-stag systm s usd wth th followng stats: =.564 bar, =-4, =.8 bar, 4 =9. bar, 5 = h Advancd hrmodynamcs NCU ME dpt 頁 5

26 (4.3.6). Mxng procss Exampl: fd watr hatr, mxng of dffrnt componnts mh mh s ms ms w ( ) ms ms xsg Exampl:Mthan mxs wth stochomtrc ar at ka nd 5, calculat th rsbl work of th mxng procss. = ka, = 8,h =767.84,s =.75 = ka,h = x*58 x =.445,s =.36* *.445 =.778 Δs sys =.53 kj/kg-k W = 4.99 kj/kg I = 4.99 kj/kg (4.3.7). at transfr procss Exampl: hat xchangr, condnsr, rgnrator mh A A mh B B mh A A mh B B mc( ) mc( ) A A A A B B B B s m ( s s ) m ( s s ) A A A B B B w h h ( s s ) [ m ( s s ) m ( s s )] A A A B B B Assum that A B, A s usd to hat up B. Advancd hrmodynamcs NCU ME dpt 頁 6

27 If mc A A mc B B, thn A A B B. h maxmum achvabl lvl of th outlt tmpratur of B s B A. owvr, mc B B ( ) mc A A B B A B B A A Dfn th ffctvnss of th hat xchangr as B A B B, ( ) B B A B ( ) A A B B A A B A B B A smacaln( ) mbcbln( ) maca[ln( ) ln( )], s A B A B, B A s maca[ln( ) ln( )] A B B A B A.5, smaca[ln( )( ) ln4] maca[ln( ) ln4] A B mc A Aln ( )/ B A A B A B If mc A A mc B B, thn A A B B, and B A. h maxmum achvabl lvl of th outlt tmpratur of B s B A. owvr, mc B B mc B B mc B B ( ) ( ) mc mc mc A A B B A B B A A A A A A Dfn th ffctvnss of th hat xchangr as B A B B, ( ) B B A B mc B B mc B B mc B B ( ) ( ) mc mc mc A A A B A B A A A A A A Advancd hrmodynamcs NCU ME dpt 頁 7

28 A B mc B B mc B B B mc B B A smacaln( ) mbcbln( ) maca[ln( ) ln( )] mc mc mc A B A A A A A A A B Exampl:ot watr at s usd to hat up ol at. It s known that mc B B mc. A =, B =, A =- ε, B = ε A A ε A B s It s notcd that vn ε>, t s stll that s > Exampl:Sa watr s usd to condns th stam flowng out of a stam turbn. It s known that th stam prssur s ka wth th qualty of 95%. h nlt watr s at 5 and th outlt watr s at 35, calculat th rsbl work. h A = 4.87,h A = 46.66,h B =664.99,h B =9.8 m A (h A -h A )= m B (h B -h B ) m A =59.8 m B s A =.3673,s A =.55,s B =7.775,s B =.649 s 59.8* =.35 kj/kg-stam-k W = kj/kg stam owvr, th warm sa watr would cool to 5 aftr flowng back to sa. As a rsult, xrgy would los agan for th coolng procss. work combng both th condnsaton and th coolng would b W = kj/kg stam h total loss of rsbl Advancd hrmodynamcs NCU ME dpt 頁 8

29 w h h ( s s ) = kj/kg stam B B B B Exampl:ot ar from th outlt of gas turbn at 7 K s usd to hat th outlt of comprssor at 5 K. s.8. Calculat th rsbl work f th rgnrator ffctvnss A A B B A = 7 K, B = 5 K, A =7-.8 = 54 K, B =66 K sc c c =.8 kj/kg- K A B A B pln( ) pln( ) pln( ) A B A B W = 5.44 kj/kg h ffct of ffctvnss on rsbl work: sc c c A B A B pln( ) pln( ) pln( ) A B A B A A A B ( ) ( ) A A A B A B ( ) ( ) B B A A B A A B B A X [ ][ ] A B A B dx d B A 4 ( )( ) B A ( )( ) A B A B Advancd hrmodynamcs NCU ME dpt 頁 9

