BILANTURI DE MATERIALE SI ENERGIE. Lucian Gavrila Bilanturi de materiale si de energie 1
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- ῬαΧάβ Παπαδάκης
- 8 χρόνια πριν
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1 BILANTURI DE MATERIALE SI ENERGIE Luc Gvrl Bltur d trl s d rg 1
2 BILANŢUL DE MATERIALE o Ptru proctr ş xplotr stlţlor dustrlor d procs st csră cuoştr clttvă ş ctttvă trllor cr crculă pr fcr puct l stlţ, î fcr ot l fucţoăr cst. o Mtrll sut dft pr: spcl chc, copozţ ş coctrţl soluţlor ş stcurlor, str d grgr, cttăţl su dbtl î puctl, scţul su zol cr trsză. Luc Gvrl Bltur d trl s d rg 2
3 BILANŢUL DE MATERIALE Dtl csr lborăr ş rzolvăr blţurlor d trl sut: o dtl ţl (prr) rfrtor l: dbtul (cpctt) stlţ, proprtăţl tr pr, proprtăţl produsulu, crctrstcl thologc spcfc stlţ; o sch thologcă stlţ ş vrtl posbl l cst; o dt stochotrc ş ctc l rcţlor cr dcurg î stlţ; o dt supr chlbrlor d rcţ ş d fză î sstl xstt î stlţ. Luc Gvrl Bltur d trl s d rg 3
4 BILANŢUL DE MATERIALE oecuţ grlă d blţ d trl st xprs lg cosrvăr tr: trl trt trl xstt trl st trl rs o Tr cuţ rprztă cttăţ su dbt, xprt pr s (dbtul sc) Luc Gvrl Bltur d trl s d rg 4
5 odfrţ: A BILANŢUL DE MATERIALE trl trt trl st portă dur d cuulr. o Ptru procsl cotu, î rg stţor, cuulr st ulă: trl rs trl xstt trl trt trl st Luc Gvrl Bltur d trl s d rg 5
6 BILANŢUL DE MATERIALE `Îtocr blţulu d trl trbu îsoţtă îtotdu d prczr: ct su zo d stlţ l cr s rfră blţul (dfr coturulu d blţ); tpulu î rport cu îcputul prlucrăr u şrj (u î czul procslor dscotu); durt d tp ptru cr s îtocşt blţul: procs cotu - p utt d tp (scudă, oră, z, ); procs dscotu ct. d subst. s rportză l o şrjă ş s rclculz l UM (kg, t, kol tc.) d tr pră su produs ft; procs î rg trztoru -blţurl sut dfrţl. Luc Gvrl Bltur d trl s d rg 6
7 BILANŢUL DE MATERIALE S pot îtoc: o blţur grl (totl su globl), ptru îtrg stlţ ş tot trll przt, o blţur prţl: ptru îtrg stlţ, dr u ptru u sgur trl; ptru tot trll, dr u ptru o prt stlţ: u utlj, o ută zoă (b dftă) uu utlj, u lt dfrţl d volu dtr-u utlj; ptru u sgur trl ş o prt stlţ (utlj, lt d utlj, lt dfrţl d volu). Luc Gvrl Bltur d trl s d rg 7
8 Blt grl - xplu SULF AER Topr-fltrr sulf Fltrr r Ardr sulf Uscr r / Dlur H 2 SO 4 ACID SULFURIC Oxdr ctltc SO 2 l SO 3 Absorbt SO 3 H2 SO 4 H2 SO 4 Luc Gvrl Bltur d trl s d rg 8
9 Blt prtl - xplu SULF Bltul sulfulu trg stlt Topr-fltrr sulf Ardr sulf Uscr r / Dlur H 2 SO 4 Oxdr ctltc SO 2 l SO 3 Absorbt SO 3 H2 SO 4 H2 SO 4 ACID SULFURIC Luc Gvrl Bltur d trl s d rg 9
10 Blt prtl - xplu Bltul tuturor trllor rctorul d cotct Gz sulfuros: SO 2 ; O 2 ; N 2 Oxdr ctltc SO 2 l SO 3 Gz sulfuros oxdt: SO 3 ; SO 2 ; O 2 ; N 2 Luc Gvrl Bltur d trl s d rg 10
11 Blt prtl - xplu Bltul SO 2 tr-u strt d ctlztor d rctorul d cotct SO 2 l trr strt Strt d ctlztor SO 2 l sr d strt Luc Gvrl Bltur d trl s d rg 11
12 BILANŢUL DE MATERIALE Mtrll lut î cosdrr î blţur pot f: o spc chc b dft (spc olculr, o, rdcl, to); o trl d copozţ dftă (strl, rzduu, cuşă, tc.). Cu jutorul cuţlor d blţ d trl pot f obţut forţ prcs supr crculţ trllor ptru cr dtrărl drct (pr câtărr su ăsurr) lpssc su prztă covt. Luc Gvrl Bltur d trl s d rg 12
13 BILANŢUL DE MATERIALE Exprr copozţ s d rcţ o să d rcţ totltt copotlor rctţ, produş d rcţ, trl rt, ctlztor cr s găssc l u ot dt î: o stlţ, u utlj, o porţu d utlj, u lt dfrţl d volu. Luc Gvrl Bltur d trl s d rg 13
14 BILANŢUL DE MATERIALE o L odul cl grl, s d rcţ st lcătută d p rctţ A I, q produş d rcţ A I ş r rt A I, cuţ crctrstcă procsulu d trsforr r for: p r q p r A A " A ' A A " Luc Gvrl Bltur d trl s d rg 14
15 BILANŢUL DE MATERIALE Copozţ s d rcţ s pot xpr pr: o ăr xtsv (uăr d ol, s, volu) o ăr tsv (frcţ olr, sc, voluc, rport olr, sc, voluc, coctrţ olr, sc, voluc, tc.). Luc Gvrl Bltur d trl s d rg 15
16 Luc Gvrl Bltur d trl s d rg 16 BILANŢUL DE MATERIALE o Mărl xtsv: xprt î [kol] su [kol/s]; xprt î [kg] su [kg/s]; xprt î [ 3 ] su [ 3 /s]. T A A A L L L " ' T A A A L L L " ' T A A A V V V V L L L " '
17 Luc Gvrl Bltur d trl s d rg 17 BILANŢUL DE MATERIALE omărl xtsv sut dtv (clusv volul, î czul gzlor dl). o C urr: p q r A A A N T p q r A A A N T p q r A A A N T V V V V V " ' " ' " ' 1
18 BILANŢUL DE MATERIALE oîtr ărl xtsv s stblsc rlţl: rspctv M V V M î cr M I sl olr [kg/kol], V M volul olr [ 3 /kol] l copoţlor. Luc Gvrl Bltur d trl s d rg 18
