1. Introduction to Chemical Engineering Therrrtodynam.ics SEVENTH E.DITION J.M. Smith H. C. Van ess M.M. Abbott

2. 1 2 J Contents ~"TROD COO: 1 I 2 2 3 5 6 8 Ll ~ ~ of'The:JUJCM:l~, 11 .._ r 4 t ' 1 .. a .... .. ._ l.Z Di.J2lt!n.siCll'1s aJlCI Un.irs ..-................ ~ ........ ................ ...... .. ,............. . ... . .. . u L4 1..5 1.6 1.7 1.1 I.J ~or Amountor Si~ - - -- .. --. ~ .................... . .. ................... ... .......... T~m:fe'. .._ .. . . .. . .............. -.. *" .... .. - ... .. ..... .. ............ - ........... - - ..... . ~ . ............ - _.._ ...... .. ~ -~ .. ~--- - .._ ...... ..... .... .. ..... ...... .. .. ~--- 'l --- .. - w~ .......... ,.,. .........,..-"'s ~ .... ~ !I . . . . ..,. .. 1 ., , . . . . . . . . . . . . . . . . . . . lol .. . . . . 4 ' . . . . . . . li 'Enttg)1 - ........... ... - ....., - .. - t .. - ~ - .. 1 ,. .. t> 1 - "' t ' ~ t r " 11 f' Hear .......... ~ . .6 . . . . . . . . . . . .. . . . _ . . .. . . . . . . . . . . . . . . ., ~ ~ .. ... ,. ~ .. , .. . .. ~ ~ , " ~ , . . . ~ '" LO l5 TBE ftRSTLAW NO otBD BASJC VO CEP1!8 21 2L lf 22 23 26 29 29 31 37 38 40 44 2.1, u 2.3 2.4 l.S 2.6 2,7 2.8 Jouk"'s ~ ... a l't P a I e I t a I a. II a I I a I a a .. . . I . I&. .. I.,~ ~ iJ a .-1 a 4 .0. ~~- - - ..~ - ~~~ - .... ""--... J/1~.1 ~ "lbe A::rsJ l..aw" of~~ ................ ., , _, ...... , .... .. 1!!1 ,. ... . . , ........ . . . Energy Bala.nce rorClosed S)'!i'ttmS _ lbmnodyoamie Swe and Stale FUDCtioa~ .............. _. . _... -. . _. _. . _~ ~m.hm-um . I a a a a a I &. a .A. a a o ~ a .- a ., a il -' "- ,. lo. .., o & a fl' '"" ., ., .,. .. .. It 1'"' !!; e ._ The- Jlt'ia.tie Rok.. ,................. ,.............. 4 . . . . . . . . . . . . lol ..... _ .. ~ _ .... __ .. _ .. _ The R~ible ~. _. . . . .... . . ......, .. ~ ,. .................................... 2.9 COMIJinf-V and LtJIISt3:fil-P ~~ a 1 1 o a o o r a o a a ~ a a~ a 2...10 &tba_lpy'......... .. .. "" ..... t . . . . . . . . . . .t . ... . . . . . . . . . . ... .. . . . . . . . . . . . . . - . . .. - .. 0 . . . . - . . . . . - .. 1.11 ~ Cs~lV .... ~ . . ... ., . .1" ,. . . . ..... . . . . . . . . . . . .. " . .... "' - . . . . . . . . . "' .1" ... ._ ;:J_ p 2.11 t. and .Eoi:rgy Balances for ()pea Syac:ms_........ _. _. ____ . _.. . . _. _. _... _ VOLUME1BJC IPllOPE.RTIES OF PURER !.J PVF Be-havior: of Pore Svbsumces ....... . DS 64 "' . . . . . . . . . . . . . . . . . . . . . . . . . . . J/1 . . . . . .. M 3..1 33 3.4 3.5 3.6 3.."1 Vtrial ~ uf State. .. ...... .... - .... ~ .. t- ... ~ .. "' , ~ . ..... , ...... ~ .. "' "" ... . ,...,. 'e !r -r , - .. ""' ... 1bc Jdeall Cia a .., a.."'._ .. .. e: -.. ~ .... _. .... ii - 5o. il,. .. ,. ..... - .. "'"' .. !" .. :5. ~-- r 10 73 Application ofk Vi..ri:al ~()liS ,_ ... _j ._ I I Jl . . . . . - " ~ .... ..._- - ~ .. n Cnl:Jit- l&Juati~ ~ofStak T" .... .......... " , ... ~ ~~ ~ ............. , ......... . .... M Oeneraliled C011elillinM for Gasc..i........... .. , ... . .... p . . . . . . . . . . . . - - - ... 99 Oenemlized Cotrelations fM Liquids ~ ~ . . _.. ,... _.. .. , . ..... T _ _ .. U:)Q vii Obras pro egidas por d r itos de aut< 3. 4 s 7 8 11&TEFFECTS 12! ~2S tl3 l3S 136 ll9 140 143 4.1 ~ u "..,u ~., 5J 52 53 ~ 5.5 5.-6 5:1 u u Sal_5ibkHtaa Eff~ Lat ~m~~s ......................4 .. .... A ~~ ........ ~ _ ..-... ... ... .... _.. S'~ Hat ol~ ........ .. .. ...~.- .. ......... .. . .- .. ...... -~- .... r ........... ... - . . . . "" . 1:1 ~_Heal of pmmati.(D_ 11 ._. a. a a a a a a 111 ~ " a a4 .._ La "to a ~H.eatof~.,. . .. ,... !t ,. ..... !! ... .. ..,. -~~~ ,. ., t'.., ,. . !t 1!. Stia11:11:1ll10 orb SeteoM:l.aw a .1 a I S "t _. I ill a 15. ,J a .L a ._ 8 II .a .. at a .-! ii if ....... . . . . . . 5 ii ... LOO u._... =--.~ QJ~~ !l-" l !"" l' !' _ .., - .,. -. . , ..... ~ p '!' !' '! .. .. ~ + !! ii ... .. - ... " - . , - " ' 11 11 e ~"'I! r ... '! ~~.c::~tum~ "11!!1 . . . . . . . .. . , :"1.~11fl,. ........ . ... .. ~ 161 163 ~ f " .... ... .. ~ ... ., ... "' jil .- t - ..... ,."' ~ r '"'- ... t T "' - ..... -- r,.. 167 ~~~oran'Ideal Gas . ~ ~;. i + 1 o " 0 T + ' r 4 rro MJitbeJDatieat Statemalt of~ SeaxJdU ~ ~ a a a r a & a a t a L l7J 61Juopy~fot()pemS~ .. .. . ....... . ............ ..... ......... .. . 176 C81oa~ of -~~ 'am..,.~._ .....................,.........,.._........t. . . . . . . . . . . . . . . . . 181 ~ WQt.k- a ... !'a -. 1.. il a ii a .- .. ., ..... 11 a a. a &.. a a .. . . 0 a.-S IL!!I O. ie+ ~ " i- 5J.O TJm Third Law4 ~ .... T J liS l88 188s.JJ Enttopy trmm tile ~ic V.ewpciJnt... ~ ._ _... ............ .. _.. _.. _........ . 6.1. u 6..3 6-A '-5 "6-1 &1 IU u ,,l ttl,., ~'~9L6 P:mperty llelatio.ns ror HOIIlOgell!e.OiliS Phases ... ~ ... r' .... ..... .... ... ., ...... _ .. _ __ .,. .. _ _ , L~~ 1'! !'! '"' "!" ... ,_ .. ., .. "1" ~-!!Til,. ~ e r-"T't-""'1 .,-~ - ~ .. r y~r" " !!'II !I: IIY till'~!'"'"!! 199 l99 208 ~Ulual Properties by Bqwmoos 1ofStare . . . . . . 21:5 ~Sy~s ._ ...... ...... ......... . 1 . ... . . . . . ..a.~ a.._ .... "'- ..&.~ ....... ~ aaa;a._. _ _ .. ~.:Jillal)lieDia~s ........... .. ....... ~ .. ., --"'"" .. ~ - - -"" --... - -,.... .. ., ,.. ... ,.. .. "' .. ..... --r ... .. tatJ:ta.of'~-ylllilllic ~s .,II ::t W II '1' I! .- !II II If P a .- II II a a II r 11 1 "I a a 'C a a .., II I a a DO 22:5 226 GcnemliudPropeny Com:.Ja.Wms for G~"' ... ....J ............... 230 ~ ~ of~es:sible Rnid:s.. II II II a I' W II II II a S II !II 'II a II ... II ... a I II II a II :t.. a a & a ~ ~~~) a r a II' ._ IS ~ a :61 a L a jl "' -. a a .._ a ... r: a 11 "'- a .._ lj co a ~ a ._. a .i. a .. "' .. ~~ft~ 19" "1~ . . . . .. ...... ., ,"' '!! '" ... . ,., .... .,_ ~"! "'r '"' .. '"'" ~"' '"'I"' ......... ., . .. ,. .. "'' ......... , , 254 2:55 268 !1-3 DeStea:m Po:weJ- l'la:DI__.. a llf llf a t. II ow t a a a , tt e t: *t a 1 a t " ill .., " a t a 4 o 2911 ~amt.~moa., ~~ . '""" ..........".: ..~~~. _. ii " ............ . ....... ~~ ....... ..... .............. .... _. 3.01 Jet:EngiJJe:s; ROC'k.l ~ . -.. ".....-'"...........~ ................ ".........., . 310 'fJie: CIJ1lOt RdifJJ.aiiDf- l. .. .. .... a 5 a il ~ .. + "' ... of oo1 .... "'! 1o ~ i p _. .... o. of o. oi .. "' .. .- ... .... ~ Tile v...-~m~ 'Cyele_.~ lP' . , t r I .. II t a .! II rlle ~ 11 . ..... .,. I' a 'I ., . J' "TTie ctlcb ofRe~t ., ... ~~ . . .. . .. . . .. . . . ... .. ... . . tl . . . . . . . . 61 . . . . . . . . .. ..lis-~ ~ri.grtliarlt~ flil.-tioPs ofT iUld P fQII' ftlN~ ~ ifi me mlroltllioo ,o[ Q and 1V fe_r any ~ ilw~ring Ibid ~ubsnmce. The deter- mimtioo I ~ values tor~~ rwcti(m and rhntCOO'clmian :md US& am~ mtaw~ AUltm"ms:ofEq. ~I I' D11LWbe~p;E,~ jp1fiCADJG~ ~pod~ PV ~urn~ Q tDCIIIY pf IJVJ~ Of [peJ" ~ ~ as; diDes u~ merefm'e 1:1 also11M IIInl~ of energ per mole or perunit ~ In lbe Stq~~ the h6e 011ilt nfptr~ b l.h:e ~al ~N rn-~ Wid,. fm tl'Ktillr 'A 'ViOid bp IEL ~ Dutdl - " w1JO b .~ bdiv i:1 1LQ . ~~ m. pc:m:alueliMii'J m19U. ud ~ ~ ~ fwpfl}"~iill'il ! (58: ~ ~ rJm fll)llt:w} L:&te~ I ~ tr!~ :110. 109.p. 3. fooaMn 2. l9(11),) Obras proteg~das por direitos de autc 51. 2.10.. .Emflalpy 'ltOI~ ~ mor1 1111: PII J'll'l'ldUellhen bas lbe Dlli$s. m mo.l- 1 or J IDOI- 1 .. to dE. English lineailfig s)'Sttm a ~ llbi1 fer (lie , v pfrdacl 'the (ft lbt~-~.. wbicll an__ses when~ ls i:il (lbr) ft)-2 Witb volwiJc ln1{fAr(lb; )-1 Thi rremlt b IHWill)' ~ed tO {Bm)(Jbm}- t ~ flWWODIby 778..16 for .in Eq.tl.llk lwwrst bWJillm)D .En:~r mperiDg uni1 for U and H i !be (Dtu)(l.bc.J-~. lBecanse U., P. and V me aH ~ fiuoct~ H as clebJJed by Eq. (2.1I) - a so a !li.1B'tc' fimmgg. l.ike V :mel V~ H is 1m in~'l; propa1}' of ~ 'Jibe; d~ fvml of IEq.{:t11) : dH =dV + d(P V} (2.14) This equation applies wbtmcwrcr a diR'cn:mtial ~ oct!UJ'I mdie em. Upon ioll!~ hbe~ m ~ fora 6nitt dwige in w sysae~ZC Exarnpre 2.8 C8ladale Au and AH for 1 kg ot water when it ts vaporl2ed at the constant mmpera~ tJJTtt or 110~ and the c:onatantpressurre of 11 01.33 kPa.. Trhe spedfiowWrne$ ofiquid and~~ at lhft$e colldilior.sare 0.100104 and 1.673 m3 kg""1 L. iF1hischange. heat in the amoont of 4258,91 kJ ts added to,the water. Solutlon~a We tate me l k@ ofwaterM ~ sy te:m..~it alone isofinliftiL and ilmagiae it ~ m a cylindby a ftiaillntcss pisn)n frldilt act~S u. ~Dtsnm ptes.'Stttl: oft U)J.:33 kPa. '" bear is addett.lbe water eva~ ~g from loiDW ro its fttmd w!umt. !qualion (2.J3) ~ writt~ ft'Jr1bc I..kg SJ5(em is: AU - tiH- 1(PV) IAH- P A V P av !!!: 101.3'3 t:JPa x (1.613 - 01 .001) m1 = 169.4 klP~un3 =1.4tN m-~ M 3 ~ 169.4 kJ Obras pro egidas por direitos de autc 52. 2.11 HEAT CAPACITY 1IJOdem ~-or btal 8$ ~ m wo ~ bf be: itb dllll tt tJJy bPs A t:apxhy for hea. 1be smaller the tempnatm:e.dlmp in a body Cl.USed by the ~or a fi' -o qua;wBy of beat. die ~ its ~Y~ ~. i& '-1 ~~, ~!~liP be ~ a. c d(lfdT.. 1'bedmicuJ&y~itb this udwil m:lkes C. lib Q. a proces~quanticy radJcr llm a sac fimt1ion. HQ- ~n. iit dOes JJ me~ ottwo quiDritiJ "'rim tbis OUIOIDded a:une that~ in~ smre ftlnmoDS,. DDalDbi~ refaled to adler stale .fmtdiom.~ HeatClpaoltyIll Consllmt M:tlume ~CftiSt#nt'WIIII:in&llrar ~) nfa.~ Is,dtflant Cy (~) (l. l6) ar . 11' 1his defmitkm ~ both lhe molarbeat~'Y and lbe ~ b&!maparity (usu- ally adW ~ btat).. dcp;ndiDJ whtlbcr rJ is tlw ~billa or spoci& ~ ~ A1-~ . . deJinidoD " DO rdem~ 10 .my ~. b niliam in an espedWJ~ simple wayto, aCOIISUIDt-whlmc [~ in.adostdsyge~ flilrwhi~l!q. (2:.16) rooy br~ dU ~c...tlT 1(ons~ V) (111) (2.18) 1'bdmw1'l: ifh Hq. r{l.IO) fara mvJctcuticaJty renniblt~ COMWitvoh:lme ~; ~: Q = 11 4.1J ==,J.nCy tiT (~ V) (2.19} T, IfllJe 'tllmDe Wies ckiDns lbe ~ !but returns at abe aid .ofthe prote ~ to i initial ue, ~be ~ ~ ri,gJub' !be Mkd ~ of~swot ~ ~ r~jb ''2 = v. iilfJd A V :J 0. ~~ cbanges in !U.fe f11Det.iaas me mdeperuleru of pmh. aDd may dlercfore be c:~ by tquab(DIS fQr il tmly mtlStatit-WIIwnc ~ witb the &aliJC Urltial W"ld lind ~ Equati (2. 