30 B A ( )( ) A B, A B h rgnrator wll los th maxmum amount of xrgy whn.5. ε A B s It s ntrstng to not that th maxmum ncras of ntropy occurs at.5. h cas of and ar of th sam rsult n trms of ntropy ncras. owvr, ths two cass ar two xtrms for nrgy rcovry. On ndcats prfct nrgy xchang, whl th othr on mans no xchang at all. h scond law analyss s not consstnt wth th frst law analyss bcaus th xrgy analyss s focusng on th convrson of thrmal nrgy to work only. h xchang of thrmal nrgy s not consdrd by th xrgy analyss unlss th xchang wll dtrorat th potntal of work convrson Advancd hrmodynamcs NCU ME dpt 頁 3

31 (4.4). Convrson ffcncy of xhaust nrgy rcovry Exhaust nrgy rcovry s an mportant ssu as nrgy ffcncy bcoms a common concrn for savng our nvronmnt. owvr, th xtnt that th xhaust can b rcovrd s not as much as w xpct. hr ar two ways to rcovry xhaust nrgy. h frst way s to convrt th xhaust nrgy to anothr form of thrmal nrgy. Ar pr hatr n th powr plant and th rgnrator n th gas turbn cycl ar xampls of thrmal nrgy utlzaton. h ffcncy of ths knd of nrgy rcovry dpnds on th ffctvnss of hat xchangr. h scond knd of nrgy rcovry s to convrt thrmal nrgy to work, thr mchancal work or lctrc work. hrmodynamc cycls ar usd for ths convrson. h ffcncy of ths knd of nrgy rcovry s lmtd by th Scond Law of thrmodynamcs. (4.4.). ow much work can b obtand from th xhaust of an ngn? h maxmum work that can b obtand s th rsbl work of th xhaust. h rsbl work for a non-ractng opn systm s V V W ( gz ) ( gz ) ( S S ) Q ( ) (.) If kntc nrgy and gravtatonal potntal nrgy can b nglctd, th rsbl work s w h h s s q (.) ( ) ( ) If th hat transfr s towards th nvronmnt, =, thn th rsbl work s w h h ( s s ) Snc th xhaust s rjctd to th nvronmnt, w hav h h, s s. Assum that xhaust s an dal gas wth constant spcfc hat, th spcfc avalabl work s Advancd hrmodynamcs NCU ME dpt 頁 3

32 w ( ) ( ) ( ) ln ln h h s s cp cp cp (.3) h spcfc nrgy that can b rlasd f th xhaust s coold to th nvronmntal tmpratur s h( h h) c ( ) (.4) p As a rsult, th maxmum ffcncy that can b rachd for th convrson of xhaust nrgy s max w cp( ) cpln ln h c ( ) p Whr s th rato of nvronmntal tmpratur to th tmpratur of xhaust stram just ssung out ngn xhaust valv. Maxmum ffcncy of xhaust nrgy rcovry (.5).6 ffcncy.4. ff xhaust tmpratur (C) Fg.4.4. h maxmum convrson ffcncy Fg shows th maxmum convrson ffcncy for th tmpratur rang of xhaust that s oftn ncountrd n normal opratons of ntrnal combuston ngns. For xampl, f th xhaust tmpratur s 4, thn th maxmum ffcncy of nrgy convrson would b 35.3%. It s notd that f a Carnot ngn runs btwn two hat rsrvors of 5 and 4, th ffcncy of ngn would b 55.7%. Advancd hrmodynamcs NCU ME dpt 頁 3

33 S h coolng procss may b rprsntd as th constant prssur curv n th S dagram. h maxmum work that can b obtand s th shadd ara. Exampl: h xhaust flow of an ntrnal combuston ngn s at 6, and th flow rat s.88 kg/sc ( 3c.c. runnng at 3 rpm). Calculat th rsbl work of th xhaust flow. ( ) ( ) ( ) ln p p p ln w h h s s c c c = kj/kg W mw =.6 kw w h v ln =.448 Assgnmnt 4.8: A gas turbn ngn s shown blow. Inlt ar s at ka and 3K. h prssur s rasd to Ma aftr comprsson, and tmpratur bcoms 5K aftr combuston. Assum that ar s an dal gas wth constant hat capacty. h comprssor and th turbn can b assumd to b sntropc. h wast nrgy n th xhaust flow s rcovrd by nfnty numbr of Carnot ngns. h atmosphrc Advancd hrmodynamcs NCU ME dpt 頁 33