19 BILANŢUL DE MATERIALE o Mărl tsv coctrţ o NU dpd d cttt d substţă d sst. o Ptru stcur oog (clusv solut) s folossc frct: olr sc voluc Luc Gvrl Bltur d trl s d rg 19
20 BILANŢUL DE MATERIALE o Frcţ olră uu copot orcr rportul dtr r. d ol cop. ( ) ş r. totl d ol d sst ( T ). o Ptru u sst fort d z copot, frcţ olră uu copot orcr v f: x 1 2 z T kol d kol copot stc Luc Gvrl Bltur d trl s d rg 20
21 BILANŢUL DE MATERIALE o Frcţ scă uu copot rportul dtr s d copot d stc ( ) ş s totlă stculu ( T ): x 1 2 z T kg d kg copot stc Luc Gvrl Bltur d trl s d rg 21
22 BILANŢUL DE MATERIALE o Frcţ volucă rportul dtr voluul uu copot orcr d stc (V ) ş voluul totl (V T ) l stculu: y V 1 V 2 V V z V V T 3 d 3 copot stc Luc Gvrl Bltur d trl s d rg 22
23 BILANŢUL DE MATERIALE o Pt. vpor ş gz, copozţ s pot xpr ş pr prsul prţl l copoţlor, clcult d lg Dlto: p y P T o Î czul gzlor ş vporlor, frcţl (proctl) olr sut urc gl cu frcţl (proctl) d volu. o Egltt u st vlblă îsă î czul lchdlor ş soldlor. Luc Gvrl Bltur d trl s d rg 23
24 Luc Gvrl Bltur d trl s d rg 24 BILANŢUL DE MATERIALE o S pot dostr uşor că su frcţlor tuturor copotlor d sst st glă cu utt: T T T z T z T T z T T T z T z T T z T T T z T z T T z V V V V V V V V V V V V y x x L L L L L L L L L L L L
25 BILANŢUL DE MATERIALE o Rportul olr rportul dtr r. d ol do copoţ dtr-u stc. o Pt. u stc cu z copoţ, coc. uu cop. orcr s pot xpr î rport cu orcr dtr cllţ (z 1) copoţ: X X M X,1,2, z 1 2 z kol d copot kol d copot kol d copot kol d copot kol d copot kol d copot 1 2 z Acst od d xprr coctrţ s utlzză frcvt î clculul oprţlor d EXTRACŢIE. Luc Gvrl Bltur d trl s d rg 25
26 BILANŢUL DE MATERIALE o Rportul sc rportul dtr sl do copoţ dtr-u stc. o Pt. u stc cu z copoţ, s pot scr urătorl rport sc ptru u cop. î rport cu orcr dtr cllţ (z 1) cop.: X X M X,1,2, z 1 2 z kg d copot kg d copot kg d copot kg d copot kg d copot kg d copot 1 2 z Acst od d xprr coctrţ s utlzză frcvt î clculul oprţlor d CRISTALIZARE DIN SOLUŢII BINARE. Luc Gvrl Bltur d trl s d rg 26
27 Luc Gvrl Bltur d trl s d rg 27 BILANŢUL DE MATERIALE o Rport voluc -F V 1,V 2,...,V,...,V z volul copoţlor 1,2,...,,...,z flţ î stc. Coctrţl copotulu sub foră d rport voluc s scru: z V V Y V V Y V V Y z z d copot d copot 2 d copot d copot 1 d copot d copot 3 3, 3 3 2, ,1 M
28 Luc Gvrl Bltur d trl s d rg 28 BILANŢUL DE MATERIALE Trcr d l frcţ l rport ş vrs s fc cu rlţ d for: y y Y x x X x x X Y Y y X X x X X x 1 ; 1 ; 1 1 ; 1 ; 1
29 BILANŢUL DE MATERIALE oî prctcă s utlzză xprr coctrţ pr: Ms su r d ol dtr-u copot d utt d volu (kg/ 3, rspctv kol/ 3 ). Dc s utlzză ltrul c utt d volu, coctrţl s xpră î kg/l (g/l) su kol/l (ol/l). Coc. soluţlor utlzt î lz chcă s pot xpr ş sub for ttrulu, dcă î g/l. Uor coctrţ soluţlor (solubltt) s xpră î gr d solut (substţă dzolvtă) l 100 g solvt (dzolvt). Luc Gvrl Bltur d trl s d rg 29
30 EXPRIMAREA BILANŢULUI DE MATERIALE COM- PO- NENT kol [kol/s] INTRARE (ALIMENTARE) kg [kg/s] 3 [ 3 /s] Frcţ olr Frcţ sc kol [kol/s] IEŞIRE (EVACUARE) kg [kg/s] 3 [ 3 /s] Frcţ olr Frcţ sc A A A V A x A x A A A V A x A x A A A ' A ' V A ' x A ' A ' x A ' A ' V A ' x A ' x A ' A A " A " V " A x A " x A " A " A " V " A x A " x A " TOTAL T T V T 1 1 T T V T 1 1 Luc Gvrl Bltur d trl s d rg 30
31 EXPRIMAREA BILANŢULUI DE MATERIALE omărl ţl sut cuoscut f d ăsurr drctă, f d blţul procsulu prcdt. o Ptru dtrr copozţ fl, fără fctu o lză copltă s d rcţ, s utlzză odll ttc d blţ d trl. Luc Gvrl Bltur d trl s d rg 31
32 EXPRIMAREA BILANŢULUI DE MATERIALE o Uor, ptru f sugstv, blţul d trl s rprztă sub foră grfcă, cuoscută sub dur d dgr Sky. o Dgr Sky o schă ctttvă fluxulu thologc, rprzttă l scră. o Fzl, oprţl su utljl procsulu drptughur d cr ş spr cr porsc ş sossc fluxurl d trl, rprztt sub for uor bz colort su hşurt dfrt. olăţ bzlor cr rprztă fluxurl d trl st proporţolă cu cttăţl d trl cr prtcpă l fluxul thologc. Luc Gvrl Bltur d trl s d rg 32
33 EXPRIMAREA BILANŢULUI DE MATERIALE Dgr Sky l gzfcr crbulor Luc Gvrl Bltur d trl s d rg 33
34 EXPRIMAREA BILANŢULUI DE MATERIALE Extr bur Istlt d vporr cu coprs cc d vpor: Abur prr TC SD Abur scudr (gt trc) SC cods Luc Gvrl Bltur d trl s d rg 34