18) tbeo tti AtJ = f ,c,,dT. beai1!1A U" Cv. and T ;eo aD run r~~. ()Q lbe Qlhcy bmid. Q aDd w~[ 00 ~ alld Eq. (~~9} is.i1 vulid ex~on Q. and W is iD ~ XIQ, only for a ~~lr.o/JilfW ~ . Thi.s is the reasoo for IDe &tinc~Wn bet'W'CCI " f-lDCiiom and Q and W~ 1ifle prin~ple lhal ~ fuol;tions an: i'.ndGpcodsmofthe PI~ is an O'n~ IIPd o~ul ~ F-or 1M alrdldon of ~ chanpa1 an II1ChJal proceu. map be f'IP'M'id'IJIlftJ' Olber pmctSSwtdcl!l :aooampll....,tbe santeChange lnS~ata. Suda au aiJmlaliif~ f'I'OCCSS IDiiJ be~ lw ex~ bef:.aa.w ,ofi: si.mPfkity. Obras proteg~das por direitos de autc 53. 4[ _ (8H)c,. !!! .~ '3T p. (:U0) APDT~ dllt1ilion ~ both ~~ Qd ~ b;3l c-a~des, depM,Jing on ~ H is the IIDD1ar o.-~pedfie e-ntbatpy. Thisbeatca..,my ~data in an esped:a_Uy iimpiC way oo,. tS~-~ d~ .:t'~ p~ rw~ eq_a.lO) d ~ll}" d1 'Wtlfaeo.: dH;;::;: c,.dT (cons&P ) {UJ) wllen:ee AH :;;;;r { f", C,. dT ~UWL~ Pl (1..1'2) Jrl fora.mcdlanicau:ymvcrsilde.COH.ii~,p pxvc=ss. dlis rc.sull~ be~ with Set~ (l.J3}~ (2.23) lkca.use H~ Crr. 3mli f ~*i:efimdions. Sq. (l.2l),applie.smany pmce forw~b ~ Ci1l Pt wbedler or DOt it is .ctually Cllllied eu1 all constant ~ H(Milft-V. ,only for- lhl: IIIIDdlia- ~, ~II*. ~~-ure ~ QA ~!tea~ .and wort be ca.k1Jlalttd by meeq-ions Q- n all. Q_, nfCtdT. and LV:;;;;; -PnAV. example 2.9 Airat1 bar andl298.15 K (~0) is ~fiSed 105 barand 298..15Kbytwo dtfleMM mechanicaly rewrsible processes: C&1cu&ale lhe ltteat and work ~eq~Jiranents and Au and.li.ll of the .air lot eacbpath. Defollowfng heat ~mea ror aJrmay be assumed Independent of ~ C~ ~20.18 Assume also for air lbai PvJT ~s a constant. reaardtess of the changes rt undergoes. At 298..,s Kanc11 oarthe rnoaarVQiumie or air 1s 0.02479 ~ mQf- _ Obras proteg1das por direitos de autc 54. 42 Solutton2.1 1o ~ ~ 1a:te 1he ~ as 1 mo1 or 40 ~onWkd mam imagm.aty pis- tnrkyliodllr ~ Beause the ~ awideral aro m~:t!y I'C~11. 1M pi " imqkted to ~ iTh lbc cylinder wi:thow Erict!GD. The .tiDal"110 ~ "" v.~ ""ll.O'J.t19H)=Q.0049B ml (a) Oming the fimsrep Cbe air t8 c-ookd 'dieeonstam pressure af I bar'UIII1il the liD.al -d..~ of0~0049S8 ml " ~ ~ lQt(~ Ofdie ldr at rlbt:- tDJ of lhisaJOiiDg*P k _, v..,. . (0~) m .>~t - Ti ~ ::298~tS . . ~ J7. QJ K: V1 01 .02479 Q =All ~ Ct dT ~ (19.:10)(59..63 .... 29SS5) ~ ....6.941 J AU = AH - A rV}1= Alf ..... I' 4 V I!Z --6.941 - ( I x J@)(tl004958.-.Q()I!..4i!J) ~ -4.958 J Dmm.g l.1JDsenmd51:eprb: votnme:isheldC(m$'bllt1 ar V::! while: tkuhtII he-filed 10 ib ~ uae. Oy &J. {2.19). 6-U ;:;; Q-- C.,fAT (2{178)(191.1S- 59.63) - USI J 1l:ktCOIIIJ!kteproce ~~ d:w: wm of iu $1~1>$- R~ At} ==- -4-;9:JS I 4.~58, ~ 0 Ute~ 1bc a.wa-pplit$ tOdiiO ~ ~, AU e: Q + W. imdlkrefan:. if);;: - 1,.983 + w !'4~ (1151 AH ~ AU+ ~.(P V). aht>appms iD the entire~~ Bm :rc;;:;; r~..Wid lhcmf'al'e, PIv, =~Y2~ ~ 6CI'Vl:; o~ ~ t.H~A1J;::;;0 (b) T~ dilfatut5tep5 ,are U5N in dUs ~to teadllhl .arnr 6il;:d StU~ ofthe air... 1n the first step themis hi9ed at a~wJwneequal to its inWal ,. un1iJ die~ ~rat ofsbarm~ba!The o:it temper.dllle aJ lhe end ofthis step8: T' =:! T1 ~ - l98.1S (I)e 1,490.15 K Obras pro egidas por direitos de autc 55. All this --ttp lhe vel~ uXJRSWit. iUd Q J;; AU-==- Cv IJ.T ~ (20.78)11.~7:5 -298. 1:5).:;; 2A.18!J In lhesecond.stepthe airis coukmm P a ~ bar m its inal ~Cue: Q ~ AH ~Cta ll 'T - C29.J0}(29&.1S - 1.490.75) ~ - 34.7mJ till e AH - A(P'Ll ) ~ AH- P dV = -34.103 = (S x 1~){(tll)(9S ,..... 0.0~4-79) = - 24.l8S J For the MCJ S~eps combined.. Q ~ 2t788 ~ 34,703;;; ~9.9,,SJ dfJ = 24.788 - 24,188 = 0 w = 4 V ~a;:: o ~ t-9.9lSl:: 9Jts ~ AH;; AV .;;;;l) The~ dlanges ~u and d H ~~for megiven chaqe in~ are lhe ~ for botb J*b$.. On lbc adler b1Wl 11be &mlwt:IB 10 pU (a) and ~(b) dw: Q d l' ~ OD the path. Examp e 2-.10 43 Celt._ llhe in~ern8l,.nef9Y ,9Jld enlhq)y cha:nges lhal oecur When air is changed from an ._ "lial state ol ~~ and 10(atm). where its mOJar YDiwne fs 36..49(ft?{lb mOfe)- 1 to a ti81 Slate at 140 F) and 1(&'ltR)AAssmne iJr aif thai PvJT is eortStam Mef thar cv:. sand c,.;;; 7(81u)(b more)-lr rF)- l. SOlution 2.11 B~ property~ u:v ~Pdmt of dJo ~ IbM lwiPplkiP otJopt, mlk!llnliommay be basc.don a{1)--gep._m~ ~ibleproce_ssm~ 1(lb mole) of llir iB (o) ~~ :ill comta_nt volume to b finD) ~ :wd l6) bcaled at~ ~ 1:0 rhe 0:na1 ~ ~ ~htw ~ l!ft ue OPJ ~ R1VLtio 5QJe.: BeatDSe PV = i T, die .rmia TJP i.s i."Qm.tlllll far step, ( .::=t"''"'fR> andb IEmpel'ULm: "1:wJga f(B' the II'WUSliCJIS ~~ a.Ta =49.97- 499.61 =-449J'O(R) A:T~ ~ 599.61 - 49.97 - S4,.70(R.) Obras protegidas par d1reitos de autc 56. rwswp'W~ by E'4$.. (2.18) and a.l5) JiUfl ._ C'V oT4 ;.- (Sl(--449~70) =- -1.248..StBtu~ .AHQm AU~ + V 6 P11 ;;; - 2J43.S T- ~ 36A9)(I -- 11 0){1.7195) = - 3,lJ~.6(8nu ~ ~r 2.l ~9S C(IIJVmti. * Pl' pmtluct from (liiM)!(fl)j~ ~1't:tch ils an~ IIDiL intoI(B lU). fOr., (b). lM >-qlum:f>f~.~if~ v,"' v. ~~ =36.4!1 ( 1 ~) (:~) .. 4l1.93(fi) BJ &p. (2..Zl}LlMI r-~ S1 6Ht, - c, Alb;; (7J(S49.70) = 3.847T9(Dtu) AV.~ =ll~ ..... P a'Vh = 3.847.9 ~ 0J(4)7.93 =- 3Q;49)rf2.7l9S) = '!t756.2(lku.)i for die11in step$ l()Jether. llfJ = -U4B.S +11563: =S00.7(BtuJ llH = =-3J4Lt5~ + 3.847..9;;;;;;; 706.3(B.tu} :2-.12 MASS AND ENERGY BALANCES FOR OPEN SYB-TEMS Altbuugb1bc {oeQs of llxl Pl~l ~- ~ oo ~ ~ cbc ~-PtS ~ ~find iJr~ ~ pliariQIL 1Mlaws ofll'll:tS.t! and eJm1Y ~00 ~y ID Q/1 Jm .m open tll tOe:Joxd;sy .eros.. ~ dleopro ysrem includes~ clo $~ a~;al ~ '111IK .temllllinderrOftlm o.erH lbftefore ~ to dle ueatmeotof cpen and fJnD to the dsvelopnmt tA ~of wkt appt"~bi!ity. Velocity, u mc: Ma Obras pro egidas por direitos de autc 57. (U.IIJ) l The a:na fOJ 1:lffl.l A ~ lbe a~seaiomd i.d'ea of a eoodUit und p - ~.ific DliJlal' tbsit)t ltboug_h 'doclty is _ l"tddr ~u,? its ~ maym1d u i ~ ~ lbr u'"~ ~ nf a streWD iD tba diredWo normal to A. flowrale"i m. r4 al:l:d q ~~ ~m.'l1f'C8 or,,g;md'Y Jib' oml of lime. Vdooity u is ,quicc ~1 lo n:z;r.urrej #$ it ~ nbt ~ ibe m~of flow. Nembde:s it is am impmtont design~- Example 2.11 Liquid no-hexane ftOw.s at a rate, of m :;::::; 0..75 kg s-1 tn a pipe.wrth inside bcto~: dilleY T"+6(pvA)& ;;; '0 ~c2.26) In dJis form1he ~fm~S-.bal.aoce ~~~ i8 ofre.n caiiJed abe CDttriJWfl)1 UjUtJtitmA The ow~ dtanc1mted ~ mte is an ~ specW for wbicb amdit"UlllS ilbin the com:ml WlUllU; do IDOl e_bange wilb lime.. 'inle rorun1l Vt)lum~ IDea 0~ ~aim a ~~L IJ1ISS offt~ lmd b ftrslor~on 1mB of'Bq. ,p )$) u~ mducing:. &j.(2~6)UK A(DPA)rs :;;;;0 1bc emu ""steady mtc... ~ noc ~Y iu.lp)J tbac ~ ~e ~ DlCJidy dm the: inllow oft~U~S.S i!,aaaly matdled by mbe omBow of m:as& Whe:n then is hut a .single e~ and a 5iPJ,le wt~ lhc JruliS ftgy.-rate mi:s me. same (OJ ibotb meams;, lben. Obras proteg~das por direitos de autc 59. 47 ,., lltA 1 ll2Al uA m::: - ~ - = ~ Vt 1 V (2!7) Beamseenagy.libJm~SS1 ~ comcn~C.d, the rate ofcbange ofenc:r" "Writhin thr concrnt 'clu~ oqu the Bet ~of~ transfu mto lbc ooadtOJ ~- StteaniS 00in: intO and ow of the mmrol 'OJWDe baw: ~d Mtb them energy in i~ i.mmmL ~- and tindic f~ d aD comribute 10 tbG ~~ chatJp of tb~ .5ysttm~ Eatb Uni~ ~ of ~m:.mt ~ltO'lics illlllamtal ~ f) + j..2 +~,. where u is me a~~ 'elocity ofbe SU'e'arn. oUmte ifi{:f~ mis qpamlt)' iD addi'lioo ID lbe hea.lrran.sfer me Qand work nne.: cf(mlJ)c [( 1 ~ ) . ] dr = - l!i U + ~u + ~ m II+ Q+wrrkrate Conarol vol:ume n~ W'OCt mte may inc;lade: WPfk(If5e'.~ ttJ111'18. r~ ~ is ~ with .-mviPs dJe !Dowmg streams lbrough ealmlees and was. The fluid at all)' eucr.mee or e.m~ a 5d of U'-e:~ ~I'~ v, u, H.~~. ~ cllall a -~~ ofQuic is fitted v;idl a :s.tirr.a dial r.Sr.diven ~ to the WB..Jiuat tbr rst.r of0..25 k,W. Hwrl'OOJdoes it * fot cbt ltltpmllute oflbc , Cf m rise ro Joc ifM Ileal is r~ tmm l.be water1 P{lf 'Uier.Cp ;;; 4.1 lk.l .q-1 I 2.11. HG4t io the amtJUnl ol 1.5 kJ is ~ to a closed ~.., wbilc ~ io~ cnerv ~ 'blf 12 tl~ How nDlb Me.Q)I is tr.11Werred as wort? Por process caumtg the 5IDle rd'umpd ~'buJ for which* t..L-ork ~ ~ l.tovl modi~ is~ 2.13. A steel eding weiplog 2 ~ bas an iniliat teAlpmdlll'e of ~ 40,kg of WUia' initially at 2SC1: b coolainrd in a pafctdy in..~trd 5tftl tant ~& S lJ. The e:rsting is JJmne&wd in k wah:r and tbe ~ aUuwcdJ to miiiO llD cquih1witmL Wb21 its linaJ ~~? ~ rcc:cof,~ or c~ UDd :USWnC eDMtam specme beati ot4.18 kJ tg-1 K- t for wuter and!0.!0 kl t,- 1 K-l foi s.r.ee.l :Z..It. AD ifib'()fi"JjB~iMe 11Did (p ~ ~) is ~I in a ilb"lilil.ud ~ylinda' fined with a frii~ piswn. Can mergy -,1Xt be~ lO cbc IU:J? ' tis me dmop miJ!Jitat'131 ~cAme ftaid wM8 me ~dt'e ~ i.ncn:ased:t:tcm P. pt1 l-15. One k8 tpsiaJ. wba1 " me ~, ~ kl ~ lbal Pvf T coMtm1.. Cv = (S/2}R.U1d C, ;: fff!)R~ (Val~ fQr Rare givRJ in PPr A.) l.JL Wamr flows t:hrougb haril.mtal coil heated &om die oo_t!k.ieby hiibm~ ltoe ~ AS it ~ tbraup rfbe Olil lbG -.-r ~ from liquid II :!U)tkPa iWd SIJ1C tu YaJXK' at ~00 tPa and ~25 C ben~ doo'ty is :J m ..- I .:d.)d its -.it ~~Y is200m s'"''. ~ the bAt mmsfm:'cd ~ ~ cW1 pe:r Wid RmSof WD9'.. E.nJbaipjj oflbe inkl and OUlkt 1m11m am~ lllfee 334.9 tl g-1; Ollifel: 2..726.5 tJ tg-1 Obras protegidas par d1reitos de autc 72. l.D~ s~ IteM!! ~t ~1 ~ lb~ 4 con~g.. in ~ ~t', lS em luna :md wil:b an inlet diame of Sem. Allbe ~ (~ 1). the. ~re WH1 ~ ~ )2>50C,apd 100~ gdJ tbe ~icy it30m s-, A!tlhe mutt~ t l). tbe steam mmpemme mdpressum ~ 2WC and 3:50 ~ Propmyvnlw:s are: lie= 1.112.5 .kJ _q-l v~ ;;;;; 38&6~ err,- H-! .. 