34 tmpratur s 3K. (3%) (). Fnd out th tmpratur n th xt of turbn. (). ow much work can b obtand by wast nrgy rcovry? (3). Fnd out th total ffcncy f wast nrgy rcovry s ncludd. Q Assgnmnt 4.9: h sam amount of hat s usd to hat up ar at ka and 3K n a constant prssur tub. h thrmal nrgy s thn rcovrd by nfnty numbr of Carnot ngns. ow much work can b obtand by thrmal nrgy rcovry? Q 3K 3K Advancd hrmodynamcs NCU ME dpt 頁 34

35 (4.4.). Sngl stag ngn h maxmum ffcncy xprssd n Equ. (.) can only b ralzd f w hav nfnty numbr of Carnot ngns arrangd n ordr along th lngth of xhaust pp and th opratng tmpraturs of ths ngns dcras contnuously such that all th hat contand n th xhaust can b utlzd. Bsds, th lngth of th pp should b long nough that th hot xhaust stram may cool down to th nvronmntal tmpratur as t lavs th xt of pp. owvr, f only fnt numbr of Carnot ngns ar avalabl, th xt tmpratur would not b as low as. hr also xsts a fnt tmpratur dffrnc btwn xhaust gas and th surfac of ngn hot sd bcaus th gas tmpratur dcrass along th lngth of pp and th ngn hot sd rmans at a constant tmpratur. If only on st of Carnot ngn s nstalld to xtract th xhaust nrgy, th hot sd tmpratur of th ngn would b lowr or at most qual to th tmpratur of xhaust stram such that hat transfr may occur from xhaust to ngn. As a rsult, th xhaust lft out of th ngn would b Q mc ( ) Whr (.) s th gas tmpratur pror to th surfac of Carnot ngn hot sd, and s th gas tmpratur just bhnd th Carnot ngn. h ngn ffcncy s c Whr ngn. s th hot sd tmpratur, and (.) c s th cold sd tmpratur of Carnot If th hat snk of Carnot ngn s xposd to th atmosphr, th hat snk tmpratur may b qual to th atmosphrc tmpratur. It s notd that w assum th hot sd tmpratur of Carnot ngn s th sam as th gas tmpratur just bhnd th Carnot ngn. h work output s th product of th amount of hat transfr at th Carnot ngn hot sd and th ngn ffcncy. Advancd hrmodynamcs NCU ME dpt 頁 35

36 c W Q mc ( )( ) (.3) In th abov quaton, th xhaust mass flow ( m ), th hat capacty (c ), th xhaust tmpratur ( ), and th ngn cold sd tmpratur ( c ) ar all known for a spcfc opratng condton. Only th ngn hot sd tmpratur ( ) s not known. It can b vard. If s hgh, th ngn ffcncy s hgh. owvr, th amount of hat transfr s low. On th othr sd, f s low, th amount of hat transfr s hgh. But th assocatd ngn ffcncy s low. valu of that would maxmz th output work. dw c mc ( ) d It can b solvd that th valu of c s hr xsts a (.4) (.5) hs s th ngn hot sd tmpratur that would maxmz th output work, and th assocatd output work s c W mc ( c)( ) mc ( )( ) (.6) c Whr s th rato of nvronmntal tmpratur to th tmpratur of xhaust stram just ssung out ngn xhaust valv. As a rsult, th maxmum convrson ffcncy for sngl stag ngn s max w ( ) h (.7) For xampl, f th xhaust tmpratur s 4, thn th maxmum ffcncy of nrgy convrson wth sngl stag of Carnot ngn would b.%. W can s that th maxmum convrson ffcncy for sngl stag ngn s much lowr than that for a srs of nfnt ngns. Advancd hrmodynamcs NCU ME dpt 頁 36

37 S h maxmum work that can b obtand wth sngl Carnot ngn can b rprsntd as th rd rctangular ara. Exampl: h xhaust flow of an ntrnal combuston ngn s at 6, and th flow rat s.88 kg/sc ( 3c.c. runnng at 3 rpm). Calculat th rsbl work of th xhaust flow f sngl Carnot ngn s usd for nrgy convrson. (4.4.3). Sngl stag wth fnt hat transfr rat If th hat transfr coffcnt btwn th xhaust gas and th plat s of fnt magntud, th tmpratur of plat would b vn lowr such that hat transfr rat and th assocatd work output ar rducd. d mc hp( w ) dx d hp ( w ) dx mc w x c hp mc (.) Advancd hrmodynamcs NCU ME dpt 頁 37