35 EXPRIMAREA BILANŢULUI DE MATERIALE Istlt d vporr cu coprs cc d vpor: A - Sol. dlut B - Abur scudr B1 - Extrbur C - Sol. coctrt D - Abur prr E Cods Luc Gvrl Bltur d trl s d rg 35
36 EXPRIMAREA BILANŢULUI DE MATERIALE Extr bur (B1) Abur Prr (D) TC Abur scudr B) (gt trc) SD (A) Cods (E) SC (C) Luc Gvrl Bltur d trl s d rg 36
37 MODELE MATEMATICE DE BILANŢ DE MATERIALE oî ch fzcă st utlzt grdul d vsr l u rcţ chc, dft pr rlţ: Λ A ν A A o Prcplul vtj l utlzăr grdulu d vsr costă î fptul că cst st A ' uc ptru toţ prtcpţ l rcţ. A ' ν A ' (20) Luc Gvrl Bltur d trl s d rg 37
38 MODELE MATEMATICE DE BILANŢ DE MATERIALE o Î gr procslor fzc s chc s utlzză cu prcădr grdul d trsforr (covrs, grd d covrs) l rcttulu ch (rcttulu vloros). of A k rcttul ch l u rcţ d for grlă: ν A ν A ' (21) A A ' Luc Gvrl Bltur d trl s d rg 38
39 MODELE MATEMATICE DE BILANŢ DE MATERIALE o Grdul d trsforr l rcttulu ch, η, s dfşt c: η ν ν A A A ν ν A ' A ' A ' (22) Luc Gvrl Bltur d trl s d rg 39
40 MODELE MATEMATICE DE BILANŢ DE MATERIALE o Prcplul vtj l utlzăr grdulu d trsforr dcurg d fptul că cst vrză îtotdu îtr 0 ş 1. od rlţl (20) ş (22) rzultă rlţ d lgătură dtr grdul d vsr l rcţ ş grdul d trsforr l copotulu ch: ν η Λ (23) Luc Gvrl Bltur d trl s d rg 40
41 MODELE MATEMATICE DE BILANŢ DE MATERIALE ocâd ν 1 ş ol, tuc. o Orc rcţ chcă pot f scrsă stfl îcât ν 1, dr îtr-u procs dustrl cocrt u s pot cosdr 1 η ol. o Utlzr grdulu d trsforr ptru îtocr blţurlor st u u vtjosă, dr ş csră. 1 Λ Luc Gvrl Bltur d trl s d rg 41
42 MODELE MATEMATICE DE BILANŢ DE MATERIALE o Procs oog (să d rcţ oofzcă) dscrs d o sgură cuţ stochotrc dpdtă, c. lgbrc prr d blţ d să d c. (22): A A ' A " A A ' A " ( 1 η ) ν ν ν ν A A ' η Luc Gvrl Bltur d trl s d rg 42 η (24)
43 MODELE MATEMATICE DE BILANŢ DE MATERIALE o Îsuâd c. (24) r. totl d ol l şr d sst (dbtul olr fl î czul procslor cotu): T Σν Σν 1 A ' A x η T ν (25) Luc Gvrl Bltur d trl s d rg 43
44 MODELE MATEMATICE DE BILANŢ DE MATERIALE onotâd cu α xprs: α Σ ν A ' ν Σ ν A x (26) cuţ (25) dv: T T ( α η ) 1 (27) Luc Gvrl Bltur d trl s d rg 44
45 MODELE MATEMATICE DE BILANŢ DE MATERIALE omăr α : α < 0 - procs cr dcurg cu cşorr uărulu d ol, α > 0 - procs cr dcurg cu ărr uărulu d ol, α 0 - procs cr dcurg fără vrţ uărulu d ol. Luc Gvrl Bltur d trl s d rg 45
46 EXEMPLE α < 0 -cşorr uărulu d ol: stz oculu: N 3H 2NH 2 2 oxdr ctltc SO 2 : SO O SO 3 Luc Gvrl Bltur d trl s d rg 46
47 EXEMPLE α > 0 -ărr uărulu d ol: rforr tulu cu bur: CH H O CO 3H oxdr ctltc oculu: 4 NH 5O 4NO 6H O Luc Gvrl Bltur d trl s d rg 47
48 EXEMPLE α 0 -fără vrţ uărulu d ol: stz HCl d lt: H Cl 2HCl 2 2 stz NO d lt: N O NO Luc Gvrl Bltur d trl s d rg 48
49 MODELE MATEMATICE DE BILANŢ DE MATERIALE oecuţl (24), îpruă cu cuţ (27) lcătusc odlul lgbrc d blţ d să prr l procsulu cosdrt. o Câd s d rcţ s coportă c u stc d gz dl, cuţl odlulu pot f xprt ş î fucţ d volu, su d utăţ sc, utlzâd rlţl d trsforr corspuzător. rspctv M V V M Luc Gvrl Bltur d trl s d rg 49
50 MODELE MATEMATICE DE BILANŢ DE MATERIALE o Rzolvr odlulu lgbrc d blţ d să prr plcă cuoştr p lâgă ărl d trr ş grdulu d trsforr η. o Acst u st o ăr drct ăsurblă, dtrâdu-s pr ăsurr u coctrţ l şr d procs. Luc Gvrl Bltur d trl s d rg 50
51 MODELE MATEMATICE DE BILANŢ DE MATERIALE odcă, d xplu, s ăsoră pot f dftă utlzâd dfţ, cst frcţ olr ş odlul lgbrc d blţ prr c fd: x x x 1 1 ( η ) α η (28) Luc Gvrl Bltur d trl s d rg 51
52 MODELE MATEMATICE DE BILANŢ DE MATERIALE o D (28) s pot xpr grdul d trsforr η, fucţ u d ăr cuoscut: η x x α x x (29) Luc Gvrl Bltur d trl s d rg 52
53 MODELE MATEMATICE DE BILANŢ DE MATERIALE odcă s d rcţ st polfzcă, su dcă î s d rcţ u loc rcţ ultpl: s dfşt cât u grd d trsforr ptru fcr rcţ stochotrc dpdtă ş/su ptru fcr trsforr d fză. lborr odlulu lgbrc d blţ d să trbu să ţă cot d succsu dsfăşurăr î tp procslor dpdt cosdrt. Luc Gvrl Bltur d trl s d rg 53
54 MODELE MATEMATICE DE BILANŢ DE MATERIALE o Ecuţl scudr d blţ d să s obţ d cuţl prr pr îlocur grdulu d trsforr fucţ d ărl d trr ş d şr ăsurt drct. Dcă s ăsoră drct coctrţ rcttulu vloros, x, grdul d trsforr s xpră d cuţ d blţ copotulu vloros (24 ): ( η ) 1 (24) Luc Gvrl Bltur d trl s d rg 54 η (30)
55 MODELE MATEMATICE DE BILANŢ DE MATERIALE o Îlocud (30) î cuţl (24) s obţ: A A A ' " A A A ' " ( ) ν ν ν ν A A ' ( ) ( ) (31) Luc Gvrl Bltur d trl s d rg 55