2:.945.1kJ g-l v1.. 661.1Serr,- Wbl; is fbe ~ Gfthe steam ar 1hell!i'JUl)exit, md what is the exit c.fiameter1 (.o) T1mx lBO~ ,of niamgen 8l C., MIIIILind in ~ -..usaLis heated tfi11S('JP'C. llow muCh ~ rs mq-~ If lh: ~ u ~lig!Dlc !Deal ~? If tht" Vlii1Lti:D1I. wellbs 1100kg udba,. a ca:p:acity ofo.su tg-l oc--..bow much ~1 ~~~uirorl (b) Foar odes orn.i:trogal at 2rxt~c is COiltained i.n a ~llinder mrnngement How lmJdJ kat liiUSl be et~ from 1bis ~ w.bkh bpt at amtant ~ lfD .CXJOI it to weitdle beiit cu~y of d.e p8lfm Wid q~:Hm.ao:- is oc- ,.~tl l.JL. In~hefoBtilring ~ Crv =3 .mCp ::= 7(&u rQ!IO)c)-L - ~ for ni:trO;en ps: (R) "l"bnx pound lliDI.c:.s ofniiio.gcn 11 M ), CODtmoedl mII dajd ~. ~ ~ to J~FJ__ How lfilldJ beat~ ~teqllllRd ifh~bas.. ~le.heM epaily?1f il '_ . , l00tlbm)md ~ b ~) of0.12f8tul)(l"-J..... ,...... bcrw OIIIdl lbeilll$~7 (b) 'Fa:u'pmmd mo ofailm at F) is eoota:inedin :t prwnlcy.l.i.mfl1:r:m-ang_e- JDmt.. l!f'!Mmucb hCid m~ I); cnr.u:--ttd :fiirQIQ ~hi$ ~~ whidJ ~ kq;Ml at wq- ~ to cool ir to 1150 if me Ileal ' city m ~ pisu>n :u.dlcyl.indcr - ~td? 2.J!., Font llheeq-Uillkm fnr the.wadcf m"ee8iblle:. ~~ c~ of l ~ ofgu in Ill piMoo(eyt:ind 51mlbly utbo mobgwlumt d tt.ps is~ by II:T V==-p+b 131 Stmn m2txl(p$a} ad (J(X)f'.F} (5t* JJ, m1~ a turbme lhrovP a )..inch..~ pt~ ith o ~ of IO(ft)(s)-1 1"hh! ob:anSt Dtm the ftlrbiDr b c.mkd through a 1CModb-diameli9"pQ:Ie md matS{j)Ma) zmd ~ lsmte l:J.Vh:l.t is thepoweroutput of11be r~? H1 == LJ22.,l(BUIH )-~, IQ_ -1.J48.6(Bto)~)-~ V] s 3tMS(ft)3(1bm)-L V1 ~ 7S"'W4(f'lj3 (lbm)-1 Obras proteg1das por direitos de autc 73. 61 2...K. O:i:dKm di~ ~ - dlll!IS:. ~- l~. l.'l:l9s.tat_lr dit ftovl of liquid wazu , C. For QDC of dtr: seu of t~ditioos ,gi-en -liD!"..~ m(in q - I) ad APIA L (iD kl?a m- 1). As.mme ID 1a O.fXXH. fQE' liqul4 ~a( 25-~ p c 996 q m- 1, and fl. :::! 9.0x lor' kg m- - .. ~ tbat die llmv w1nrbole:At. ~(a) D tg 2 em. u:::: i m s-1 (bJ D - S ~ u = I (0 s-1 1(c) D ~ 2 em.. u ;:;;;:: S m - I (d) =:Sga ~s m-s-t 2.AL Sil.~ ~t ~ p1~ msia~~ m~ ~~ ,e~roleum lf'rac... limlation tem: medml~ ~ ~ i~ n-bllf~ and n~ A ~ biR:I oft&csc- ~ in '"li;JIOfltiq~d GQQifibrium ~n 1 ~ '~t On~- ~y plmse-rule variables in addilioo to T and P do the: oompos:itions oftl:Je ~-s ~ IfT and Pare m~n die same. ~ l.ba'e. any way rube ~tioo oftbe t~ Qtm-. w1be.. eao be - pel (h) adding or reJilD!iq ~) witbmd &ff'~ mt.~ ofitr ? 24 lEiby1me a turbine 10bar and 4SO IK-. aDd ~ Ql l {:atml) and l l:S ~ ~ m1!:! 4.5 kg ~-Ii ~ fbt, r.;Usl c ofi'~ mtbinc. Stmc fillY ~um )'00 fl:lake_ Dma: Ht =7' 1.1 ll:l ~ 536.9'kJ .t~1 C/i =US~~ :!OO)(Ilfl/ kV'to_m 2A1 ~ hca:tin1 olahGID!:10 ~ i& ~m~III__~!emust b.lliQdekd.~lUI open ~ ~ .apaD.Sion orthe ~. air m. etmm~DJ. ~ results in leabg.e of:atr w dJO out.doc>J~ J umin& ~bot tJJC molar pr~~ of air lwing the ~ arc ~ eme ~ ~bose c l.be air in me ~ ibow mat ~ .Wld itOOle ~ )fieM the followmg di:tfa-cntia~ GJUlion; Q= ~PV~+~~- dJ 41 ~ a~ 1IIm we of brat Uiln!fer lD lh:. air :in~ hllnc. and r is time. Quantilies p . v" n:. and (j refer ro [~ mioldie~. 1.44.. ((J) WattrHow ~~~M-IIOU!eutopn.:Ubose. Filllil u ~ rormin ~I'Jru., of fine ~Jt /'1. !DDRml ~ Pl.. ~ b;n;e d!t~ D1~ d POUlc Obras proteg~das por direitos de autc 75. 61 CUtkt di~ 8}. ~ $teady ftw~ WM1 ~ ~IPric ~ 1Jr liquid .let mndded tm m1.-om~ luicl, Hz_- R t := (~- Pi)Jp ('W' ~ I[~Qf't, {b)1llfi ~ me 1t1uw canntJI ~ imly i~ we ~~ T1 > 7i, owm.g to 1DI.tid liictioo. Hence. 81 - H1 _. C(T2 ~ Td + (P2 ~ Pt)/p, where C is.the specific hc;nuf~ ~DilaU!yi bow~ ir:dusiQnof~~don~ lhe mt of :. 3.1 btte ~a~ line.~ tbe~ ~~at a iin~ empenmue and~ , v.. v (a) ftpn. U IV ~ fora ~ ~ 61) ov.riug,:501idl. liquid, ;;aM "'P . (b) ' ov.riag .&q,lid.l - pat. - 'apOf -- - '4!.ilb ISOI!llzmiS. Fl~ l.l{b) tti ucpJid, li~ md vapor regiom ofme PY diagm.m.~im ruur ~ ~- ~ oo Fi.Jl- )..1 ~"~fin= and ~ pn:ta 1llwlTc do not c~ aph3...~ boundary. On Fig. ]..2(b) It' iiolherm labe1ed T > T~ is Ibe,refore ~ ~ iliges bbded. T1 aDd T2 :ue for iUhcribQ] 1mnpen.twes. and Clllltiist of lhree seg- mems. The lxirizonlal segme01.~ot eatb is0lberm ~ .iJO possa.'ble. ~ofliquid Wid ~ iD equitibri1llD. magi.QI from J IKplid the ldt eudlO 1001, wpor me rig)n end. 'Tbe llocws of lbe~ end polm.!S i!l me dfime-sbaped trur'e hbelc:d BCfJ. the left filJf of wtri@ (frmn /J w C)~ ingie.~ l.iquKb ar dmir vuporization (boilliDB) ~ Wldl me dght ft3Ir(from C w IJ ~~ V"apUU:i ut thEir~ t~ Liquids and ~~ by BCD ;n iaid to beAiatmtd..and eoexi.Btin1 ~ ~ conoeaed b1 ~ ~ sejtneJil of rhc :butbe (it rbe ~ ~ ~tk to dlt: i c:rm- AJsccalled lhe '~ ~~ it ~"CUI b-:r ~J pvHrt un Pi~. Ji.J where an isomerm ~ Jine)1~a wporimlioD C~Un~e. Tbc ~ liqui~ ll=Fna . un*r dcnm; BCIJ; 1b.e ~IJ:..Uqr~~d regioo lies mtbe Lefr cf the ~tf.d..ti.qpid eunre BC.. and ibe ~~..WJ:pt)r 1rcgkln li. to Obras proteg~das por direitos de autc 79. 61 ri.,&bl of the :sidiirulied-'!'lfD' CID' mcb ifih!fJIC- ~ tu cxH.t, Wid me vitla.l upaMion 'Gold ~ M: Z -11 PV=RT Mol~ i~~do in faa nisi!~ tmdififl~lhe~rwd ~rofmal~ As~ is.red'ueed,;d eom:mnttem;per.U.l~Rl. v inaA50! and abe ~"bvtiom. o{'lllc~~ B/ V. C/ V2, D/ V1 ... mf4. (3J2). ~- Fot P .-..a Z ~ nniry~ noU:~eroose of any dlaDge iD lbEI virial coefliclems~ bW ~ " hecomc:,s, ~ Thgs in tilt: l1mh 45. P -+ 1. 1M equatiOJJ (l!f ~te ftid~ to t.&e ~ ~i~ form as tor llbe lbypillbetical mse or B =C - - O~ i.e.... or pv ...... RT w~ bow fl&'OJD tbe ,phase rule that lbe internal energy of a re:ai gas is ~ Jlll'lCtkm of ~ a' "-ell as Df ~ 1bi5 ~ dtpmdr,n~ resoJts,ftomJ fOIUS be~~ lht mol~ IfsuciJ f~ did DOlt:~~. no c~ would be ~ rn ida l.be ~ Jntermoleculardistma.t. aDd dlm:vfo.re oo enagy wouJd be rcqWK:d mbt:ing about ~ ~urc:~m aJlSat~~~mpnarll~ -~ lbDliQ~.~ofiDIIIKulu ~ons. 'lbe in1eroaJ eoe~gY Gf.a. p dependS oa ~only. 'The.se ~darDQm ofthe lbdtavrorof ~ ps tll wbidJ DO iJlmJIDt)(a.'IL_Jar ~~ ,p;.. aOO'of I~ - m~~ limJf Q:i ~ .,~ ~ro lead mm, cte1inloon of an ideal gas as Qlle .-bose ~'VP~ bch3Yior. ~~by: (3.15) ,fmpllfld Property Relllflotls for an ldttslGo: The ~fiDitiM of hem .ca,pxhy at ~ ~ Eq. (2.161. Bids for a ldcaJ ps to the ~CUI'IdtJSioo that Cv i.l :) funQino of~ QJdr- (aU) ~dU(T) Cv = iT v '::' ttT :;: c."en TbrJ detlniog cqlllltJon for emhalJY~ fq. Q..lJ1~ ~lied w i*4l . ICJUb to die~ llw H mnaa f~n arrem~ only: 11 ~ U +PV= U(TI +llT= HCI')> (3.17) Obras protegidas par d1reitos de autc 86. The ~t capacity ~OJJII}l:. (3.18~ A msefui.~ut~m~~ befw~ c,.l1.ld c.,~ fm lU1 itt~~~ fimi diffmoruwull ofEq. t3.17t. dH 4U C, ,dT = JT + R =c,.+ R t(3.19) 1'1dt tqUation CIOa not lmpiJ thll c, and Cv .__.............. gon- stanl tDr am ldiNd ps1 but 1anly that they wry with tempewature In sur:h away that U1elrdlllerence II eqt... loR.. F Q fll Obras proteg1das por direitos de autc 87. 3..3. The lde.al Gat 1S ~ ~j ~~ Q ckpeMJ 1D Oll1y on T1m:l T2 but also onltbe p~b of~ p.mceg. An aRi:J:'el,y analcJow discusil:on awlie:s to lire erOalpy H ofan_ ideaJ ~ cSec Sec.2.Il.) The ide:t1l gas is a nwld ftnid ~ by :simple prt1pf'11J rtkdlms, wllidJ =n fe.. ~dy 8(JOd ~io:R$ wbm applied 10 ~ psr In~ t.'ltlt!IJiaJitnu. , - m pressuresup'10 a few bars m:&f dho be ~~ ideaL and simple equoaiom dJwl apply. EquIIDns for Procas C~ for lrleal Gasss ~~provide '.'Ut and he-.n ~ 1be wort of:.. mecb:micatly mwsible c~rcm t~OCCM ~ &iveo b)Eq. (J.l~ ~R writt~ for~ mil or,_ OJOle-; dW~ - PdV fGt an i.aJ p.s ia .lift)! d~ysrem pltll.~ .. 1 fi.tsllaw as ~ b)l Elt (2.6) Wl'imm fer 3 unit mass tOr Ill molt=. may be eambined 'ilh Eq. (3.20a) ~o 3itr. Su~tioo for dW and ttQillliDQ r.x IQ yields Jll Jd$dOO ~tl tor ... idca1 gas in my l:l'lecb.mia.Uy Mt'eftibJe e~~tem [JIIOCCM: dQ ~ CvdT + PdV This ~equatim COGIIains die ,!ariab'Jes, P. V. and T. oo)f c.n of .tlxb me inde~ WotkUJJ eqnabon$ for dQ and d W ~ oo wbidl paif M' lhese wriaM is selected ~ ~dent 'Le., rt.q)OO wbidl ~ i diminaled by Eq. (3..l4J.. VlidJ P ; RTIIt. ,fiJI drQ ~ C;dT- R'T-- p I dV(3.22) dW~ - RTV (1.24) dW.!!!!! - 11. dT lt.T!f (l.25J With T !SI P VIR,. me W'Oft is simply t1W ~P'dV.. and "lUiJhC'v .given api:n by IBq. (l..l~ Cv Cr dQ~ RVdP + RPdV (3.26} Tl:mr tqmlOOoj may br: ~a1 fm itb] ~ ID WJit,mt kinds of~ llS. ... scribed,in what iofll~. 1he ammJpti.ens implidl if_n the-ir dni11ticm ~ 1hll the iY!*JD . do~ ,ODd lhepi'(JCeSS u mecbaDlc:aU)I,~ Ob as protegtdas por dlteitos de autc 88. 16 By tp. (3.20b)and (:Ulb), - l'2 ib - - ~By &J -(3..'22)1and (3.2-4)~ Q- MTbl ~;;;;:~niT m - v1 P1 8)' -" (3.23) and {3.15) W =-ItTln ~ - ITb1 ~ Nee111at D.r --W~ a rm111 trun moton rmmEq. (2..3i 'fhadj~ lsobaJic Proeess By Eq- fl..ZU,).and (J.2lb), .6r.J ~ JCvJ1 cuxJ ~ lkp. (3..24) and (].25)_ a- jc,rtr AH~ fc,dT Na~e lfW Q :.- AH~ a mwll also gjm. by Eq. (213). Tlaefore. Ia=- tiN =ICrtlT (~P)I lsOcbOtie (ConstantV) ~~mcasa Equ rns(l.21lb) ilfld Q.2lf.l}~ app~y: .All; JCvdT and aH e Ic,cJr By:Eq. (3.22) and a&c lmiccquatioa far ,.v:rk, Q--JcvdT end W==--/PdV=O Note dl:l1J Q';;;; 4lJ. tt resukabo p~ ;y ~ 11U)). 1b:tdore, IQ"' IJ.U"' JCvdl (, aV) I (128) {l-29) Obras pro egidas por direitos de autc 89. Adiabatic Process; Constant Heat Capacities An adia.baJi.G pnxess is one foJ- ~trldt Ume is DO beat tnmsfer be1wecm the ~ mci it& M~ITOWJCiirlp; L~~ d1(] - 0. Eam ofEq (3.22)'. (3.24), aDd 0.-26) ll1af tbeie'fore be _~l ~zero. huegnU]on llh Cv and Cp .~dim y~ sinlple rebtians allllJO.! de wriables. r. p .aDJ,t v. vaDd rfl) ~~y reversible ildiaba11e rem~nil tV ~1'1 of ideaJJ pses. fereumple,. F.q. (3.22) bec:omes dT R dV T = - Cv V Silni.bdyll!q_;i. (l.24JImild Or26) l!!ad 10~ !! ~ (!l)~fi./C, aDd Tl Pt, 1beseequaaiom rmt~ also be c;xpres5ed r~n-1 =~ (3.30a) T pU -rl!