38 x, w w c x x L, w w L L ( ) w w L Q mc ( ) mc ( )( ) w L c WQ Q mc ( ) mc ( w)( )( ) w c L L c c c W mc ( )( )( ) mc ( ) c L W ( ) mc ( ) Exampl: h xhaust flow of an ntrnal combuston ngn s at 6, and th flow rat s.88 kg/sc ( 3c.c. runnng at 3 rpm). h damtr of xhaust pp s cm, and th lngth s mtrs. Calculat th rsbl work of th xhaust flow f sngl Carnot ngn s usd for nrgy convrson. w (4.4.4). Mult stag ngns If mor than on st of Carnot ngns ar nstalld n th xhaust pp and ths ngns ar arrangd n srs on by on, mor nrgy could b xtractd bcaus Advancd hrmodynamcs NCU ME dpt 頁 38

39 ths ngns could b opratd at dffrnt tmpraturs. Engns locatd at downstram of xhaust flow oprat at lowr tmpratur than thos locatd at upstram. As a rsult, nrgy that could not b xtractd by upstram ngns could b trappd by downstram ngns. h nt convrson ffcncy s thus hghr. For th cas that two ngns ar nstalld, th total hat transfr s Q mc ( ) mc ( ) (3.) m m Whr m s th hot sd tmpratur of th frst ngn, and tmpratur of th scond ngn. s th hot sd It s notd that w assum as th hot gas lavs th frst ngn, t s n qulbrum wth th ngn such that ts tmpratur s dntcal to th ngn hot sd tmpratur. lavs th scond ngn, ts tmpratur s th sam as h total work output s c c W mc ( m)( ) mc ( m )( ) hr ar two varabls, m For th sam rason, as th hot gas. m and, that could b vard to chang th work output. h maxmum work could b obtand as th followng. dw c c mc ( ) mc ( ) d m m dw mc ( ) d m c h valus of m and that could maxmz th output work output ar m c,, c c m m m c /3 /3 m c /3 /3 c h output work and th convrson ffcncy ar thus Advancd hrmodynamcs NCU ME dpt 頁 39

40 W mc ( )( ) mc ( )( ) /3 /3 c /3 /3 /3 /3 c c /3 /3 c c /3 /3 c c W c c c c c mc ( )( ) ( )( ) max ( )( ) ( )( ) S h maxmum work that can b obtand wth two Carnot ngns can b rprsntd as th two rd rctangular. For xampl, f th xhaust tmpratur s 4, thn th maxmum ffcncy of nrgy convrson wth two stags of Carnot ngn would b 5.6%. For th cas that thr ngns ar nstalld, th total hat transfr and th total work ar Q mc ( ) mc ( ) mc ( ) m m m m Wmc ( )( ) mc ( )( ) mc ( )( ) c c c m m m m m m h maxmzaton procss s qut th sam as that of two ngn. Advancd hrmodynamcs NCU ME dpt 頁 4

41 W mc ( ) mc ( ) c c m m m W mc ( ) mc ( ) m c c m m W mc ( ) m c c c m m m m m c c m m m 4 m m m 3 3 m m c 6 3 m c c c m c m m c W mc ( )( ) ( )( ) ( )( ) max ( )( ) ( )( ) ( )( ) Advancd hrmodynamcs NCU ME dpt 頁 4

42 For xampl, f th xhaust tmpratur s 4, thn th maxmum ffcncy of nrgy convrson wth thr stags of Carnot ngn would b 8.%. S h maxmum work that can b obtand wth thr Carnot ngns can b rprsntd as th thr rd rctangular boxs. h optmzaton procss could b xtrapolatd to th cas that N stags of ngns ar nstalld n srs. h convrson ffcncy s max N N N N N ( )( ) Enrgy rcovry ffcncy maxmum ffcncy stags of Carnot ngn 3 C 4 C 5 C 6 C 7 C 8 C Fg.4.4. h convrson ffcncy for mult stag ngns Fg shows th maxmum convrson ffcncy for mult stag ngns Advancd hrmodynamcs NCU ME dpt 頁 4