56 MODELE MATEMATICE DE BILANŢ DE MATERIALE o Îsuâd rlţl (31) s obţ xprs uărulu totl d ol: T ud T 1 1 β β β x x Σν A' ν Σν A (32) Luc Gvrl Bltur d trl s d rg 56
57 MODELE MATEMATICE DE BILANŢ DE MATERIALE o Îlocud (32) î cuţl (31), ţâd cot d cuţ d dfţ frcţ olr s obţ odlul lgbrc d blţ d să scudr: A A ' A " T T T T γ x x x x A A ' A " 1 β x γ 1 β x k ν ν ν ν A A ' ( x γ ) ( x γ ) x x Luc Gvrl Bltur d trl s d rg 57 (33)
58 BILANŢ DE MATERIALE ÎN REGIM STAŢIONAR A v, ρ, S R E v, ρ, S Î cofortt cu sch d fgur, s cosdră că î rcptul R, flt î rg stţor, tră fludul A ş s fludul E. v ρ S v (34) ρ S Egltt dbtlor clor două flud, î cofortt cu cuţ cosrvr s st dtă d rlţ (34): Luc Gvrl Bltur d trl s d rg 58
59 Luc Gvrl Bltur d trl s d rg 59 BILANŢ DE MATERIALE ÎN REGIM STAŢIONAR odcă î rcpt tră ş s ult flud, cuţ (34) dv: o Î czul coductlor crculr (S πd 2 /4), cuţ d blţ cpătă for: S v S v ρ ρ (35) ( ) ( ) d v d v 2 2 ρ ρ (36)
60 BILANŢ DE MATERIALE ÎN REGIM STAŢIONAR oecuţ d blţ copotulu A k d flud r for: v ρ x S v ρ x S (37) oî cuţl d sus: v vtz fludulu, ăsurtă prpdculr p scţu coduct [/s], ρ dstt fludulu [kg/ 3 ], Sr scţu coduct [ 2 ], d dtrul tror l coduct [], x frcţ scă copotulu A k î flud [dsol]. Luc Gvrl Bltur d trl s d rg 60
61 BILANŢ DE MATERIALE ÎN REGIM STAŢIONAR oidc ş s rfră l flud ltt, rspctv vcut d rcpt, o Sul după rspctv după cuprd tot fludl ltt, rspctv vcut. oprodusul vx ρ cu utăţl [kg/( 2.s)] portă dur d vtză scă su flux. Luc Gvrl Bltur d trl s d rg 61
62 BILANŢ DE MATERIALE ÎN REGIM STAŢIONAR odcă stcr î rcptul R pot f cosdrtă prfctă, tuc ş ρ u clş vlor î tot coductl d vcur d rcpt. x Luc Gvrl Bltur d trl s d rg 62
63 BILANŢ DE MATERIALE ÎN REGIM NESTAŢIONAR ocodţ d rg stţor plcă vrţ î tp prtrlor procsulu, clusv vrţ cuulăr o blţul d trl s îtocşt ptru u trvl d tp ftzl, dt. Luc Gvrl Bltur d trl s d rg 63
64 BILANŢ DE MATERIALE ÎN REGIM NESTAŢIONAR A v, ρ, S R E v, ρ, S ocuţ blţulu d trl î rg stţor r xprs: v ρ S dt M v ρ S dt M M t dt (38) Luc Gvrl Bltur d trl s d rg 64
65 BILANŢ DE MATERIALE ÎN REGIM NESTAŢIONAR o Tr I ş III d cuţ rprztă sul slor d flud ltt, rspctv vcut d stlţ î trvlul d tp dt. o Trul M rprztă cuulr (zstr) xsttă î stlţ pâă l otul t, r ultul tr rprztă cuulr l otul (t dt). Luc Gvrl Bltur d trl s d rg 65
66 BILANŢ DE MATERIALE ÎN REGIM NESTAŢIONAR o Efctuâd clcull, cuţ (38) dv: v ρ S M odcă dbtl sut vrbl, vtzl v ş v s îlocusc cu rlţ d for: v f o î cr: v rprztă vtz fludulu l otul t 0, st u cofct; v ş sut spcfc fcăr coduct cu dbt vrbl. v ρ ( t) v t S t (39) (40) Luc Gvrl Bltur d trl s d rg 66
67 Luc Gvrl Bltur d trl s d rg 67 BILANŢ DE MATERIALE ÎN REGIM NESTAŢIONAR oblţul uu copot orcr A k s scr sub for: odfrţd ultul bru, (41) dv: ( ) t M x x S v x S v ρ ρ (41) t x M t M x x S v x S v ρ ρ (42)
68 BILANŢ DE MATERIALE ÎN REGIM NESTAŢIONAR CU TRANSFORMARE CHIMICĂ o Î cst codţ î cuţ (42) s troduc u tr ou, r,tr t cr xpră vtz d forr, dtortă rcţ chc, copotulu A k. oecuţ (42) dv: r v ρ S x v ρ S x t x M M t x t (43) Luc Gvrl Bltur d trl s d rg 68
69 BILANŢ DE MATERIALE ÎN REGIM NESTAŢIONAR o Trul CU TRANSFORMARE CHIMICĂ r t st cosdrt: poztv dcă A k st produs d rcţ; gtv dcă A k st rctt; o Lg cosrvăr tr pu c: r A t 0 (44) tuc câd sur s fc după toţ copoţ A cr trv î rcţ (rctţ ş produş d rcţ). Luc Gvrl Bltur d trl s d rg 69
70 APLICATIE o 1000 kg solut pos d glucoz (C 6 H 12 O 6 ) vd coctrt 20% sc (x 0,2), s supu frtt lcoolc. Std c grdul d trsforr glucoz tol st d 65% s cr: Itocr bltulu d trl p copot s p fz; Copltr tblulu d blt; Aflr coctrt d lcool (% sc) dup frtt. Trsr dgr Sky; Luc Gvrl Bltur d trl s d rg 70
71 Rzolvr o Ecut crctrstc procsulu: [ C H O H O] [ C H OH H O C H O ] [ CO ] g l o Ecut rct stochotrc dpdt: H O frtt lcoolc C H OH C 2 CO x 46 2 x 44 l 2 o Ms olculr, kg/kol Luc Gvrl Bltur d trl s d rg 71
72 Rzolvr o Dfr grdulu d trsforr glucoz: η G G G G Et OH ν Et OH ν G Et OH G CO ν ν 2 2 CO G 2 CO G 0,65 Luc Gvrl Bltur d trl s d rg 72
73 Luc Gvrl Bltur d trl s d rg 73 Rzolvr o Modl ttc d blt d s prr ( utt olr): ( ) η η η η G T T O H O H G CO CO G OH Et OH Et G G