~ : cons_t. {~.JOb} p V)' :: t"''ni:SL O.llk> EqUIItiOM (8.38) ara Nstrictld In appllealionIQ,ro.l '91JM'o with c.o.u- atant heat capaclliea undergoing rnedtan.icaQy reveiSibte c expalllSIDil or compression. W = tl.fJ =Car AT (331) f3.Jl)1 Altmlr.Mh-efQmls ofEQ.'332) r~t ift:v it dkntnattd in ra~(1(ofthe ~-c;;ilp~ nn{o y: y 5 c, Cr + R _ I + !!:__ m C~~ R C.,- Cy Cu y -1 3trCt aodCJi ~~L y h.~1 Fu. i.lll iJbl CD illlt ~ lho:a ilbl: br.1t ~l:ltl ~ u: 'lbb.l.!l aim:~~ C,. - Cy = ll crt11 ~ ~ mr moaamrli:: , Cp Cy ~IIIJ ~ VFJII't ~ll::ct.ltler=l.oy i.l ~ ~-eiO~ ~ l]Jeo~ ~~~ Obras proteg das por dn eitos de auto 90. R. AT' W c: c, AT ~ - y ..... ~ ~ RTa PI V1 and RT1 ~ h.V:z. tbi1- ~on m_ay be writtr:o: w~ 12 - R1l ;;; P,~ ... ,...,~ y-~ y-i Bqoa1km ~.J2~ and (3~:3) am ~raJ for ooiabatir ~Mel~~ 055as ma e1osu~ ~ ~ ~ u oot. ixcau5C f .. v. and T IJ'e ~ tUDC- u ". ~ of path. Howe.~ ~ _ Vi aJe usually Ufikoowm. Elfmmation ~~ "1 ~mat eq. p.:u,bl' Eq. ~(J.D:l. 'lUiid Ollly tor meebaniicatty re~ proe~ ~ w me ~ . W c P1 Vt [-(!1){1-ll/f _~]- 0 RTt [(!!1)(y-W'r- ~] y - 1 ~ y-1 ~ 1heSliDe remit is obt111:'kldiwbe.n l.be rek1ioo belween P and V giwn by Bq. (3~) is ~ far tbe inl~ W ; - f P dV~ Equa~ (3.34) is ll'al1donly fm ideal wilbamstant ~w:a~~. m,Rdiabalie. med'wlically ~ e~ ~ Whm apptit to JQJ &p. O..JCJ)t ~ 0.34) often yield~ ;appmx i~ poov'"l((~ ~ ~ t1om idtalll.)' ~ ~ ~ty ~11. For~~~ ;Y - 161; ~ ~ of y are lA for dmtnmic ~ 9."Qd J..) far tri:m;ple po)yaro~Dic; [QSti wdi ~. SG.l. NH aDd C& Polytruplc Procasa BecmsepDiytmpfu' Da:Ooi "''.nming m:t.my ways~n plit}"lRJpicp1i)C'tW W~ II mudd M ~ "~ lith~ a~~ it ~~a~ ~ted i~Jy tbc em~ cq_wdioo: Ip 'Vi =t'OmiMt I (3.J5a) Pot~ .~ ~ticm; ~$ m lPAp~ (3.lflfi,l ~ 3.30b) ~ ~iJ~ derived~ Irvf- 1 = COOitum (-..lSb> I!:p fl ~'' = romwu (3..35c) I 'Vbe:ntherelalion between P &md V is ~'~ ~ Bq.1(-J.JSat evalualioooffP dV )ttl:lds Eq. (3.34) wm r ~P - by &; - w~ 2.'. [(~)~'~~'-I] (3.J6) Moreu~ for amstmn ben ~hies. die first b.w sol~'ld mr f2 yields: e (1 ..... y)llT~ [(!2)---l~fl - ]-r {).3'"T'i Q (1-1 (y-- l) I Pt l ~, Obras proteg~das por direitos de autc 91. 19 'fbi;t ~ described i.D b seclion ~ lo rrhe four p:Dm4 mown 1 00 Mg. 3..6 for spectliC ~Of6: ~~ ~ B) Eq.U..l~ ). ! = 0. t l5otbmnal ~: B)Bq.{l.JSb). & 1, Adidlatic- ~; " = . ~proem: By E4 (3.35a). dV/dP ~ v1Pd; '"" COQ$blJ'It V1 8 e!! v 1IJTeYerslble Process ~J.(( ~CIIpol)~ ~~by ~ c. Ql'- Ml ~deeloped in this seaion ba~ been dmiwfor medwlicamy l'e~ dosed- system PI~ for ideal pses. H~w, dKtse equatio~ whicb give fJlfJPUfY dttlnge dU ~ dII, .aU. and 6 H- are 'ah'd fm" iideal g rega:nt~ess, ol t:he ~ They !appfy equally to ra"'GmNe mdl ~le JM~ io both doied uod tp1m , btawse c~ in properties dqx-nd ~oldy 01l dJe initial And final SUit~ of ~he.~~ On lbe olbtr ~ an eqotUioa,for Q or 'W. ~ .it is equal to a pr"'O)ee1y dcmge. - uhjcet w the rastrio- iiomo ofdetiiwtioo. The.l"'Ot of an ~'1Kt pf(IC1::S$ 1$ ~~la!lcd by a two-_,~re. :Fifit, W :b ~ fwa mccb:mically !It~~ lhal ~ tbtsmx e~ o ~ lk :a.mW ~ ~ ~ tbis iliMUb is tmlbi;plied ordiidcd hy an ellidftlt)l to live tbe actual wor Iftbe pwcess produtc51 wor~ the absolute value for tile mrmJ~ ~ ~:s mq.~:mF aru1 rmust t.e nwltipticd by m~J ~ 1rme~ ~ wodr-. me value fo:r l:Jlc~11Je process is too MmlJ and mus.t be dividr:d &y an rdf:iamey. Applic:i11iCJttS. orlktC'ii.tifqlfSi andequadOM.mfbi& 8eCiiM ~ IDMrr-..mt'l iAmt; e2.a~f~Ples mmn follow. In (WtJtiU'. the work ~of i~~"blc proo~, is ~ in Ex~ 3. _ Obras protegidas par d1reitos de autc 92. Example3.2 Nr is ~ from an Initial Slide of 1 bar and ~c to a final stale of 5 bar and ~--c by tftr8e diffefGntmedilanieaOy 11JVersh)le prvceSMI in a dosl3dsystarre (a) Heal1ng at constant ~ume tiJowed by oooling a1 constant pmssum. (b) rsothemlal compresslen. (C) Adtabatle~ressian follawed by QJdlog at conscan~ YOJUIQQ. ASsume air 1o be an ideal gas wlth the ,constant heat eapadtiee. c. :;; CS/Z)R and Cp c (7{2)R. CBic*le the,l'IOJk reqdred, hea1 lnlnsferred. and the changes in intema1 energy ,Bf'd enthalpf of the u tor eadlrprocess. -e ~ :So1vHonU ~ tlte S)$ltiU U$ l mollofair. !Pot R == tt3~4 J mo~- K-~. Obras protegidas por dkeitos de auto 93. J.J. 1beJdnJ G:JS (t") The btitl:l] step of ~c ~QD ~ llhe .!litIt to lu Wial 'Ot~ of 0.()0495:8 m', By Eq, r3.Xkl)'.lhe tempeli'atllm at this poim ~ W = C" AT= ~20.185)(S67..57- 298. 1 ~ = '~(JO() J (J- 4U = Cv(Tt - T') = -.5~600 l ThWi for pmc (c). Q =-5IJ()OJ1 Altboogb the pro;peny cha:ngeg A~U aod1 A II are uro for ~ ~ Q lJDdl I~' aN p:nb,.dopmdent, bUI beJe Q :;; - W. P:"~ 3,1 s1KJws each ~ on a P v diagrum. kitlliSC' ~ wmt f-or cadi of ~ fiedlam'CGH)' tcver&~:"ll* p~ ~'ell ~ lV .=. -- j' P d V. the WOI'k for each prneess is propaniomtl totheltOt1d ~ bdi)Vf die paths 00 die , v diQnm fftii1J 1to2. The~"e mes of I~~. correspond( D d:~~e n~ wl~~e5 01 W. Example 3.3 81 An ldeal gas undergoes.the fDIIowJng sequence of ~Y ~~ processes in a closed sys.tem: (a) from an initial raaae.r ~as Ollf4ed virial equati~ is iUu~ traled.by the .~'ebb/Rubin eqwmon:6 RT BoRT - At! - C.,/i 2 bRT -a p.;;:..V + Vl + Vl .au c ( r) -y+ V~ + Vl Tl l + yl exp Vl wi'L~ Aot Bo~ Co, a.. b. t . urul f ue WJ em.~ fm a Civcn fluid.. 11liis ~n umJ ~ m~mJ despite rlbe:ir amtplexity. are used in lfle. petmleum and~ indu.._qrles forli.pt h~ gjla &w odJef~ ~l~o~xm~ered ~ example3.8 Reported wlues for ihe 1riaJ coetflcien1s ol isopropan011 vaporat 2(WC are: C81Ctdate vand zfor iso~ Yai)OJ at 200"C and 10 bar~ r(S} The idaaJ-ga$ ecp.aatioa; (b) ~A (3.$8}; (c) &tpr~iotl r(3.40). SOlution 3.8 The lute ~~:pmiiW'e is T 473.l.S K. and 1he approptriate 'lttue of me ps coo~ is R;;;;; 83.14a:n' bar ma~- 1 K- 1 (a) For 1111 ideal! ~ Z =I. and II;;;;; R:= (13.14) 1~.15) ~ 3934eJ1i3 moJ- 1 (b) S~"ing Eq. O.JB) for V gi~ . RT . V ~ p + B == 3'"934 - JSB ~ 3;546~ 1.1l!Cd1 Obras protegidas par d1reitos de autc 102. 90 PV V ~' _ Z:!!:; RT e! lrl'/ P - 33M ~G.90l4 RT( 11 c)v, ~ p t + v; + Y.i y -0 bm'e V'(l s:z J~ lhe ideal-p alae. INumerieal!ly. vl e 3$34 [t- 338 - ~000 ~] ~ 3~39)9]4 1(3~- I' ~ ~ ilmdioa Tr:.. pressure is a moooumica1ty de~ function wUb ~ IIIObr ;.'OIIDJlt, The~~ ~~d Tc)reonf4i-ps tbeb~ tifilm(tOH crtC ~e otJtbe Mikal.point. Fer l.be H81htmn T~ < r~. the pressme~ m;pidlJin diesubcooJed- ilq,Uiid ~011 witb i:Dcm~Sing If; a'ta~~lh~ ~,.fiqv]d line. if101!S through D mitJj.. mAim. rises lQ a m~i mlill ~(!ben da.'ft:~ ~ing dJcu~liiJPOT liite~ndQOO!m'tling downward into tbe ~lapel' regimt. ~ iS()(hcrms do 001 e.xbimt dri;S &mOOih rAmir:ion from saJ.I.UI1ated liquid to .satumrd ~ I'Utber, tllcy eomain a hOri_zomaJ ~ with.in the: ~ R!p~ wbr~ s:atn:rmed liqtrid .md ~d ~pot ~] in. varying pmporti aJi me ~ina ar wpor ~ 1lli5~r2 5tl0wn hy (Do~ lint in FiS- 3.11-.l~ M~)'tic. utd we ~J.II as ~-i.mhle ihe unJieillistie~:Mer ofeguatim!l ofstate in the. two"ffl:.se regicn. Actual~.., tbb i'V ~or ji(Cdidtd in dtl ~em by pro:J~Cf cubic equations of smre is not ~Dy ficrliious. Ifpressure is decreased on a sal~ ltQUid tkvuid of~ sit~ iDa carefully,ooutm.11lcdape~~doesontOt-carTIUldliquid persis:ba!mr to~ well ~ow its wpa!f pn:ssum. Similarly. raising Ole pressure on a Sidllmfed Dp' in a smtnbleaperimesttdoes nm cameamdeos~and vapm-~ ~ w~ well ,.............. ~btl rr n! Tiih non m:rit~~ , IDI!'bl!""'-lli.le--~ .nf ~--.~t:.n..u arul~IYT~ Tr,. ~to Fig. 3.1 ~ ~ lhat solution (or V aJ any ~ value.of 'P yjdd$ ml)i Dille i.1dl rtJOI- For ~ aitiml ~nm (T : T.,.t m ol!lo ~ eseept m lbc! ~ ~ Q.~ ~ :m: thn ~ a_D ~].to Yc. f ~:lit T ~ fc,. lbe eq:uatitm may emitm one or line mal ii'OOIS, d~n@. on dte ~ A1.tboQJb ~ roots are CCZIJ and po$iti.'e, lbcy are oot ph)'-sh.'a.ll)' sm'bk: ~ foe lht:: ponioo ,of an isc:Jdta1l1 I.J.infbelween S3IID"atcdi tiqufd and smunled vapgr(UDd!l'me -"dbme~ Only {(W the YIJII)r(1( SQnut;Jfif}fn lftl$$~ p w ~ dJt ~ Vm(liq) and V~f~1ip), sJ:ablt Wtes,l}~ litlhe ends of lhe tuizolDI portico of1he true isotfJemL foJ olfxr ~s '( . indicated by dm IKBiz.olilll ~~on Fig. 3~l l :dxn,~ .mdtbdQw 'P a~).. ~he mctOcst ~ k f.kruid ,ur "tiquirl-~ vokuDe.. :tnd me ~est Is il wpt>J 01' ""wporal.flueq 'IOlWJIIe. The lhird NGt.l}rinJ between tb ... ~ ~ qffJO !iignifi~ Obras protegidas par d1reitos de autc 104. l'llm'tl.IJ.; . u !1--~-cn bya cubit:ti)idiiofi of sm.1bc.iDtradu.aioooft.M: 1111) daVlub.eqQI.tioo. uvaal hUDC!IMcutric ~8 of rtD hM beeP~- AQ are~~ of abe~ llT 81V - 9)p:::. - ______"""=""'........_ _ V - b (V ..... f,)(Vl +rV + 1) UM. b., 9, It. ~ ond I'] ue p;uameten hir::b .in seaera:J ~ OD. lempamule and ( far mix-- tures)~ Allhough this cqdioo IJlPUl'S .0 ~ ~ ih:xibilil)'~ illm mheralt ~tNitm ~ ofrils cubic loop,10 It ~to~~ diN w.t..s ~loq wJmQ JJ =b., e-a.and -1-o~ An imponam dw of cubic eqlHIIi~ mw.lb fn.HP the ~(d!DJ equ:ltiora !irb 1hc a,_ ' ;RniDI!IIts.: 6 =a(f) M..~ AIC1dll... ,w.. 19. pp.. ~ll. 1m,At~G. d! C~Ba. Snid Jn_ K. c.01i6 s R..1... ~ Jr.. .l1J'.41-'10. AIL D.C... 19?9. Obras proteg1das por direitos de autc 105. RT a(T) p:::::!! .....,_,..... v .... b (' +.;b)(l' +O"tb) (3.42} 1?ro ~ ~ ti and u are pure 1na.mbas..tbe -il.l'lle fur aU ~~ w~ ~ aers a{T) and b m-e~ dtpendmt. 1k~~~nee ofo(71 i-~e elcll equa_lioo of~~ For the 9iDn del Wub ~ a(T) ~a is a~ ~dod.~=' t:1 = 0. "'*"""Illation tJfE(JUalltJIM)f..stafe ~ 'Jbt 01JIIStml5 is WI Glq~D of 5late- fw a_ -pulieular may 1Je il ~ by a m lD availab1e PVT diwt.. ~For mbk equations of ~ bo'lAoeat. a.uitiblc ~~ we U$lally ~ fivm ~fur tbc eritiad amstu T,. ;md Pc. 