43 nstalld n srs opratd at svral xhaust tmpraturs. It s notd that ncrasng th stag numbr of th Carnot ngns would nhanc th xhaust nrgy utlzaton ffcncy. owvr, thr s a lmt of ffcncy that can b rachd. As a mattr of fact, th ncras n ffcncy gts lowr and lowr as numbr of stags xcds fv. Exampl: h xhaust flow of an ntrnal combuston ngn s at 6, and th flow rat s.88 kg/sc ( 3c.c. runnng at 3 rpm). Calculat th rsbl work of th xhaust flow f two Carnot ngns n srs ar usd for nrgy convrson. Advancd hrmodynamcs NCU ME dpt 頁 43

44 (4.5). Comprssd ar nrgy (4.5.). ow much work can b dlvrd from a bottl of hgh prssur ar? Now w hav a bottl of hgh prssur ar at and. What s th maxmum work that can b dlvrd from ths bottl of ar? tmpratur s and th nvronmntal prssur s. Assum that th nvronmntal h ar contand n th bottl can b rlasd out and thn xpands through a turbn, and producs work. th nvronmnt. systm. v h fnal stat of th ar should b dntcal to that of As a rsult, th maxmum work would b th avalablty of th w uu ss vv q ( ) ( ) ( ) If th procss s adabatc, q, th rsbl work s v w Rln ( vv ) R ln R ( ) v v w R v ln Exampl: Comprssd ar s stord n a bottl of L at bars and 5, calculat th maxmum work that can b dlvrd from ths bottl of ar. m W V =.69 kg R mr = 365 kj (ln ) If hat transfr occurs durng ths procss from a hat sourc othr than th nvronmnt, th rsbl work s Advancd hrmodynamcs NCU ME dpt 頁 44

45 w R R q v ln ( ) ( ) h hat transfr from othr hat sourc s usd to hat up th ar flowng out of th bottl. If th tmpratur of ar s rasd to as t flows nto th workng dvc, th rsbl work s w R ln R ( ) c ( )( ) v p k cp( )( ) cp( )( ) R k W k mr ln k Exampl: Comprssd ar s stord n a bottl of L at bars and 5, calculat th maxmum work f th tmpratur of ar s rasd to as t flows out of th bottl. W k mr ln k = 4375 kj (4.5.). ow to obtan th nrgy stord n bottl? Assum that a prfct turbn s usd to convrt th nrgy of comprssd ar. h turbn can oprat at any prssur rato, and th ffcncy s.. h work s k k dw cp dm whr and ar th tmpratur and th prssur of ar at th ntranc of turbn. Advancd hrmodynamcs NCU ME dpt 頁 45

46 Intally, th bottl contans ar at and, and th volum of bottl s V. As th prssur of bottl gts down to, th ar cass to flow out of bottl, and no mor work can b don. (4.5..). Adabatc procss If all th procss s adabatc, th varatons of prssur and mass nsd th bottl ar k k m m m V R k k dm m d( ) k As a rsult, th work o turbn s k k k k k dw cp m d k X k k k k k k k m k k k V k dw cp X X X dx X dx k k k k k V k k W X X k k Advancd hrmodynamcs NCU ME dpt 頁 46

47 (4.5..). Ar prhatng If a hatr s usd n th upstram of turbn to hat up ar to th tmpratur of, th work s k k k k k k k V k k V k dw cp dm X X dx X dx k k k k k k V W X kx (4.5..3). Bottl hatng If th bottl s hatd such that ts tmpratur rmans at durng th whol procss, th varaton of mass nsd th bottl s m m th work s k k k k k k k V k dw cp dm cp mdx X dx k k k k k V W X kx Exampl: Comprssd ar s stord n a bottl of L at bars and 5, calculat th work that can b dlvrd from ths bottl of ar by ways of adabatc procss, ar prhatng, and bottl hatng. V m =.69 kg R Advancd hrmodynamcs NCU ME dpt 頁 47