74 Luc Gvrl Bltur d trl s d rg 74 Rzolvr o Exprr bltulu prr utt sc (. M): ( ) T G G CO OH Et G O H CO OH Et G T O H O H O H O H G G CO CO CO CO CO G G OH Et OH Et OH Et OH Et OH Et G G G G M M M M M M M M M M M M η η η η
75 o Vlor urc: INTRARI Rzolvr G T x G 10000,2 200 kg H 2 O T x H 2 O T (1 x G ) 1000(1 0,2) 10000,8 800 kg Et OH 0 CO 2 0 T G H 2 O kg Luc Gvrl Bltur d trl s d rg 75
76 o Vlor urc: IESIRI G 2 Et OH CO H 2 O G ( 1 η) 200( 1 0,65) CO H 2 Et OH 2 O 2 M 2 M CO G kg M M Et OH G G Rzolvr G 2000,35 η 0 2 η kg 0,65 0,65 63,55 kg 66,44 kg T G Et OH CO 2 H 2 O 70 66,44 63, ,99 kg 1000 kg Luc Gvrl Bltur d trl s d rg 76
77 o Tblul d blt Fz Gz Lchd Copot C 6 H 12 O 6 H 2 O Totl grl Rzolvr trr kg C 2 H 5 -OH ,44 0,0709 Totl [] l ,00 936,44 0,9997 CO ,55 1,00 Totl [] g ,55 1, x 0,20 0,80 - kg ,99 sr 0,0745 0,8543 Luc Gvrl Bltur d trl s d rg 77 x -
78 Rzolvr o Coctrt lcoolulu solut dup frtt: x Et OH Et OH [] l 66,44 936,44 0,0709 o su 7,09% sc. Luc Gvrl Bltur d trl s d rg 78
79 Dgr Sky: Solut tl Ap 800 kg Glucoz 200 kg Frtt lcoolc Ap 800 kg Glucoz 70 kg Etol 66,44 kg CO 2 63,56 kg Solut fl Fz gzos Luc Gvrl Bltur d trl s d rg 79
80 BILANŢUL ENERGIILOR oaş cu blţul d trl st xprs lg cosrvăr tr, blţul rglor st xprs prcpulu cosrvăr rg. oblţul rglor srvşt l: urărr fluxurlor rgtc prtr-o stlţ, stblr rdtlor rgtc, dsor uor utlj. Luc Gvrl Bltur d trl s d rg 80
81 BILANŢUL ENERGIILOR oecuţ grlă d blţ rgtc ptru u cotur d blţ stblt î prlbl (stlţ, utlj, porţu d utlj, lt dfrţl d volu) r for: E E E r E (45) E rgl trt (ltt) î sst, E rgl xstt î sst l otul ţl, E r rgl răs î sst î otul fl, E rgl şt d sst. Luc Gvrl Bltur d trl s d rg 81
82 BILANŢUL ENERGIILOR oc ş î czul blţulu d trl, blţul rgtc s îtocşt ptru o durtă prstbltă: durt prlucrăr u şrj (dcă procsul st dscotuu), utt d tp (scudă, oră, z, ) î czul procslor cotu. Luc Gvrl Bltur d trl s d rg 82
83 BILANŢUL ENERGIILOR o Acuulr d rg st dtă d dfrţ: E E E r E (46) o Ptru procsl cr dcurg î rg stţor, cuulr d rg st ulă. Luc Gvrl Bltur d trl s d rg 83
84 BILANŢUL ENERGIILOR S pot îtoc: o blţur rgtc totl (grl), ptru îtrg stlţ, o blţur rgtc prţl: ptru u sgur utlj, ptru o porţu d utlj, ptru u lt dfrţl d volu. o Ergl s trsforă cu uşurţă dtr-o foră îtr-lt u s pot toc blţur prţl, rfrtor l u sgur fl d rg. Luc Gvrl Bltur d trl s d rg 84
85 BILANŢUL ENERGIILOR - xplu Blt globl, p trg stlt d vporr AR GN AS AS AS AP CB SD Solut Abur prr (AP) Abur scudr (AS) Gz codsbl (GN) Ap d rcr (AR) SC Luc Gvrl Bltur d trl s d rg 85
86 BILANŢUL ENERGIILOR - xplu Blt prtl, p u sgur corp d vporr AR GN AS AS AS AP CB SD Solut Abur prr (AP) Abur scudr (AS) Gz codsbl (GN) Ap d rcr (AR) Luc Gvrl Bltur d trl s d rg 86 SC
87 FORME DE ENERGIE o Erg potţlă su rg d pozţ, E p, rzulttă d pozţ p vrtclă corpurlor, î rport cu u pl orzotl rbtrr d rfrţă: E p g z (47) s corpulu [kg], g cclrţ grvtţolă [/s 2 ], z îălţ [] l cr s flă corpul fţă d plul orzotl d rfrţă. Luc Gvrl Bltur d trl s d rg 87
88 FORME DE ENERGIE o Erg ctcă su rg d şcr, E c, corspuzător şcăr corpurlor: E c o Erg tră, U, - o proprtt trscă corpurlor, fucţ d tur, str ş cttt lor: U 1 v 2 (48) 2 u (49) u rg tră scă [J/kg]. Luc Gvrl Bltur d trl s d rg 88
89 FORME DE ENERGIE o Lucrul xtror su rg d prsu, L, lucrul fctut d dul xtror ptru troduc u flud î sst, su lucrul fctut d sst ptru vcu u flud d sst: V v s L P dv P dv s P v s (50) 0 P prsu [P], V voluul [ 3 ] s [kg], v s voluul spcfc [ 3 /kg]. 0 Luc Gvrl Bltur d trl s d rg 89
90 FORME DE ENERGIE o Erg ccă, W, trodusă î sst prtr-o popă prtr-u gttor o Căldur, Q, trodusă d xtror pr prţ uu rzrvor pr suprfţ d trsfr trc o Alt for d rg rg d suprfţă, rg lctrcă, rg gtcă, rg luosă uzul, s gljză î probll curt Luc Gvrl Bltur d trl s d rg 90
91 BILANŢUL TERMIC o Ptru jortt procslor fzc, fzco-chc, chc, bochc cr s ptrc î botholog su î thologl dustr ltr, blţul rglor s pot splfc l for cuoscută sub dur d blţ trc. Luc Gvrl Bltur d trl s d rg 91
92 BILANŢUL TERMIC o Splfcr gljr: lucrulu cc, vrţ rg potţl, vrţ rg ctc, rg lctrc, rg gtc, rg luos, tc., Acst u rror pot v u rol portt. Luc Gvrl Bltur d trl s d rg 92
93 BILANŢUL TERMIC oblţul trc r l bză prcpul îtâ l trodc, cofor căru rg sstulu ş rg dulu xtror, cosdrt îpruă, rprztă o costtă. o Altfl spus: ΔE ΔE sst xtror 0 (51) Luc Gvrl Bltur d trl s d rg 93