'Bce.ause lbe:rcri1ical~exbihit.s a. bwizoomJ inleeaion a mecrilimpoinL ~-e nm)' im~ me~m~ rolllliliom;. .......... -o(aP) .av r~ - Vt1tae me ~pt Htr demot~ t1x mtiGd poinL OOT~n1huicm etEq. (142) Jidds ~ sioos rorboth da'il-'nfn I which mil)~ be eqwttedlo za'!O for p ~ "~~ T ~ ~.. WUI v ~ Vr-. 'l'bc' cqwnfou of ~ rpay it~lf be rittm fnr dJt; critieal coodi1~ Th dJrlM ~c commfure~mts~ Pr~ V. ~ T4!'... r~~(1t-)i< :md ,b. Oftbc~ "Wa) UJtmd lht!lile~itfon dlt QJ05t ~! u-dimi__na.tion Q:rVc (II yic:Jd ~ rcl.atiq ll(1'c} tmd b ro Pc Wid ~. The ~ I& drat Pt rmd Tc ;n: USillllly moreaccUJroml)r krl~ than Ycv- AJJ equiVDkot. but li1'ICIDli migbdOf'ili'anL ~ .is :il1.muated ror the van dar Waab equatlott. Becatlse v = v for-mdJ gfabe l.im= ~at die critb;aJl point. 4V ~ Vc)'J- 0 01 ~:,l - 3Vc-V1 + l l-';v- vel._ 0 (A.) IEqWt.tioo (3.41)_. WJilmll for r(T' ~ Tt.. P P..}anda;~ in ~l)nODlial fa~ hmtot11i6: MTc I{C} 3Vi = ,!.. ( D) vJ =ab (8)lVt=b+- (' - - Pc Pc ft. Sot~ Eq. (D) rora..-~ die RMlll with &f- ()"' mil l"iq forb Bi 'a= lP,.V,- 1 b ~ 3"" Obras protegidas par d1reitos de autc 106. Substilutiao for' b-in Eq. (C) allows solutio ror v~ ldc.b UD! then be. eliminated &om the ~us. fOf a iDJdb: V.. = !RT~ a== !!~ b::.!RT{' .. 8 Pe: . 6-1 ~t. 8 Pc AllbmJg.lllhese ~~ taa)' not )4eld me beJtl. ~e. ~ ~tey pnwJde n:-:mm:hl -.';d- ucs wbidJ elk~ alnlo$t __Lhrtq bt ~ ~ ~ ~s, od ~ (in ~ mwmsiw P VT diim.)riR- o:far:n~Of~~ fdb.tdly ~~~ $Ubsdbdinn fur ~ r,a fhe equaticm r. lfle, ailfa.1 ~'hill:ty &c:IDI' recluces it im- i&tdy to: 7 ' " " (' 3 ~Iii RTc = i A L~ w.JD$ frcr ~, aJIIPbcable a.Jde to all ~. res-vlts wfr_never abe purtJ.t:Mr~rs ofa llftl.i~ ~ of _ a arc fnd by itnpositim ,of~ critial ~ Dnrem~t Yalucs 11e fmmd far d" ~of , as iDdicned inTable l .JJ. p..98.Unfm:uuately. the wJ:ues so~ doDD( in ammJ ~ hb dJost ~ rwom.~nml wJ of 'fc .Pr., :md v~~ eaCh c:hemiealripedes ln fact bas bs fi1l value of z,. ).ltRm'a', lht: r.il pveo ill TMble D~l ut App. B for ~1111obs ~ are almost aJJIsroalllt tbm ;my I f the equ.atian ues gi'ret~ inT.lb1e :tJ. An a.D ~ apptim to dx pncric cubic. 1:4 OAl:)~ )lidds e-~om for ~~~(~)r aqdiJ. Pofrtbtf~ .ll~T; a(T(")=11- PG- 1lti$1itSUltb tdlmdcdII) eiJlptlaltnr:s.odltfrman ~be-m~ byi.ollrodutliod a d.imte~ fnndioD tt(Tr) 11mbemmes mtity allbe critical~ 111.m .a( T) ='f#a(T;)~T} Prr; Fnnaim~a-(J;.) b. an empirirBJ ~. speciiclD a partirolar-~tim ofI tarer(Thl)it 3.l). ~ b - ai,~n b)': In g artd .P .m pun IHIIIIben... ~of pmim1arftP11"ion1 ofSlUle tomifbr ~ ,ll5$],.,In~ ~ r1. Themoda:odc:vdopmm1 ofeubi~ ~uaJkms of~tr; ~ iaililted in 1949 bypublic:aOou of lbl: Rod[Ldl!Kw...S QUO~~~ I'' :;;;;; RT ~ Q~tT ) 'lf - b 'Ill'' + b) wliet'ea(T) is fl~ IJJ f4- ~(3.4S) witba(T,) = Tr- lf.!. Obras proteg~das por direitos de autc 107. 95 ~talobs:c:rvationshowsdw oompressihil.i:ry faaors Z ftll'diftman fluidS exhibit simi- lar"behmor w hm coneb1cd as a funaioo of'nuiJJd rmlf"ITillll? T, ad rriil:ICmaJcm iii. wlue2l'O forqa.~ 'b:ypton. a:ndl :~-eoon.:md~I data yield bilby fadun r.. a1tJ chR!e ftums that am ~~ &y the same ear- wllcft z ~Pft'd - a~ of r,. ami Pr- Thii is die basic~ 1)1' abe rollowiQg .dr~r.ptDURifflUttfJrelll of-ror~gSUIR'.S. u nu1dl ha'vtnlllileume value ofc., Whllll1 campued ill 'he ume T,. lllld r#'. hiYIIiboUI:.,. ..,.. 'llllue af z, and au devlilde tran. klllll~ ... bllulviGf10..,.,........ d!grae.. V8pw& ~LID Roots ot the Genstte CWk &,llfJtloll ~at State Altholagli Mt rna)~ t ~tly tbf . dJrtt I:O(JU. ~}w ~DCftc oubic ~D of~ F.q. ~ 4l~ in JDCiice fM llOft: ~Y mlved by tcer-dlfi-e ~u Con~ protitlllS tiC 'IDiiiA Jikdy 3~~ ~~~oiJcn tbet:quaBoiJ ~ ~ W ~ fwm RUt~ (O lbe !iOJu- rum:f.t.lJ' ;1.parricular ll'OOL. For the ~ ~ ~ ~ vaporor v~llike ~l.tlllle. Eq. ().42}1ii mu1h.i.l'i.rl ~ ""' (V ~ li.. I :- - ti..-...... IL-. -~ ~Vol~~ v 1 . ""J RT .., caD~ ll,l!lli' Wlltlttn. "';;;;; RT +b-- a(1) V - b (l.49) P I' tV+ E"bj(.' +ob) Solution ror V may be by trial; iitemdon~ with me sol'"~ ~ of n~ p.1 ~- AD i:nitial~Y~~inJate fw v i111 lhe idea4:-ps 'i'alue 1ri1P. For rc~ dns lJalue is :5D.bsritu1ed on Ulo rilbt .., ofEq. (3.49). The mWiiDM ~of 'V"'a lbc ldl tt.-n mumed to the right side. amt 11m~ coruimles Wltil ~ ~Jwtge mv - saitlbliy sm:(H. AIDi equroinn for Z equiwlem rto :Eq. (3.49) lsi ~med by ts.Ub!titmiil!l V - ZRT/ P_In ~ dJt ~()0 oft 'tl difDCMi . S,(~Ua~~Lidcs Jtadoik) ~ 1bm.. u ~ lliZl bibtltnm CDiDfiUitr ~ ~ rnr~~ t:a'I~~Do- ~~oae r.-IJiialq ," b"I:' QJ H II:~ ;kmr._ Jlpft ~ [~~ !be a>U.~~f wlxt.- Obras pro egidas por direitos de autc 109. Vflh.~ ~Ml(Jq$ aq_ (3-49) ~~ z - p z =l +I$ -qp(Z +EIJ)(.Z +o-Jl) Equatir!XIS fl..SO) a_nd. (J..Sl)1in ~OtPtrinatioo iYJ Eq . (3.45) Wld (3.46) ~d: _ '*'afT,.t ~3.53) q = Q T, kaatiw solution of'F.AJ1. (3.52) il:ani "'-ilb the value Z ;::;; I substituted 011 lbc rig)rt side.. ~mtrula.md mur of.Z is mumed to~ rigmsideandtbe~ rotu:in~~o~ The liiW 't'aiue: of l yiecb the rolume root mrougb v o::o ZRTI I'. Uquld & Llqukf.Uke Roots 111 the Generic Cubk: Equation ofSflile Sqwuioo (3.49) may be. solvedfor die V in~ oumaumt' ofllle fumJ traaion to p'e: [ ItT + bP - V P]V~lt +(V+dJ)(V+ab) - o'T) TJtis. tqnaMP v.ieh n ~n~~ting ~ue: (}f V = b oD lht right &lilt move18f:S uptm li~Cioo 1ti a liquidor 6quid-fte'I'OOt. AlP Q&laUDP fur 2 oqoi'ralc.nt tO Eq. O..SS) i.s obtained wht:n Bq. (3--52) il ~1wd f'oc U.C Z in me numernror ofthe final tmction: (3.56) Par lwation a 5UU'tiog value of Z ;;;; ~ is ~utcd oD 100 right side. Onoe Z i blown. lbe UUDliH't)ol is v= l liTIP. ~ons ofstate w.bi.cb espress Z as ~funaioo of 4 and P,- :m:: Aid mbe:g;t:t~c~ ~of ~ir jaJcnl .appLi-cability w ~J .s~ 8.Dd liquitb.. A.IIIY ~~ioll ors_~ ~ ~ put :into ubis. form liJ pro.ide l1i genernliz:ed c:onelaDon for me~ of ft . This ;dlow ak ~:nioo w~ ,,.,~~ fmm "'rJY li:min=d infuli'llUII!iOo.. ~of~ SIKb as ~ vuo dli4 WW,s and ltedlkbil"wmg eq~o~ wmch ~ . Z a~ funtJiic'IOS.of 1,. and P, only, yiekl ~ corresponding ~ oorrelatioos. The ~d/Kwoo.g (SRI() equ:aoon14 aodllbe ftmg/Robinson (PR) equation." i01 wmcb tbc:i aemtric raetuT cntn'S lhrou.Jh fW'Imoo a'T,: {l)) a~ ilD add:itiQmil par~l'd'~ ~ thtc-p,3F~ ~l'il" &t3ites oomllations. The numerical :m:~prneldS far paramd~ ,f .. a. 0. and ~L both for lh'* ~eqwmom and for lhe y.m der ~ and Rtdli:di/K~ equiiliom. a11e ~"en lll Tllb!e l. L. ~aN also gJval for a(T,.: ~) for the: SRK mid Pit.~ Obras protegidas por direi os de aut 110. T-81*11: Paramtta- ~ r.Bqluu~nos til~ rFior use wltb f.q~. (3.49) lb-rougb (3.56) ~ ofSm~ f:f(f,.) (J f 9 "'vd~ (18731 1 0 0 118 21164 RK l949J r,-n I 0 0.08664 1.42141 SRK (1972) SH.(Tr~ c;)t I 0 0.08664 t,.4Z1 PR ~ 1916) arRtTt ; ~;~ ]+J'2 ~-Ji o.omo 0.4S724 1msn{T,.; m) ~ [I + ~0.480 + LS74 Qi - 0..~16~) ( t - T1n)r t aPR(Tr: m) ~ [I +(0.3'7464 +l.54'226,r>- 0.26992wl) (l - T~r-)t Example3~9 Z,. l/8 i/3 113 1 Ct30140 'flivl.m that the vapor pressure oll1-butane at 350 K is 9..4573 bar. flllld the~ molar 'V01umes of (a) saftmlted..wpo~ and (b) satu~qlid ~e, at ~se oonditions as gM3n by the~ RedlicWKwong equation. Sot:uUon 3.8 ~ of4 und Pc for rr-butant- &om App. B )lidd: Po =9.4S13 =0-249, r 37.96 ~ " P"'..u:uuett:rq i si-w:en byEq. {3.54) witb n, ~ , anda ( 1'r} fm tlr RK tqmttion from 11tble J. l ~ +r;.-l /l . ,T.- rz 0.42-741(O .,.,.,J,-sn 6 A.ota f ~ ~ """' r = .DL,.,. 'J = . UIHO QT, o Ou08ti64 PammeterfJ is found fmm E.q. (3S3): fJ ~a!! ~ ~(o.o:s664)(0.23IJ !!!!!! o.D26ll4 T,. 0.81ll lQ) 111: the ~m ~.. write dJo RX Curm of Eq. (3.52) w~h mut c;~pcm suhstinuieooruppi"'Jlriate ~ for f and (J fmm1Dible.ll: (Z ~ jl') Z- I +jJ - qJJZCZ +~) Obras proteg1das por direitos de autc 111. v~ ~!!!!.- (0.831)5)(S3.14)~ 331) ~ ac-.:5 cniJ mo~ -11 1' 9.4573 -..~~ . H~ ~ i:h 2.~11 cmJ moJ- l_ fb) FM tbesalllta1fXIliquid. npp3ry Eq~ (3.56) io its.ltK !Dtilll: Z :; " ~ ZmZ + JJ) ( 1 +tl- Z) qfj . 01 l - o ~-~? I z z o ., (t.o~2~4 - Z) .....u:w..:.ll-1 + ,..( + 0. 26-l4l &60o18 (OOlQ ( .. )1 ~ ' 14) 'The: inmaJ*P~ sub.stitwion ufZ = Poo ~be right sideoflhi:scquadoo. lterntin bds fU wtn-asc~ OP ~ ~ l = 0~043)I. ~. u l = ZRT .: ~0. l D(83J 4)t3S0) ~ 1~'1 1 _ 3 , t-1 ~ p ~~l ~- c~~l AD cxperimelibd ~II is ~ I'..0.._~ fOOl~t, Ru com~a.. m~ oi v~ md v1~for lbe 1Dt1llic:m ofEL 3.9 by WI tom of~be'~ ~___tiom of~ (;Qmida,r;d ~ ;goe mJillm~ foDow - votc,ml mo)- 1 ''fan,mm-~ &p. vdf RK SRK PR E:t;p. ""'w R.K SRK P.R. ~482 2..667 ~j,S 2.$20 ~~86 1 1J~to 191.0 '33.3 l27.8 l fli6 The s ~l'DI'!~ and lbe ~Rmf!Robimca ~were d.~'eloped spedlie11Dy for wpuflli:q--u:id .lifmiuma.4k~JiamiwJ1 (S~- 14.21. Roat;s of equanom m ~ are llwt'il! ~il)l fatmd wilb a snfrwa:re package udl m l~ or MBPie,. iD which itamioo is an intcgnd .,. af abe eqmuion..sobing IOlltine. Sturtin~ vaiue1 ~ bounds may be R~~Q.um,d~ - lllllN be awrupri m till: partkaJI:r ~ of in~ A M~ ~for $0l~ng Ex. J.9 i given in App-. D..!. 3~6 GENERALIZED CORRELAnCJNS FOR GASES ~ ~livn5 fbl_d ~use. Mflli.t (Kif.JQ_JQr ~re COITidmnm of 1be ltind1rde- "-eloped by Pitzer and~ ror the rtom~Miity fitd z mid ror the &:omd illial codli~B.1l6 16St;c- ~- up. dl. Obras protegidas por dkeitos de auto 112. 'Tk! oomlatioo rw Z15: Z ~ zO+ mZL (3~7)t whele zO a.nd Z I are fundkm oftdb 7;. ami P~. Whim m= 0. ~is abe e:a~ for~ simpTe a~ abe~ ~rm~ nnd Z0 ~ ldtt~~~l widl z."Th1:b.g~'lizcd~ lationfar l as tt funmonrofT,. and P, bn;donc:lata forjl;L~.qon. byploo,,IDJ xmonJ;Jmides ~ fdDt~ocshi_p Z0 - ~(T,. P,). By~. Ibis mpraadS a~ ~pood~ COI'IdaD for- Z. Because the~ ttnn off.q~ {3r..f1) b a ~lath"dy small~ roth" ~L on.