48 W mr = 365 kj (ln ) k k k V k k W X X k k = 4748 kj Advancd hrmodynamcs NCU ME dpt 頁 48

49 (4.6). Chmcal Exrgy Chmcal xrgy s dfnd as th maxmum work that can b obtand whn th systm s ractd wth ar n th nvronmnt. Chmcal xrgy dpnds on th tmpratur and prssur of a systm as wll as on th composton. If th tmpratur, prssur or composton of a systm dffrs from th nvronmnt's stat, thn th ovrall systm wll hav xrgy. Ful s burnd wth ar to form products n a constant volum chambr. In gnral, th nvronmnt s dfnd as th composton of ar at 5 C and atm of prssur. Ar conssts of N =75.67%, O =.35%, O(g)=3.%, CO =.3% and othr gass=.83%. mpratur as wll as prssur n th chambr wll b rasd up du to th hat rlas of combuston. Work can b don as th tmpratur of systm s hghr than th nvronmnt tmpratur and th systm prssur s also hghr that th atmosphrc prssur. Bsds, th products of combuston contan hgh lvls of CO and O, and th O concntraton s much lss than that n th nvronmnt. h dffrnc n concntratons can also b usd to dlvr work. h total work that s obtand by th tmpratur dffrnc, prssur dffrnc and th concntraton dffrnc s calld th chmcal xrgy. For xampl, mthan s burnd wth stochomtrc amount of ar n a constant prssur procss. h racton s as followng. C ( O 3.76 N ) CO O 7.5N 4 () () (3) (4) Ful roducts Exhaust Ar hyscal work Mxng work Advancd hrmodynamcs NCU ME dpt 頁 49

50 Stat : mthan and ar at 98K and.3 ka. Stat : hgh tmpratur products of combuston. Stat 3: combuston products at 98K and.3 ka. Stat 4: combuston products mx wth nvronmnt ar. Mthan and ar s burnd n an adabatc chambr n whch prssur rmans th sam. h products of combuston ar at th adabatc flam tmpratur. If th ar s at th standard condton (98K,.3 ka), th adabatc flam tmpratur can b dtrmnd wth th consrvaton of nthalpy. R h h 7.5h h R C O N f, C 4 4 h h 7.5h h h ( h h ) 7.5 h CO O N f, CO CO f, O O N In a constant prssur procss, th nthalpy of th systm rmans th sam. h h h ( h h ) 7.5 h f, C f, CO CO f, O O N 4 abf c c 7.5c d h h h p, CO p, O p, N f, C f, CO f, O 4 Whr h kj/kmol. f, C 4 =-7487 kj/kmol, h f, CO =-3935 kj/kmol, and h =-48 f, O S s s s s s R x s R x C O 7.5 N C ( O ln O ) 7.5( N ln N ) abf 4 4 S s s 7.5s s Rln x ( s Rln x ) 7.5( s Rln x ) CO O N CO CO O O N N c c 7.5c pco, p, O pn, d Advancd hrmodynamcs NCU ME dpt 頁 5

51 7.5 CO O N CO ln O N C 4 O N 7.5 ( xo x ) N R S S s s s s s s R abf c c 7.5c pco, p, O pn, d ( x x x ) Whr th ntropy of ach spcs at th standard condton can b found n th tabl blow. Entrops at 5 and atm ( S R) / m C N 3.3 CO 3.76 O(l) 8.4 O 4.66 CO 5.7 O(g).7 N h rsbl work n ths procss s W ( ) ( S S) h actual work s zro. So th combuston procss s a loss of rsbl work. 3 h hgh tmpratur products flow through a channl n whch som convrson dvcs ar usd to convrt thrmal nrgy to mchancal nrgy untl th tmpratur of products gts n qulbrum wth th nvronmnt. h h 7.5h c c 7.5c d 3 CO O N p, CO p, O p, N S S c c 7.5c 3 pco, p, O pn, abf h rsbl work that th burnd gas may produc as t cools down to th nvronmnt tmpratur s W ( S S ) 3 3 abf d 3 4 h products of combuston mx wth nvronmntal ar such that th molar fracton of ach componnt coms to th quvalnt valu that xts n th Advancd hrmodynamcs NCU ME dpt 頁 5

52 atmosphrc ar. Durng ths procss, th tmpratur rmans th sam ( xco x OxN ) CO N S S R ln ( x x Ox ) h rsbl work of th mxng procss s W ( S S ) h rsbl work of th whol procss s th sum of th rsbl work of ach ndvdual procss. W ( ) ( S S ) ( S S ) ( S S ) ( S S ) 3 4 abf c c 7.5c d h h h 3 p, CO p, O p, N f, C4 f, CO f, O ( x CO x O) 4 CO ln O C 4 O ( xo ) S S s s s s R W h s ( h s ) ( h s ) ( h s ) f, C C f, CO CO f, O O f, O O R 4 4 ( xco x O) ln ( xo ) g g g g R ln C O CO O 4 whr g h s C f, C C g h s CO f, CO CO g h s O f, O O g h s O f, O O ( xco x O) ( xo ) Advancd hrmodynamcs NCU ME dpt 頁 5