94 BILANŢUL TERMIC o Dorc rg (l prsu costtă) st îsăş tlp, cuţ grlă blţulu trc î rg stţor r for: Q Q Q Q Q xt r (52) oq tlp (cttăţ d căldură), Luc Gvrl Bltur d trl s d rg 94
95 BILANŢUL TERMIC Q tlpl trt (ltt) î sst, Q tlpl xstt î sst l otul ţl, Q r tlpl răs î sst î otul fl, Q tlpl şt d sst, Q xt tlp schbtă d sst (cdtă su prtă) cu dul îcojurător. Luc Gvrl Bltur d trl s d rg 95
96 BILANŢUL TERMIC o Î czul procslor cotu cr dcurg î rg stţor, cuţ (52) dv: Q Q xt Q (53) o Pt. procs dbtc (fără schb d căldură cu dul îcojurător), trul Q xt s ulză ş c. (53) s rduc l: Q Q (54) Luc Gvrl Bltur d trl s d rg 96
97 BILANŢUL TERMIC oecuţ (53) s pot scr ş sub for: Q Q Q A procs xt Q A (55) prul tr su ct. d căldură trodus î sst d cătr fluxurl d trl trt, l dol tr su ct. d căldură grt su cosut î procs pr: rcţ chc su bochc, procs d trsforr d fză, procs d trsfr d să îtr fz, ultul tr su ct. d căldură vcut d sst d cătr fluxurl d trl şt. Luc Gvrl Bltur d trl s d rg 97
98 BILANŢUL TERMIC o Prul ş ultul tr l c. (55) s cocrtzză î fucţ d tur fzlor. o Ptru o fză gzosă (stc d gz dl), tlp pot f clcultă dtv: T T Q[] C dt Q[] C dt (56) g 298 p o Dbtl olr l cop. l trr/şr d procs, sut cuoscut d blţul d trl, cr s fctuză îtotdu ît blţulu trc. otp.t ş T s ăsoră l trr, rspctv şr d procsul cosdrt. g Luc Gvrl Bltur d trl s d rg p
99 BILANŢUL TERMIC optru o fză lchdă cr s coportă c o soluţ dlă (soluţ ft dlută) sut vlbl rlţl (56) stblt ptru gz dl. o Î czul soluţlor rl (coctrt), tlp u s pot dtr dtv. Luc Gvrl Bltur d trl s d rg 99
100 BILANŢUL TERMIC o Cpctăţl trc olr Cp [J/(kol.K)], sc C [J/(kg.K)] l soluţlor rl vrză fucţ d coctrţ ş d tprtură: C p[] l f ( x, T ) (57) C [] l f ( x, T ) (57b) Luc Gvrl Bltur d trl s d rg 100
101 BILANŢUL TERMIC o Î cst codţ, cuţl (56) dv: Q [] l [] l T C p ( x T ), dt (58) 298 Q [] l [] l T C p ( x, T ) dt (58) 298 Luc Gvrl Bltur d trl s d rg 101
102 BILANŢUL TERMIC Ptru fz sold s plcă: orlţl (56) î czul î cr copotl fz sold forză u stc cc, orlţl (58) î czul î cr copotl fz sold forză o soluţ soldă. Luc Gvrl Bltur d trl s d rg 102
103 BILANŢUL TERMIC o Dtrr vlorlor urc l căldurlor trodus/vcut d sst cu fluxurl d trl trt/şt, cstă cuoştr: tur fzlor plct î procs, copozţ ţl ş fl, blţulu d să, tprturlor ţl (T) ş fl (T), uor dt xprtl su cuţ prc ptru clculul cpctăţlor trc olr su sc l copotlor ş fzlor plct î procs. Luc Gvrl Bltur d trl s d rg 103
104 BILANŢUL TERMIC optru substţ pur, cpctt trcă olră l prsu costtă, dftă pr rlţ: C p H T (59) st corltă cu tprtur sub pr trdul uor cuţ d tpul: C C C p p p d g b h T T T P c f T T 2 2 (60) Luc Gvrl Bltur d trl s d rg 104
105 BILANŢUL TERMIC o Uor s pot utlz vlor d cpctăţ trc olr, dftă pr rlţ: C p T 2 1 T 1 T 2 T 1 C p ( T ) dt (61) o Î grl, fctul prsu supr cpctăţ trc s pot glj. Luc Gvrl Bltur d trl s d rg 105
106 BILANŢUL TERMIC o Ptru clcul rguros d gr, prcu ş ptru s put prt utlzr progrlor d clcultor, sut prfrt cuţl d tp (60). o Acst prt tgrr ltcă cuţlor (56). o Vlorl cpctăţlor trc, prcu ş vlorl cofcţlor d cuţl (60) sut tblt î: ul, îdrur, oogrf d spcltt. Luc Gvrl Bltur d trl s d rg 106
107 Expl: o Cpctt trc sc lptlu C tgrl (cu 3,2% grs) s pot clcul cu cut: 93, ,6659 4, T T 2 optrulpt coctrt vd tr 4,3 s 60% grs, cpctt trc sc s pot clcul tot cu cut d for: C bt c T 2 Luc Gvrl Bltur d trl s d rg J kg K
108 Expl: cr cofct, b s c sut fuct d cotutul d grs (% sc), G, l lptlu: 6292, ,3113 x G b 3,8887 4,7517 x G c 1, , x G C b T c T 2 J kg K Luc Gvrl Bltur d trl s d rg 108
109 Expl: o Cpctt trc sc st, fuct d cotutul d grs, G (% sc) s d tprtur, T (K), s pot clcul cu o rlt d for: C 3895,1 12,752G 1,0312G T kg K J ( 273) Luc Gvrl Bltur d trl s d rg 109
110 BILANŢUL TERMIC o Trul ΣQ procs s dtră p bz dtlor trodc, î fucţ d tpul d procs: trsforr chcă, trsforr bochcă, trsforr d fză, trsfr trfzc. Luc Gvrl Bltur d trl s d rg 110
111 BILANŢUL TERMIC o L odul cl grl, cst tr pot f xprt sub for: Q procs Q Q Q rj tr. tf. j j (62) o prul tr fctul trc l rcţlor (chc su bochc) plct î procs, o l dol tr fctul trc l procslor d trsforr d fză, o ultul tr fctul trc l procslor d trsfr d substţă îtr fzl plct î procs. Luc Gvrl Bltur d trl s d rg 111
112 BILANŢUL TERMIC o Efctul trc l u rcţ chc st dt d produsul dtr tlp d rcţ ş uărul d ol d rctt (dbtul olr) cosuţ: Q rj j η ν j j ( 0 ) Δ H Rj T (63) Luc Gvrl Bltur d trl s d rg 112