& amt~ dorcsDtll i~uce laJF~~ and ocondiilioorm 1Jl Qi:ll.ybe csedi lkme tirquick lbal1ess accurate1estima1J:s of Z binare obtainedfrom a d'lree-parameter ~ Eq-uation (357) a simp lillearrr:tlilioo ~D Z and m for p-'Cil wine oi T,. uod P.,. &peri1Dellta1 rdata fm Z for DCJOSimple fluids plotted . 6> at ~stmd Tr and P,. do iftdeed yldd appminwely SUii~f! b Wid dleir ~ rp!IOYade U)oes ror Z 1 from whicb the.~ function z ll - ~ tfT~~ P,.) can be comtmcfedl Of .&..o. l!i:- . tu:_IIWI!I ~.:..,. .-._:f...LI - L ...,_... ~--~ L r Y ........._ ~ V- _jl.1 '--- I.U!i.l n~ "l la- Jl!n r&WDS i:l"111!.i1Qtt;. "lY!IQ ~ ~~ Vw0.012. z = zO+wz= cum-7 + (0.012)(0.258) :c 0.8'90 p ~ ~ e (0.890)(1'.7.302)(SlU.b1' = 1 u_ftfa.tml ~lf 2 7~ - J Bec:mtseabe ac.entri~; fllnnris .tmallthe~ mx1 ~pat;amr;tct tv~l h)'~ Jndations In' litde dilf&eut. Bath me 'RedfichiK"001 eqDiUion alld lbe~ oom~biliityfactmr ~give ~CIS dose10 lhc e.'q*~ i1:JICfltll ~dur- of 185(Btm). ThLt isuimbiJiiy mlbe.~~ iria~~ ~ ~ data indicn~ ttw ~br ~urr i 23Jl2 bar 11t tbet givm oond'i- tioa& Thus tim ideal--gas equtioo yie:lds an Wlb-wm bigb by aboo.I I~. wbe_re.as die' ifid~~nt~ca p iim ~in ~:shlmial ~ vri1b~ ~ ~ 1hwgh,munaniais _a [pOlzr moleenle. Obras pro egidas por direitos de autc 121. 109 3.7 GENERALIZED~ CORRELATIONS FOR IUQUIOS~ Allhougb llhe II!IOlar "{}IWJ~CS ofliquids. e&D be ~~ by me:ms ofge~ cubic cqUia~ bn~ of Sitale~ rifle ~ 1ftaJitm JJ01 of mp W:CUGICJ'. ~. diS ~~~T ~ iD:J~ dab for ~l!d rytui&. and Fis. 3.1J illllm'alt.s curres ror both liqbidi m1pses.. Wl.oe8 for ibofb phases 3ft pnwided in TnbJes. E.l duoogb E.~t KeaJIL oo 'W. that this co~Oil :i tn(Xtl ~~e fc. and fionlly 9p3nde(l ~to its origioalstatc. (b) ~ ~ rlntVe.rst$ ~,., tbe same thanps.0f$18tC. bul edt ~ is rllCVeJ'5'ibl~ with m etficieocy of ~ compared ilb dte ~ tnecblmioilly re- ,ctSibJe p~ Nm.r. 1k bn'tiaJ mp mn no L01tpt be ad.iababc. Caku1at.e Q.. Mt., AU. Wid AH for cacb 51ep of d. proceiiS and fCJI' me cyde. Take rCp = Q(Z)Il and Cv = (5/l)R. J..tt. 0..eubk mdtJ'ofan~ ut tiOO KtBnd JiCDl tfa ~ IJJ lb~ li:m.e:5 ~15 initial ~a$~lS: (a} By DX.iwlieally ~ isothe_rm:d ~~~ (bJ fty ~y fO'>Wbk. adi.mtie process. Obras proteg1das por direitos de autc 127. (d oy ap Mti~~twic., ~~Pille mwbicb ~ uapinM ~ ~ pressure of lOOiP.). Fureach .caw; catculme mefinal temperumrc.. ~ wxllbe: ViCft dot~t: b~ die ,~ c, ;;;;;;:21 J mol-~ K ~. ,1.21. OUt: mo!e of air. ioilially at 1S(rlC arul 8 bat" g___~ die Ciliiowifii ~ rewslble ~K. )[ re.lpmdi j.DJleiJD3Dy tOri ~fe sud~ Wt whei1 Jt ' 6-ooied at ClW'Clnl 'Oltunc tO -SrC ~IJ final ~ ~ 3bar. A~miq aiJ i5 an idcallp fm whim Cp = f1fl.>R and Cv ~ (S/2)R. mlctliD.tc: W, Q, I.IU, :and AH. 3..11.. AD Ptm .[:IS ftOW5 1bro~ a .00~ '1:lbo at iteady smm. Nofle.at hi added and oo sbali ""lit ~~ The ctem-stdiottal arm of ~be cubt t~ with ~ad l~ha atWiCS the ""Cwml)' lO dm~ Daaiw: tm QUiltioo rfdalin,g. tbe ~ tD the Yelocil' ofmep.. If~ m 150>c 110W$put011e ~of IJlttllbont a ~-doci'f orl.S 1D - I.. 'ftiud is iU. tmtpGnture at ;motbusecUcm VbeR..iii vdoeity is 5) m ...) ? let Cp == (7/ 'JtR- ~ One IIDOie Cl!an ide..1l ~ ioililalfrr at WC WKI J bar. i1. ohau,ged ro 130 C omd l&!bat by thKe diifamt~Y revmfb1e prt'IC'eSSe The- firs:l he=nrd at oons.l.n' vo1umc ~ its ~ is 1W"C; Olen it is~ ~lly umi1 _its~ i LObaf. Tbe -:15 i- a-, ~...A .- h'iliWlf!tlionl lliif'lllio~...- .o!il .:-. t~nn""'"r.Jhll.._ J~... "'~ :. tr.- .!llliCI'I- ~~- I!P'YI~!i'!"'U r"_,.,....,..,..lQ},g IW' .,.....::;::;;ill!iO.::nrH,.... I5 ~' ""'- !li.JIIi'll" ris CMipessedl~D:y ro 10 bar. 1"bc gr~ Hw fln.-t ~ ~~y tQ 1.0 txar; rbm it "'heate-d at co~ pieS.Sliiie to I30-C. CaJcul!ate Q.. tt. Atl. ami A H irn eacb case. Tm Cp ,_ 0/2)R :md c,., :;;;o (:5/l)R"' Allemati"-dtr.~ Cr = (SJ2,)Rdd Cv ~ (3n)lt'.. 121 Om! mota :anideal,gas. initifilly m3tfCami I bar. ~ abefcdlOwiD,J rtDedJan it.illy ~~ ~ k is.mrnpmssr:d ~Jy JO ,&~point $liCb mat wiMo k is hBated al eoD5Iam voh.lmr: tD IlOPC irs fiJ1:1:1l pn:s.sureis 1:! bar. Cakuial~ Q, ~ AU. uoo A .H rmlbr ~~Take Cp ={1{2)R m:xJ Cv ":"" (5/Z)R, 334. ~~ ofitWO tep ( I)One mole ,ofmatT =lOOK aDd P =we baris cool'edat co~ rot-ume ro 1' !!!!!!! 310 K..(l)1"Thl!: .U1$ dJmhcakd mc:O()~ ~llfr WJtil its temp!ra1UJ!e rcacle5 8001 X. llf dlis t~ pwee:s:sc is mplaced by a sin!Je ~~on ofi~Jc.:iitr ~ 800 K OJJd 4 bittv Somt; 1imdprtssurc P, whM die Wl!'tleof p that rnaka lbe ~-k ofthetwo~lhe.a.rt'ie? Assume~ t(MfSihility and~ mas .n ide~~~ wid~ Cr ~ (1/ 2)R and Cv ;; fS/Z)R. ~ A.sebemc 01 fimliltg ~mterna1 volume v~ ora1P "' cylinder,~ otme foDDw"rftl ~- 1be cylindctfillpi with~ I*$ l(J a low ~ P1m tmd (;(1Qr~JC1Cd ~ a s:rnaU Line and! veilr"C to ao C'aeualal~e~ uDt of kllown vnlllme Vl.'1.be ,.'ldve Obras proteg1das por direitos de autc 128. 116 is opet1ftl. liOdl s~ flow~ lhroo,gb the ltine into Ole memnre tiint. After me i)!'Sicm mtums to 0$ init"a1 m~ a scn.mh'r ~ 1nlruidiiCC'r ~a Juc lor ox- prq..~ cf'tlnge .6 P i.n ~~~t cyllndn. Deretmint tfiC cylinder ~i,lme v~ fTOm lbl! (Wlowing dala: v~ e 25fi 001,~ J:.Pj P, r= -O.C6l9. ~ A~~~ oom.-'QOd~ eyliDda u-~ with nonoonducting. frieti01r L~ flootin; pisrun w,bk-fl div~ the ~~ iBIDSecliuml A and .B. lil'lie tvto bft':- 'lions ~ ~~1 ~ of air., inilKIDy ~ tfJc ~ conditions. Ta = m k a.od ~ = lt4nn). All ~{.';1) lbMting danmt:in SK-Jion A iJl. ~~ and rbe :rir tcm- ~~~ ~ TA iDSectioo .4 because.ofheatmmster.. ~ndl Ta in Scdion B ~of~ ~~sitlfi lb~ ~ .. ow.tJy ~pi OD. 1'AC air~ an ida~ gr w"llb cP !:; 111.,. and 1m nA be the .DIIIIftz olodes orm iD ~on A. For me p -~~onoo ~ mYing of'.qwmtiti 1fn) TA. Ts, and (1{111f,. if ll(fimd);; 1.2S(~IIJliJ (,") Ts~ QJJJA,. and Pl(kEt if TA - 42,5K.. (d T4. Q/RA md Pf~ if Ta ~ l25lt. 1 (d) TAt Tas rnd .P~fittaO, if ~Q/nA ~ l kJ mul-L. 121.. ODemo1~ of;m ic:leal &as~~~~~ W'KI~ocs- 411 3:rbiiara_r, ~ iQII)'~~- Show ~t: U II ( - A = -. - ,A PV) r - ~~ J.28. ~ 1D ~W fw (be YiOJk qf ~)w)ica__lly ~"e~ ~ ~CD of mad of ap from m iniliai ~ore P, La ,. frul ~rt ~ wbm tbr equation ,. tit~ I~ -.iria1 apamioo IF..q. (3.J~l] 'tn!J'IcatW ~ 2' el-8P 119.. A oet11d #fl.S :i ~bed b-y tho~ l'tf~: i'v .;;. Itt + (b-!!.._)p R-T ~ ,fJ. is a~~ a_od U, a ~1iou ofT ooly. F'lJJ tbq,~determine ~icms llfU'.Ie: i~ (.l~ilUy ~and (be lb:ln'ltd ~ ~lii.-i~nl (tJ'P/8TJr-- , ~pmsi_i s!wdd wmaiD oo1y r. P. e.d8/dT. awJ ~ Obras proteg1das por direitos de autc 129. 117 Cakulare the 'Aut of ID;ldlanieaii.Y~ibl~ ~ ~ of I mol of methyl~ dtlorid:e from J bm to ss bar at -~~c.. Dase wc:ubliom Oil the foU.owing rollD,S.gf the virial eqwtioo; 13L .tDy ~~~of state valid fot [5(-~ l'O rkJtf0-pi'S511~ limitimp_lics a(uJISdofwfrial ooeffiaem. SOOw a.at tbe ieeOOd .:md_ lhinl viriw ~ ilnpfiedby the ~ cubic tqoltioo ofo. f.q.(3.42). IJ'Z'.: B ~ ,. _ a(T) - v R'T S~ize me m;~~ll for B to die RedlidlllKwr;mg ~ o 5lalC. ~ ~ iD ~ dnced fonn+imd compare 11 ~ricidll)' wtut tbe ~ized ooaeJation iiY B rw- ~iu;qJlf; fluids. ~ (3.65). ~u:55 what JtJg fiud J.D. rCalcolate Z amd V far dhylene at :ZSCC uml 121barby the.following eqwl]OM: r(BJ The tJlmCate.d,mal equarlon fEq. (3.40)) idJ ~be fot!bwml uJ!Qim_mt:IJ values of ririal ~~Is: 6 =-140 em :i.'Dol-] C = 1 200 cm.6 mo~-J1 (b) 1ibe ~ vlrill eq!JiUttMI [F.q. (l .J8)), witb a -aloe of B from the;genaafized lPi1uJ"OWKl~ [Eq. (3.63))- (.t ) The ltedlk'biK1mg aJUn'lion. ,{J) The Soin~lidtJiK,."Omg equation. (d ~Peo~ ~. 3.31 Calcuh.te l and V far e(h:me a1. SO~ and l5 bar by ft. folowing eqwniom: (a) The ~~ virial ~uarion [Eq. Cl~40)) owilh che f'elkrwin1 eJpm~ 'llloes of virW eoetficiena: (b) nt UU~ Wfial ~ P!q. (3.31}], widi a valueof B lNiu mettrErid~ Acze:r~n [Eq. (3.63)). (c) ~ B.cdliebiKwongoq,QILiiQn_ (d) ~ Soa:,dR;cdJidblltwon.g ~A '(t ) 'lbePeng/Robl equation. Obras proteg1das por direitos de autc 130. ll .oons: (b)lbe truncated viriru equatioo [Eq. (3..38)~. with u "Wllo of a fNm the poonalized Piaercorrelarioo{!Eq. 0 .63)1. ~c) The RedlicbiKweog ~OIL (J) Tbe SoovdltdJiebfKWOD!equmoo. E~) The~;gllto~ equation" For mlfur be.ufitmridt, Tc :: 18.7 K, Pi: = 7.6 bar.. lie = 198 (:rn' mol- l.. and w-0.216. l.l$. De~ Z ~ v far~ at lS(PC and 1.800 k1 by the f~ a) The. uunc:m:ed 'irid ~qu:nion CEq. (J.40)) ritb 11~ folllbwing ~~ vaJtz of'll{i:ri;l l~c:ali: . l-36!. With ~ to ttbc virial ~n~ Eqs_ (3.1J)ud i).l2). mowthat. JJ = - I.. (az)aP T.I'"=O B=(~).ap r .p::O ~pe: l/ V. U7.. ~ (3.12) when UIIlea!ed to/uiUfCmlS ~J:el)" nzpmsoots(be VQ~da for memaue ,gns, 01 ' c with~ (a) Use~ data ro prepare a plot ofZ w. P fot oldlm;ne ar19C from 41)to 200 bar. (b) To1lilmt pJCSsures do lEqs,. .3.381 andl Cl.39J'Pf'O'Vide good qproiimations7 138.. Cakvlate lbe IDlliir "'ktlDe of utunded li.quid .IU!d me IDOlar rol.wDe of ~d_ted ;tpor by the Rcdlic:liiKIli0118 cqatdicm for' (JIIi.: of ~ rolkJwius and ~ ~ults 'Q.ith,.,uua round by suimble generaJi1.ad anel.atiC v.11cfc P c: 16--.54 bar. (0 lsobu~ at lWC wbac P === 20.03 bar. d~} ~eat 1~~ v.~ P -;; 24.0~ bar. ({) f5obotanc- at t_ C,,,.berer :;lt..Sl ba (rn) C.b.lorioe at 6Cf'C ,.,hcte P ~ .., Ul21 b:sr. (n} Chlorin.~ 70'"C ~ P L =22.49 fl..1& (o) Clblorinea:~ l(fC ~ PJiat :27.43 bar. {p) Ollori.ne.at90 c where p . ;;; 33.08. bar. (q) SwfvrdioLkk m: C~ IQA -18..66~. (r) Sulfur dla..tidr t 9i(pC where P -= l3.3~ lm. s) Solfurdimdeat ft(QilC'VbcTC p s>A ~28.74 C,r) Sblflll'diaxi*: .u IWC i~Ja'e P st~ 15.01 bm:. lt9 3.!9. Use tbe SoowJR.edlid11K.wong equi.tiorJrttl mlatl:ate che moTar vatome:s of~ liquid and5a~ma~al ..--.parrwUJt ml~i~ and~ li~ IJ)t ...,_of~ pensor Pb. 3.38 iiiM (.