53 In gnral, for th ful of CO, a b c th racton of th ful wth stochomtrc ar s b c b b c CO a b c ( a )( O 3.76 N) aco O ( a )3.76N 4 4 h rsbl work of ths ful s b c a 4 b c b yo F ( ) O CO O ln b 4 a yco y O W g a g ag g R Whr g h s X f, X Ar conssts of N =75.67%, O =.35%, O(g)=3.%, CO =.3% and othr gass=.83%. y O =.35 y =.3 CO y =.3 O Ful a b c R ln y b c a 4 yo b a CO y O 668 C C 3 O C 653 C C 5 O Assgnmnt : Fnd th rsbl work of hydrogn at 98K and.3 ka. ( O 3.76 N ) O.88 N a, b, c Advancd hrmodynamcs NCU ME dpt 頁 53

54 yo W g g O g O R ln y O g h s = = f, g h s = = O f, O O g h s = = O f, O O Assgnmnt : Fnd th rsbl work of mthanol at 98K and.3 ka. 3 C O ( O 3.76 N ) CO O 5.64 N a, b 4, c 3 3 yo W gc ln 3O go g CO g O R yco y g h s = 3 CO fco, CO O Advancd hrmodynamcs NCU ME dpt 頁 54

55 It s notd that W LV S. If S, thn W LV. W can s that all th fuls lstd n th abov tabl hav a hghr chmcal xrgy than th hatng valu. hat s, th ntropy chang of racton s postv. Exampl: Fnd th rsbl work of th procss of hydrogn gnraton wth mthanol rformaton at 98K and.3 ka. C O O CO 3 3 Q C 3 O CO +3 O Advancd hrmodynamcs NCU ME dpt 頁 55

56 (4.7). ydrogn nrgy (4.6.). ow much powr can b dlvrd from a contnuous flow of ar and hydrogn mxtur at and? If th kntc nrgy and potntal nrgy varatons can b nglctd, th rsbl work for strams of ar and ful at an approprat rato s W ( ) mphp maha mf hf mpsp masa mf sf h purst form of th racton of hydrogn and oxygn s O O h =, For on kmol of hydrogn, th hat of racton at and s h O =, s =3.57, h O( g) =-48 kj/kmol s O =5.3, s O =88.7 kj/kmol-k, LV h h.5h =-48 kj/kmol O O W LV ( s s.5 s ) = = 8599 kj/kmol O( g ) O hs s th maxmum nrgy that can b obtand from th racton of pur hydrogn and pur oxygn. (4.6.). Constant prssur combuston If hydrogn and oxygn s mxd togthr to form combustbl mxtur, and thn s gntd at constant prssur nvronmnt. hr wll two stps to complt ths procss. h ntal stat s( S, ). h frst stp s th mxng of hydrogn and oxygn. Enthalpy rmans constant and ntropy ncrass. Aftr mxng procss, th stat s( S, ), but S S,. h scond stp s adabatc constant prssur combuston. Enthalpy rmans constant and ntropy ncrass. Aftr combuston procss, th stat s( S3, 3), but S S, 3. 3 Advancd hrmodynamcs NCU ME dpt 頁 56

57 AS a rsult, th rsbl work aftr th combuston procss bcoms W LV ( S S ) LV ( S S ) 3 h lost work s causd by mxng and combuston procss. Now w hav a bottl of hgh prssur ar at and. What s th maxmum work that can b dlvrd from ths bottl of ar? Assum that th nvronmntal tmpratur s and th nvronmntal prssur s. h ar contand n th bottl can b rlasd out and thn xpands through a turbn, and producs work. h fnal stat of th ar should b dntcal to that of th nvronmnt. As a rsult, th maxmum work would b w ( ) ( ) ( ) ln u u s s q R ( O 3.76 N ) O.88 N For on kmol of hydrogn, th hat of racton s h =, h O =, s =3.57, h N =, s O =5.3, h O( g) =-48 kj/kmol s N =9.5, s O =88.7 kj/kmol-k, LV h.88h h.5h.88h =48 kj/kmol O N O N W LV (.88s s s.5s.88 s ) = = N O( g ) O N Advancd hrmodynamcs NCU ME dpt 頁 57