113 BILANŢUL TERMIC 0 Δ Rj H T - rprztă tlp d rcţ l tprtur T [kj/ol]; j η j j - rprztă uărul d ol d rctt A k trsfort î rcţ j. S îprt pr ν j dorc î rcţl î cr ν 1 j tlp d rcţ d lg lu Hss st rporttă l ν j. j Luc Gvrl Bltur d trl s d rg 113
114 BILANŢUL TERMIC o Î czul rcţlor ultpl s dtră su lgbrcă fctlor trc l rcţlor dvdul. o Etlp d rcţ vrză, î grl, cu tprtur ş cu prsu. o Î jortt czurlor (xcpţ făcâd procsl cr dcurg l P > 5 MP) fluţ prsu supr tlp d rcţ pot f gljtă. Luc Gvrl Bltur d trl s d rg 114
115 BILANŢUL TERMIC ovrţ tlp d rcţ cu tprtur pot f xprtă pr trdul lg lu Krchhoff. o Î for s tgrlă, cst r xprs: T Δ R H 0 T Δ R H ΔC p ( T ) dt (64) 298 Luc Gvrl Bltur d trl s d rg 115
116 oud: Δ C BILANŢUL TERMIC p ν C A ' o r tlp d rcţ stdrd s clculză d 0 tlpl olr d forr d lt ( ΔH f ) cu rlţ: Δ R H o Etlpl olr d forr d lt sut tblt î îdruătorl d spcltt. pa ' ΔH ν ΔH 298 fa 0 A ' 0 fa ' ν A C A pa 0 (65) ν (66) Luc Gvrl Bltur d trl s d rg 116
117 BILANŢUL TERMIC o Î ul czur, ptru vrţ c l tp., s pot folos î locul cuţ (64) o cuţ splfctă, cosdrâd o vlor d ptru cpctt trcă olră: Δ R H 0 T Δ R H ΔC ( T 298) o Ptru clcul proxtv, su î lps uor rlţ Cp f(t), tgrl d cuţ (64) s pot glj, cosdrâd: p (67) Δ 0 R H T Δ R H (68) Luc Gvrl Bltur d trl s d rg 117
118 BILANŢUL TERMIC o Efctul trc l procslor d trsforr d fză st dt d produsul dtr r. d ol d copot trsfort (cr trc dtr-o str d grgr î lt) ş tlp trsforăr d fză: Q tr. η [ η ] ( ΔH ) [ tr. ( ΔH ) tr. î cr ] rprztă grdul d trsforr d fză l copotulu A k î procsul d trsforr d fză. Luc Gvrl Bltur d trl s d rg 118 (69)
119 BILANŢUL TERMIC o Etlp trsforărlor d fză s dtră p bz rlţlor: Pt. procsl d vporr codsr: ΔH vp ΔH cod ΔH 0 ΔH 0 ( g ) ( l ) Pt. procsl d sublr dsublr: ΔH subl ΔH dsubl ΔH 0 ΔH 0 ( g ) ( s ) Pt. procsl d soldfcr topr: ΔH soldfcr ΔH topr ΔH ΔH 0 0 ( s ) ( l ) (70) (71) (72) Luc Gvrl Bltur d trl s d rg 119
120 ΔH dz ΔH rt ΔH sol BILANŢUL TERMIC o Efctul trc l procslor d trsfr d substţă st dt d rlţ: Q tf ( ΔH ) ( H ) η Δ. [ ] tf. tf. (73) η [ rprztă grdul d trcr l ] copotulu A k dtr-o fză î lt î procsul ltr ΔH tf. rprztă tlp procsulu ltr cosdrt. Luc Gvrl Bltur d trl s d rg 120
121 BILANŢUL TERMIC o Dtr procsl ltr d trsfr trfzc, portt d puct d vdr trc sut: dzolvr crstlzr dlur Luc Gvrl Bltur d trl s d rg 121
122 BILANŢUL TERMIC o Etlp d dzolvr dpd, î prul râd, d tur ş str solutulu ş solvtulu. o L dzolvr crstllor oc îtr-u solvt polr (p d xplu), procsul costă d două tp cu fct trc cotrr: Luc Gvrl Bltur d trl s d rg 122
123 BILANŢUL TERMIC o procsul d dstrugr rţl crstl ş trcr olor î soluţ, sub cţu dpollor solvtulu; procsul st dotr, fd crctrzt d tlp d rţ, ΔH rt > 0; o procsul d solvtr (trcţu dtr o substţ dzolvt ş olcull solvtulu); procsul st xotr, fd crctrzt d tlp d solvtr, ΔH sol < 0. Luc Gvrl Bltur d trl s d rg 123
124 BILANŢUL TERMIC o Etlp d dzolvr st su lgbrcă clor două fct trc d s cotrr: ΔH dz ΔH rt ΔH sol ΔH rt > ΔH sol dzolvr st dotr utorăcr soluţ. Subst. cu dzolvr dotră sut sărurl cu rţl crstl stbl, cr u forză hdrţ su sut crstlohdrţ cu u uăr r d olcul d pă. ΔH rt < ΔH sol dzolvr st xotr îcălzr soluţ. (74) Subst. cu dzolvr xotră sut, d rgulă, L ş G cr u u rg d rţ, î proc. d dzolvr prdoâd fctul d solvtr. Luc Gvrl Bltur d trl s d rg 124
125 BILANŢUL TERMIC o Vlorl tlp d dzolvr sut rportt l u ol d substţă dzolvtă îtr-o cttt r d solvt (pst 300 d ol) l tp. stdrd tlp tgrlă d dzolvr. o Etlp dfrţlă d dzolvr fctul trc l dzolvăr uu ol d substţă îtr-o cttt ft r d soluţ. ocl două ăr pot să dfr ult îtr l, ls î czul soluţlor coctrt. o Etlp d dzolvr vrză fucţ d coctrţ soluţ fort; odpdţ ΔH dz f(x A ) s dt. xprtl. Luc Gvrl Bltur d trl s d rg 125
126 BILANŢUL TERMIC o Etlp d crstlzr (ΔH crst ) st cosdrtă, î clcull thc, glă ş d s cotrr cu tlp d dzolvr. o Î rltt, codţ ΔH crst ΔH dz st dorcd substţ s dzolvă îtr-o soluţ prop sturtă, l tprtur l cr ultror r loc crstlzr. o Pt. clcul rguros, tlp d crstlzr s dtră cu rlţ: ΔH crst ΔH dz ΔH dl (75) î cr ΔH dl tlp d dlur soluţ sturt pâă l o coc. tât d că după cr u st fluţtă d vtul dlur ultroră. Luc Gvrl Bltur d trl s d rg 126