()ID~ resohs willl rai:D.es fouod by mimble gent.ralb.ed ~ .:tAO.. Usetbe ~ .equa.donm ,C31_m~ 1hemolarvolnm.esol:SaUJ.rata'lliquicland sa.tur.u~d vapor for the 5Ubs~ and rondilions ptn by G~W oi diG Pif1J. of Pb.. 33 and~ results wiJb wJmf!S found by Stiliah~ g;eae:mlfad correJmiom.. .14L Emmatt: ~bet Col.kl~ fd) The volume -e-up.ed b)' 18 1tgofetby1:ene at ss~c .met 351m. (h} 1"bE ~ n e~~ contai:nrd iDa ~m3 cylfoder at SlrC arull15 barr. lAL "lbr~pUC mt111f mlu:me(Jfa [pattirulu~ndl ~ 23,000em'mol... atlOO KaPd 1 baf_ .oUberdam :tVe~-.t~ilabh. Withoot -- - Ji:ibiJ:~p be ~ior. de2.rmlne I~ ~E~ ofrlbc roolar rol:D.JDeotlbe ~apar i!llJW K md 5 bR 3Al. 1b a good approximatim. what is abe molar YOI.llfe ofethanol v,apor at 48:l'?C und 6.000 kPa? How~ this ~t ~~ witnlbeldW~ ~? ~ A o..3s-,m3 '~ i l1.'Rdmstore~ propane;~ mwpm pnmu~~e. Safely rt'(JMidu- otlon ~ tbat _ atcanp:raw~ atJlQ K ~liquid nnbi~no~ lbim ~ of tiH: kiUIJ wh.u:oerof ltle vessel. ffJI ~ euodit~ ddmn.irJc ilhc of y,apor and 'tiE lil'J:m or llUJiid iifi die ~l ~ m K -tile VdJ'Of~of~ is 11 6.0 bar~ Obras protegidas par d1reitos de autc 132. 3..4:5. A JO..tfil :aank ronml:ni 14 m3 ofliquidn>fil1qe In tqtri1Ibtium 'Witb iju ~at 2.'PC P.Wmate the mas of~ vapormebB. ' The"1lPW ptreSSUJ'e ofn...IJI.Ilme 3l d:J.e ~~ ' .;t43~ (a) '11le .uf.e~Jr.meeoruaiiled iuaO.IS-m.J ~ Q;t ~Candl l4,.000kP'il. (b~ 1'he tem;pennure at wbidl A10 kg of rdJnme itored iD & 0.15-m~ '~ ~ a )ilt:S$CQ~ 20.000kPa lAl . 'Th wt1a1 ~ does ooe JiU ,a O.Ls.ml ~ at 2C jn, ordu lD S:~ 40 kg of cthy~Goe mil"l 3.4&.. !If 15 - afJilO bta 0.4-m1 cootru:fiefis beattdto .uxFC. l!kh$1 ~ , de~~? 149. ~ ~ holds ~:c ~~ lSrC and UOO tr.. If it . btated to 23rC. whn pteHUR is ~~? 150.. What . tbcpm:rsureina rOJ...ml ~ WRll l1 i5 ebupdwith. 1'0 k, ofcobcm d''tonde iit.31PC'? lSL A rigid ~ filkd to-~ mvo1n~ with liquid mti!Opo at its QOJ'ID.d MiliDI point.~ adoaied torwmn lo 2.S~C. Wbn ~ ~ ~? Thl= mniDr vo'lulne of lkptid1nitqm at i1s n~ Idling point. ~ 34.1em" moJ- l. l~ 1'be ~ifie votmne ofi8obulnD! liqW4m: 3WK Wid 4 bar~ JL824anl &-t_Ettitpb: tM ~ftc Wlwnc 415 K and 1S tm- JAl.. Tbed!mityofHqoidin-peDtaoe i&0.630 gcm-l at 18 and ~ bar. ES'timate it8 ~) a.t ~4(FC and 120bat. l.S. l!stimaterthe volurJJEcblloge ofvaporization forammonia at2CJ C. At this b:mpemWre die 'AQJOT~ ofammoaiais 8Si'1PL 3.!16. P VT data 1mJ be tOea h)' m~ fDIJCJ~Ni~ p~ A ma.:!1. m ef a nbs.tnoce of l:llOblr ./11 introduced intoa tbnn~ ~II ofkoo-wn lOlBI lo'1;)]UJK IV~. 'Tbe ~ u ~"Cttw ~ 3Dd.lbe: ~ T mdl ~ p11rt IliC'au.ttd.. (.a~ Aftmldma:tdy wlmpaecnfateerroa,are aDownble mlibe. ~ variahk$1m,. V', T and P) uebe muimum.allowable morinabe ~~com~bility raaor z ls: Jil:'1' (b~ ~Y bat perce.ntage e.trer'S are allGVtable in me measured ~ 1if die maximum ~ Cll1:ll: iD calcolmed w:alnes ofdlO seoond vidal ~IU B !d ~ ? Asmmethrn Z ~ 0.9an:d ~bat VIIDes of 8 iiJe calcuhtedl b)' Bq. (:1..19)_ Obras proteg1das por direitos de autc 133. 121 3.51. f0fra;p$.~bt lhc R~dV'JtWQII~ r41~ IU1d fw2 ~ ~~~ Tc1de-mop a:~ itnu for~ lWO li:rniitQJ sl~ um (az)~'"-o aP .,. lim ~(~)Ji- aP r JA U 140(H}l d g~ ~ "' ~ 60f) *-Pel L(atD) ~ atuh'dclll t(J l(lal) 'Of~ .~ foell roran am~~ what u.."'OOd be rbe voJirme cfthe ta:nt ~ to bold ~ .. l,DODipsil) and 60(- F) in .amount cqui~.~" l()(pl) ufpsollne? Y9" ~a gpodestimate for l.bt: ~Dlty facu Z of lUI'IIHd fl)'dm,p ..,.. porat2S .KQd 3.213b3f_ f'w ~an~'~~ z= O~nS7. Lim(~) ....of.-o ap r (a) Stmw Um'ltbe ~ -wiD$11 ~ocm~ B b fft'O ~the Boyle~ (b) US~C lbe ~ oorrelation for B~ Eq. (3.6l). 10. eslimne tbe tttditt:rtl Bo)'k ttmp~nnu~ JVtsDupk tluids.. Ul~ N~ gas (~ pg~ ~) is dcti'fwed to a c.R) via pipdine It a voliW'Itltllic rate,of 150 million SL"U1datidcubic feet~ day. A~~oondltfons;are sorA ~-~). ~: (a) ,.. 'Ul'llllldric ddivet}1 nne macrusloubic fcei perday. (b) 1ihe mobrcKm'aY rate inkmo1 per hour. (c:) 1i1e ps velocity at delil'a) ewdilioos in'm- m. The piJ* k 2-4(1n) ~~ ltd ~ilh it$& di~ or n-~ m). s~ oondil~ are filf'F) wullfatm). J.Q. Some ~ding--s:atcscomtaU'&D$ tl5C'ihc~~ ~ilriUry bctocX;: Pllbcf Ibmdie~ fookrtu, as a third~ The t'iJiQ ~ofCD11'ela00n (age~ on ~.. Pc..md Zeo-. tbB CltDer on fc,. Pc. aodl ~~} woold be eq:DNalent ,.~ tbme a Olli!- to-o.ne ~_ndf~ bdwrrn~ ~ ond 414 n.dllta of App. B .allow a 1m of l&h ~~- ~ a pl'Qt of Zc w. GJ to ~ bow ,..,"en Zc 001'11'Clltes -..rilh f. ~a Jlirtear~ (Z~ !!!!!!-a + btJJ) f rumpolar~. 1.63~ Fagun: 33 wggesu ibm 1he ~ 'lJ.mbs afccnsmm o"Olome) am approidlm.rely lrnight~ma PT d:iaJI'IUIL ~r ~ tbt:lollowiDi m.ocJ:el imp~y linear~ (a) Conmmt-P~ equation for liquids.. Cb) hlml-p ~ (t) v-nn lkr Wuh equlltioo. Obras proteg1das por direitos de autc 134. 1..,..,. - 3..61L Sbowo ~ is the Equanoo ofSnJr-en in'fable J.l foc {a} 11be Redlichlkwoog equalicn ofsmte. ~~b}' 1beSo~biKwoogcqumiuoof~ { ) 1bc a-.r.JD..-,l..~Tio- N'Ui.W111 . rlt"Fft..,- c: 1 _ !!! ~-L~ II'~- ,.,.,.._..OQ fJ .,.l.@&.e_ 1 69. Suppose Z w. P, dar:t arr axililahfe m arnsmnt T1 Show tflm rhe ~ demmy- series ~ rirW a:oefficient can bederived ffltiiD.~dam via the~ Bm lim (Z ~ I )ZTr/P7 Pi~ 3.7D~ H~ th: ~lilt of dx ~ing pttJbttm and d.alu {rum table E.l to tJbtiln a ia1ur of fix ~ ftmm a T,= 1. ~c~are the resub wilh1lbe -n~ne implied.by Eq. (3..65)~ :111. 1be fOOolring cnnvrrsa.tian was ~rbeard in theoomdluof.a targoeogioe-ma linn. ~- t~~gilleer. '"'HL boss. 'Wby dtt bis SI'IUleT Old.limer: "1 1iM!l,y "WOD 111 w~ with Hany ~. from Resca:n:h. He bet me l1hal I ooolda"l oome up wiD a ~t but ~ eslimaM fm llhc mobr 'cDme o1 u "' 80Jl.at ~c aud 300 bu. NotbinJ to it; I used llhc ideal..ps equation,. and got Bhout 83 cm1 :mol-1 Harry sh.ook bbl ~ but paidup_ Wbm do )'(ru tbiQk llhoul tbW:?" Hn.~~ C~oosnbi~g. hi dltnno ao; , think roo mus.t be li~ ri&ln.... Arpin 11 dle !italtd ~ is DOt :m idea1l p,_~i... ~ ~ric.dly wily b oltki:mcr won his ~ 3.'72. f"'rw mol of calcium earbide ~e eombioed witb H) mol roC water ma dOii'e'CL ri.Pl hi,gta--~~ 'CSSC& q JiROO cm-1 :i-qtr_rnaJ ~mpcy YO!~ ~kfie p..4 " ~ bylk~ cac2(:r} +2H!O(l) .....,. C2Hl(t} + Q(OUh(:r) 1btl: vessel contains packing with a ~1)' of 40Ill to pmreot explo!We ~ ..:....... r~t.~H= IKll . ~t:ne. ,_. o _ ...:. as~c and t ...___ ~- lh.e .. m'I'''IU (/1 .. _ _~~ . - _ WllJ I, I. (d .A balance afa~J~Ddinmand ~ im ilia tbal z - ~ A I ole m.an.i~ ps it. !~ I fmwltfth ~ QlCIJO ~tKl$OJ ~), J_;rs.. wnre1b; pmnl foml ~utao equation or.srutt ~: Z - I +ZLtl'(p) - Z (T. p) w~ z,.,(J)) Jt(Ot$J.ts ~from fql1ll ioos. ..m1 Z (T.. p) ~on;. ~ from iltll'aCti Wh:d are the repulsive Dl a~~ranift comn"'bmioos lo lllt dn- . ~ vf~? 176.. ~ below are marproposed ~ wthe i1WIJ der w.li equatioo ~f ~ Ate myor lfiOdiliclti____,i)lfi) IWI.~ Elplaio ~fuiJ)r; fqtmJmts sucb ~~& ""'II ~~ adiJ.&:: in 'rofo:oJe.'3 do notcpalify. RT a (c1) p ;; " ~ b - v RT a (b~ p = ( V -- b)! V' RT II 1 { 1 c) p: lf (V .... b) - ~ IT a (d) ~'=7 - i2 1'17... n..b J'dl!.,..nc~ ln lPb. .,_4] . ~ge; mto he,zg) ideal~ ~ ~-:elop m I~ givin& '~be bi:AiseboTd air~ ~ ~ oi~ 111. A pden I.KKw 1'ith1fie ''il'ata' '~Lhe &'hut :.md die ocw.zle dosed in ate snn.- full of liquid Y.,-atef. Initially., the~ B at ~(pC andt6 b M~ &i)fi'lit LUbe ~ lrmpmlturt olthe watu rises to~ C. Owing n.lhe iD.aease iu tempea..twe. uad ~ aodlllhe. rlastidty ofm ~ lhr intemal diatncrrr oftlhe bose~ hy 0..3'4! . ~ the final~ 0ftbe 'V.."'ta' mlbe bose.. Data: P, ow) ~ 250 X lr I(~I~ r(ave) ...- 45 X 1CJ6 ba:r~ 1 Obras proteg1das por direitos de autc 137. Chapter4 Heat Effects Heat U"'UD&fer is a c:emmon operaritm1i:Q r.be ~h~ iodostry, COD5ida;, mr ~le. the mao~re t'l edlytez glyeoj (an a1uifreeze ~) by lbe oxidarion ofeabylate Lo ethy~ hie ---AI __._ . h A.AI--.-: t t I "'fl.._ ----lih.. ....it...!-- "' . .. ~ 'Ut. . iiUIIJ l:l$ ~~.q,~Sotq~ ~ YH!M(Jn "0 gl)t'O~ UIIH.~IJ~ OXlUllYIUU matiJoD itl lllOSt cuedlJ"e when cmied omm a.em~ oem 250~C The. l'ml.~ et.bylcfc ODd a:ir.. are thecd't~.re beturd to this ~ bd'tn they cnaa- the~ 1'bepKbeaw design depe::nds em tbe me ofbeat imlafec "JJM combustion ~Lions of edlylen-C! with ~y~ in1the ~ bed ~d to ~ lbr: ~. Hcwo,v, heal is.IUIIIJKJYed from the Maeror. and b re~ d.~ IK)( fise mucll tiborr 259':-c _ Higlmr ~ promote lbo production or c~.. :m UD:~ produ(.'t. ~ip of the ~or requires lknm.vledge of the be:at~trll:M[er mte-. mid ~his depen& 00 lbe: beat ~ ~iatall witbl lite dJmDca.J mJCtiom.. lbc- ~:ylaJC' oxide pmduet .is bydi:Dd to g]ycoJ by aMoqxioo ia ~ llm1 k -~"Uivcd M l only ~ ot t~Jc ~ dtllflge and d~ $OIUliOo ~ bgJ: ruso ~ Q{ dJe llydrn:tioa rcaaioo between tbe disso1f'ed edlylene oxide and water. l?mny. thegly-eall& mcoiettd rto1n waau by dUtillatioo, a~~ of~ aDd ~em. wbidJ re-sults in the ~p:ntltioo. 0f a solution iioto itico~ts.. AJ] cf t1J,o importml he.al ~etreas are iDu.~ed by this relaiD:'dy simple cbemkalm:mu-- factwing ~- Io oonlrd$l m sm.sible heat ~ Yhicb ll.J'e dl~ by lmnJ:tCiilltU~~e dnmg:es. tk:hat etfects ofchemical 1!eadioo. pba&e ~oo. aoo d'ie ~ and separm- lien of salntitxts Drt ,.._............ _.. .L.r.- ,,'l'iifl'rinu-nna~ - .. "" -...~..- - .............,........ ~ . _~'""m~ ~~~,....,.... QJ.,..... '"""~.4!1 ~- .o~AQg tiU ~.uno u;;;,rnper:l- tme. Indaischapterwe apply tbelJDOdyna.mi . m meet.~, of~~ ordle~eft'~ lh1l1 ~ pbysit4ll ruld clitmical opentio:DS. H/R is dbncmicn___lcs$., tbelllllits ofCp arc p-emed by tbe c.b.oiee of R. M mown in CIJaiL16. for ~,rdir Uk41-l'tl hm.t ~- ru~lb:m lite acCWIJ llearm- pxily ~ DAd mdle evaluaJionofmcb lhamodymnnic properties IS the cntlWp-y. 11Je:ream is that ~~Y t"'l"ahmtiou .i:s rmo11 o:m~niemdy aecompli~. in t."V ;ps; lim-, caJeutruion of "n.tues :foro.llypotbetical h!Ml~~ Jf(Jl~ wllemiA idealr-gns heal ~tie! BB ~ secoud. OIJI'RlCOOn of d)e ideaJ-~ VDlu to the real-gas w~ A Ral ps t~ ~1 in~ ~ JimU ~ P ... 