127 BILANŢ TERMIC ÎN REGIM ADIABAT o Cttt d căldură schbtă cu dul xtror st ulă. oistlţ su utljul ptru cr s fctuză blţul sut prfct zolt trc ş u sut prvăzut cu suprfţ tror d trsfr d căldură. o Rgul dbt rg dl, xstâd trl prfct zolt (vâd coductvtt trcă λ 0). oexstă totuş procs dustrl cr pot f cosdrt că dcurg î rg trc dbt. Luc Gvrl Bltur d trl s d rg 127
128 BILANŢ TERMIC ÎN REGIM ADIABAT o Pt. rgul dbt, c. (55) cpătă for: Q Q A procs Q A (76) o Probl cr s pu: dtrr vlor tprtur fl s d rcţ, T, cuoscâd tprtur ţlă s d rcţ, T ş blţul d trl. Luc Gvrl Bltur d trl s d rg 128
129 BILANŢ TERMIC ÎN REGIM IZOTERM o Rgul trc zotr st crctrzt pr gltt tprturlor l trr ş şr d procs: T T costt (77) o Probl cr s pu: dtrr cttăţ d căldură schbt cu xtrorul stfl îcât tprtur î procs să răâă costtă. Luc Gvrl Bltur d trl s d rg 129
130 BILANŢ TERMIC ÎN REGIM IZOTERM o Cttt d căldură schbtă cu xtrorul s dtră p bz cuţ (55) pusă sub for: Q xt Q Q Q procs A A (78) Luc Gvrl Bltur d trl s d rg 130
131 BILANŢ TERMIC ÎN REGIM NONADIABAT ŞI NONIZOTERM o Mjortt procslor dustrl dcurg î rg ozotr ş odbt, codţ î cr: Q xt 0 T T o Scopul îtocr blţulu trc: d dtr vlor căldur schbt cu xtrorul, Q xt, stfl îcât procsul să dcurgă îtr ltl d tprtură T ş T, cu grdul d trsforr η ş l copozţ ţlă dtă. Luc Gvrl Bltur d trl s d rg 131
132 BILANŢ TERMIC ÎN REGIM NONADIABAT ŞI NONIZOTERM o Tr cuţ (55) sut xplctţ î fucţ d cst ăr: Q A F1 A, (, x T ) Q A F2 A η, (, x, T ) Q procs F η 3, (, T ) (79) (80) (81) Luc Gvrl Bltur d trl s d rg 132
133 BILANŢ TERMIC ÎN REGIM NONADIABAT ŞI NONIZOTERM oecuţ (55) dv: Q xt F ( ), x,, T, T F F F η A (82) o P bz vlor Q xt clcult cofor rlţ (82) s proctză î cotur sstul d trsfr d căldură, p bz cuţ grl trsfrulu trc: Q K AΔ (83) xt T cuţ d cr s dtră r suprfţ csr d trsfr d căldură, A. Luc Gvrl Bltur d trl s d rg 133
134 APLICATIE o S supu frtr ctc 100 kg solut pos cu 10% (sc) tol. Grdul d trsforr tolulu cd ctc st d 95%. C cttt d cldur trbu dprtt d sst ptru c procsul s dcurg codt zotr l t 35 0 C? o Not: s gljz portul d cldur l rulu csr procsulu d oxdr. Luc Gvrl Bltur d trl s d rg 134
135 REZOLVARE o Procsul d frtt ctc dcurg cofor cut crctrstc: [ Et OH H O] [ O N ] [ H AC H O Et OH ] [ ] 2 L N2 O2 G o S rct bochc globl: 2 L Actobctr ct CH CH OH O CH 3 COOH H 2O o P bz odllor ttc d blt d s, cu η Et-OH 0,95 s obt urtorul tbl d blt d trl: 2 2 G Actobctr ct Luc Gvrl Bltur d trl s d rg 135
136 Fz Lchd Gzos Copot Et-OH H-Ac H 2 O Totl fz lchd Totl fz gzos TOTAL GENERAL REZOLVARE kg O ,3125 3,392 0,1060 N 2 32,92 1, ,92 1, ,92 142,92 Itl kol 0, ,2174 1,4881 6,7055 kg 0,5 12,39 93, ,607 36, ,919 Fl kol 0,0109 0,2065 5,2065 5,4239 1,2816 6,7055 Luc Gvrl Bltur d trl s d rg 136
137 REZOLVARE Q procs Q r Q lchd FERMENTATIE ACETICA LA T ct. (Q procs ) Q r Q lchd Q xtror Luc Gvrl Bltur d trl s d rg 137
138 REZOLVARE o Ecut grl d blt trc: [] L [] G procs [] L [] G Q Q Q Q Q xtror oexprsq xt (cttt d cldur cr trbu dprtt ptru t t ct.): Q Q xtror Q [] L Q [] L Q [] G Q [] G Q procs Q [] L Q [] L Q procs Luc Gvrl Bltur d trl s d rg 138
139 REZOLVARE o Clculul cldurlor trt: Q [] L Q sol. Et-OH10% [] L C [] L ( ) T 273 C [] L C 0 t 35 C sol. Et-OH10% 4270 kg J K Q [] L , J Luc Gvrl Bltur d trl s d rg 139
140 REZOLVARE o Clculul cldurlor st: Q [] L Q sol. H-Ac11,6% [] L C [] L ( ) T 273 C [] L C 0 t 35 C sol. H-Ac10% 3700 kg J K * Q [] L 106, ,80610 * - I lps dtlor xprtl, C s- clcult dtv, cu cut: 6 J Luc Gvrl Bltur d trl s d rg 140
141 REZOLVARE C 0 t 35 C H Ac11,6% x H 2 O C t 35 H O 2 0 C x H Ac C 0 t 35 C H Ac J 0, , , kg K o Coctrt Et-OH solut fl fd fort c (0,47%), s- gljt portul cstu l C. Luc Gvrl Bltur d trl s d rg 141
142 oclcululq procs : Q procs M Et OH Et OH Q rct η Et OH REZOLVARE Et OH M ( 0 Δ H ) ( 0 ) ( 0 H H ) Et OH Δ η Δ R η Et OH T R Et OH T Et OH R 298 Δ R ( 0 0 ) ( 0 0 H H H H ) H f CH3 COOH f H2O f CH3 CH2 -OH f O2 H 0 f CH 3 -COOH (L) H 2 O (L) C 2 H 5 -OH (L) O 2 (G) J/ol -484,9-187,02-277,6 0 Luc Gvrl Bltur d trl s d rg 142
143 oclcululq procs : Δ H R Q procs ,40,95 REZOLVARE 484,9 187,02 444,32 227,6 444,32 J/ol 91, J oclcululq xt : Q xtror Q Q Q [] L [] L procs 14, , , , J 1,231MJ Luc Gvrl Bltur d trl s d rg 143
ELEMENTE DE CALCUL INTEGRAL F R lim lim lim lim (criteriul cu şiruri); lim lim = lim ; Limite de funcńii NotaŃii: f :D R, D R, α - punct de acumulare a lui D;
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