0; i.f it ~~ to m:n11in ideal when ~d to aGPite prasur:e. il would cxisr ma bypolbeliall ideal-go ,~.. In i5UCb snncs psr.s ht~'"Q propef'- lies dmll .reflect lbeir molecular stl'Odlm.'! just as do reaJJ gases. Ideal~ beat ~ fdesignated by c;and c~') are tberefore different tor~ g~ atmougb fanctiom 0f -- -;- - ~ ~nr -, -_.~~,:lfe~..-u1J _ ~ lcleal-p betlnc=apama in~ smoolldy witb ~ WDpe_ralW'e rowmt an upper limit. wflldiJ is.~ached wtw!n au ~ ronniooal. and vi.braJiooal !'llOdes of ~war mmioo m f11Uy c:.clted Lst'C' Eq. (16.18)]. The-~ of ~Vft on c!' tor~ ru~mgm. WUie.4 :uXI! .e~ dioxide ig illlnsll'illed in Flg. 4.1. Tempetill~~te depemleDce u ex- pressedaii8J;t1iadly by ~lions~ a$ J!q~ (4.4),htR. ~ ci' _/!.. = A ' B1' -+CT1 +DT- 2 R Obras proteg1das por direitos de autc 140. 128 v-~ of the.~ are ,gi.vea in Thble C.I of App. C fM .a mtmbett of f!!llJ.1TJ.m_Oft ~ and iDJipniepscs. M~ ~ bul tmm:c COIIIJJ]m ~.an found in the .litera1ure.l 11.,.re4J: ~btal Q~ol~oi~ ~ m4OAtbondioxide. lu ilresWl oflq. (3.19~ l(be tWV> ~ beatJ capacitifi are related~ c~J c' .___y_ - _L_I R - R Tbef~Qnpa~ &~~of C~1 IR follow5 fRm1 thC ~~~~~ofC~11R- The deem of (empaamre oo C~~ ar C ~~ ae detennilled lby ell~ Q'k)SL aftea f'Ivm ~ data and knowkdge of molmllat t1Ufe lllrough ,takalafio blued oo ~ ~mcs. Where ~bl clru::a .ue .001 ~~ mt:thods of eafmariun ilJe empluyaL ~ibed by lkid. PrausnitT.. and Poling} Alfbougb i:dl:al-p bi:atmpaciti .are ~ly ~forn:al~ only 111 uro ~" 1be dqJartuK: ofrea1 ~ &-om iidealily i5 5ddomiigniicant at~ below~~ and Ml'eC;tmd c~8 are wuaUJy rooa~ to their tme be&t~ties. IStt P~A. AI:rand l. L .l.ft. tlriti4 P1itiD ~ 'OL 6. pp. 169-J'"J9. t l~ mil n bltdtapt;)by. M::O aho T. E. Dn1i1mi R. P. Dmncr~ IL M. S ad C. C. . .~ ~ P~tn .oftw. a~ tPi!fll ~. ~i(lf fr.vd~11n.t-.PA,es1if,ll ,!JJS_ 2J.Jr1 ~aE.~ mJl f .O"CGffRdJ.'IJI~ P~~ of~tJ1IfdUquidxf Stfl ed...dgp.l. 11k< L0-1- 2..164 x zo- o +l1J.lSl2 Gas mix~ ofcoostam QOIDposition behave aactlly as do pure gases.. In ;m ideal...ps ~ dJt: 11:l01r:culrs ~ Jk) ip01,1Cm.~ em 1 f)nc aQC4teri ~ r:.aCb ,gaS QL'St$ m~Rt (If ttte others. The. id'eal-.p beat eapacny of Q mix.tnre is tlerefom me mol~weigtned wm ofthe bcal eapaci1ies ,of~ individual ~ Th.us for~ A. B. aDd C ~ molar lmu capad1y Dfa IDD.mte ift tbe ideal-g;.tbi stare ts; (4.6) where 1C~. C~~., aDd C? are die mtllat beat C11~Jlie:s, of pure A. B. mid C ill the i.~p sme ......A, l 1 Mild am - ...1 e.....-li"" . ~ ,... A. JB. -- _Jc __ mQI)_liJill,.i ~os- ~ with~ die beat~ afal'tids and liqvids~R fuwJd by ~Ill. Pamxr e1iers rw1be lemperanue deperulei'J:Ce ofc,.asrei~ by Bq. (4.4) 3J!e ~veo [ora few mJids andlliqpid$ inThtlksC.2 aoclC.l of App. C. Cond:Jtiom rorthebatcapacities oftnm solids and liqnids are gjven by Peny imd -=- ~9.~7s J R.epresemlllive llXJIDptttef ~ fer C1Hlurnion . IF'or added &.tJ"bility ~ prognms also~val~ the dimensionless.qwtn1ity (Cp )H1R as giYelll by Eq. (4.8_t. The 118ht-bafid side' of~ ~ is ~Oiher fum;iion, ~H(TG,T:A.B~C,~D)~ Wdh tbis ddinitioo. Eq. {4.8) ~~ (~=)#! == MCPH(TO'.T;A,BC.D) Obras proteg das por dir eitos de auto 144. Exampla4.3 What mIM 1iMI temperaiW'e when heal in the arncAmt o1 o~.4 x to6(Btli~ ts added to .25(b mol),of ammoofa irlttiafly a1500(~F) in a staady-tlafl process at 1(atm)? Solution 4.3 ~All isdk: nbJpy ~~c b l(lb moJJ1 Q ~ 111 !J.H,. md Q GA x lo6~B - ;;;;;; _ ~ l~OOO(Bw)(Ib muJ)-1 n 25 ~ lat~pac::iiy eqlidioo ~tempera~ lD kelvins;mtltftlfe..Cc()U~H -of ID .. to tileS1 S)'5tml is indkated. .Beawse 1J mot~ is 11K[Llivalent w o..4299(i9m)(lb DK.1)~1 .. di~ dlr: ~108 rmrlt by M299: .l!.R = 1~/0.4299 = 37.218 J 11D~I~L With _ 500 + 459~67 _ 3 .._. .S K To= = s 011.. ~ ~.8 l~mtkm beswee.n Ibis equdoo and 13q. (4.lD) .llm1S ilb o "'"'W: T a: To. nD(l I1XID~ 00 the final ~ue: r- 1..2SOK Obras proteg1das por direitos de autc 145. 133 4..2 LATENT HEATS ,OF'PURE SUBSTANCES Vhm tJ ~ ~~ i!i liqudfcdlh>m the iOiid ~eor va~ frwin the~ lll.;om.tat preDlll'e, DO dlaQge in lempb""rii:Ure OCC:.utS; bOW"eV~ me ~ ret[~ lbe trannet of a finim 3llliOWL1 ~r ~ ~0 me tqtb~. T"bese be dlects 3l'e caled b Wenl beat of fos.ion aDd lbe JA~CDL heal of "iapoRDiioo.. SimihltJy. lbae are beats ef tnm&ti.tm ~mp;tn~ the cb;m~ of a 5Ubmmoc &om ~on~ solid state to anolha; for ~ me beai ~ 'ben tbowh' ~lme .solfw('mmge8 to r.ha JDOIIDCiintc Ullcrure _ 95ec BDd 1 bar is 360 J for each ,-nmNJ.tom. 1'be cbarnefaistic f~ g.f aD ~ (Wocases u the coeU~ce of ~ro phases. Ac e~ to 1he ~ rule. a twc"'PhMt- system c-~sring Qf a .smear~ ~ 1wtivllriant. and hs inlemire starte its ~ by mespecifiemoo ofjiN ooe inrensh-e. property. Thus me I~ beat ~ompanying a pba:5e dw:lge 6 a f'UDCiio-n oft~ only. Wid ts Rlau::d to other s.ystm~ p~ b'n ex=t ~enoodynamk INJlWien: I ~H=HV~ I .Rrora pute ~at Ee~ f, liN laJ:cut .beat! &1""= vWmne dJange ~~~Ole plwe dt3Dge .tJ m ~ sanw~tiofJ ~ The derivatioo ofthi5 ~Oll, bmwD as dJe OlapcynmC4U .00. is ,h'Cllm Chap. 6. (4.l n Wb:eo Eq. (4.11) ~ oppl1ied r:o lhe va;poriZ3Wm ofa pure llquid, dP'd / dT is tbe dope of dJ "rlij)Ot ~v~.,t~ mrve at fhe temperamre of~ A V is the difference ~..:en molar VllltDCS t~f s:arurat4 !'aPOf ;and! 5illtunl~ itiqui~ od H uthe ktmt beat CJf vaporizatiOIL T1als 'alues orAH ftlil)r be c:iilctdatm f.roln ~r~ Wid "''IU~Die1ri.c dara. u.tmt beats ltla~ al$o bt tneamftdl eal~tricalty. &pcriJ:DSDtal ,.'a]'uc.JW are availabls nt s.elecUd empcm.wres fbi' 1D3AY ~.4 CoQelati{t.OS forthe l~ ~ ,of~ nm- ~ ~a, fuootion of ~em~ :m::girm by O;mbed et at! Ne.~ da.m are oot a.lw.-a.Ji- a'W:ilmle all'be ~ of inlerest, and it;! ~ c~ dJc dant ~lll'y for ~P' plitca.tion of Eq. (4.1 l} ar:G also DO( lmoWiD~ Jo 1bjg eveat appt~CMimate ~ ~R rused for esaima~eS tJfme lteat effect ac~-mnpm~~ing u pb.ue ~~ BQ:ause beats ofYB~n ~ by far lbc most iropoRa~U &om a [pDcQcal point of vi:ew. ~)' h!.iYG rccci~d most aiiCPtioo"' Olle ~~ ~ use of a ~mnluoon ~ lmOWB as UNIVAP.6 Al:terrunhemeth- ods~ one oftwo~ filedi-cti.on of dx:. ~ of ~z;atitm ilt dk- ~ lxiiliog poiuc.. i-,,, ~ ;.~ ~~ .m-; 'Of ~ ~ Ht~:~Jmpilere. lined as lOt.325 h "'i. ~ acd V. $~ R.."it(' a.emi~ lnQ 8cra No. n. ~~ O"dri l ; R.. H. Pmy aod 0 . GRm..10p. dl.. ~. "" ~- ll 'b~ tl :d.. trp. dL Obras protegidas por direi os de aut 146. ll-+ &imatioo ol1be IJireilt of ~ w any ~~ from lh knOvn ntlw at a single t=-,c:n~~ Rough~~ of brent ~h. ,of wporimllon for pure liqoi& m dleir nor:mal boilin& points are giMm ~ T'trJUIOf.t~ rok; ~Hn - 10 RT,. wbere T. u~ absml~ lml~ ofth~ ~ bo-il.iog poi.nl.. 'Tile units of AH~.., R.. :md T" IIDlS[ be dx&m so dmll!..J4/ RT4 is dimemicmless. Dating fii'1Jfl 1884. ~flU, n.1ik ~1illJ [prtrtidc$ a simplic chec1 oo w:Ktba values ~tJtawd by othamtrbods ~ ~able:. ~t="Dtative ~val~ for tbtt ratio am Ar.. S.O: h~~ 8.7~ 01. 9.1~ HCJ. E0.4~ C~(i~ 10.5: M~~i. ~ 0;6 and H20. 13.L Ofthe' same.~. t.H am quite m simple. Is me eqwmon pmposed by Riedel:1 AHfJ 1.091HI'I! P4'" ~ ] Ol3) - - ;;;::;; R l'lf 0.930 - Tr. (4.tl) wbem llr. i tbt:, tri~ ~ in hats and Tr.. i8 abe raiuced t~ure m T~. Equation (4.12) is ~mpri~)' ~fur an e-mpiricull expression~ eno ~y exceed 5 ~IlL Appli~ to water i1 gi-es: A II. IJ)92{l:n 2Z(t55 - LO13J k ... q:_ ~ c a m.J,,:,u RT. 0.930 - 0.517 AN~ = (l3.S6)(8.3J4)(373.1.S) =42..065 J IDOJ- "fbil ~ to12.334 J g- 1~ mesteaiJ)..tJ.ble l"BBIu orU:S7 J g- 1 is lo1a- by 3.4 ~PL slimali gf the )atml ~ of~~ of" pUn;: liquid at any lelnfXI.oil1Jre firotn me known 'Mle'.at a stqte ~may be~ on a known ~til ~oron t1 value ~ ~ fq. (4~1'2}. ~ ~ PfOPQ~ JYr:. Wn~ ha.!t. found ~id'.c ~ept:mct:: All! == (I~ T,.,)G..J& Ha ' - r~ (4.l3) Exam:ple 4.4 Given that llhe latent heat of 'VaPorization o1 water at 1,DCVC IS 2.257 J g- 1, estimate the latentheat at ~C~ Obras pro egidas por direitos de autc 147. Solution 4.4 let AH1 ~ la.tcnt beul. u1 'IOO'jC ~ 2...251 J g-1 Alil - late.ru lle&n m JOO"'C T,_ = :)1'l~15/M1.l =0..511 T~ ::;; S7J.I:51641.1 c V.a6 Then by f.q. t4.13). (1-0886)0 All,.- 1(2..'2:51) 1 -n~-n 'Ole 'Vllloe given iD (be stean1 tables is 1.406J @-. 4.3 STANDARD HEAT OF REAC110N 135 llear e~ disc~ so far lm'e bem b physical ~- Cbe:mical J~~:aCOOIQ s,ls_o ~ accompanied either by lbe mmsfeJI' ,of Ileal ot by rempe:mture chaoges during m.e COOi':Sle of Lreaclion-in 50IDU Q'WS !Jylbolb. 1besc,eifects arc ~o5 of die mtfenmees rn nwlec- lolarSlna(llJ.1r"' andlber.efore iaenergy,ofa.fle~ .and mtclnn~- f'llli ~Pk~llbcresctnnts in aeomtJusiHJo JeXtion ~~energy on.IKXOOIIl ofrtbeir wucrure lhaD do the~ ~, and~ CIJCEIY mU5it either be tlan5fmcd to the 5UH1JWldinp as but or produce [pnJducts at anelevated temperam:re. E.acb. of lbe vust I1UIIlbeJ of posstb!e cbemicaJ .fleaetiOOS may fbt" cmied OUI Ut many di.OefeRI W!)'&l dfidI~R:".JCtiiJli CtJ..I'!ri< ouf m 3 putirular way isal:.compliD~ ~ ~ p:I!Jtku}w beat dfect. iabu:latioo of.tttl possible bea.t effects for all powole reactioos Lis tmpo:.,~ib2e.. We diete&JJ'C wlwtal~ die br-at r.~ for rcuctioos. ~ out in dh"tTS~: way~ lirom Illata for reacii.oJJS Cill'lied our in a stMdmd -ay. 1ldsreduces 'lhr .reqll:ircdldma to ~ rniDUnUDL The hal ~te.G wilb a spxijc chemitai reactiQO d~ on the l~ of lbolh lile fC)CIDntS Stnd product&. A Qt'Htmt:eut (sla.ll1e, the Gwcill c:oergy ba]an~ :&J. (2.J2)t reduces to Q = ~H Obras protegidas por direi os de aut 148. 136 for p~ ofdati ~OD widJ respect to dJe rre.aaioo. oA +bB ~ 1L+mld the~ h~ ofn;aclitm U ~4S 1beeolfpy'*"ang ~a ~(lies ofA and b mol~ of B iD dimSll!llldanl ~s m lc~rtlllmr T l'l:ad toform I'moles ofL and m molesd"M in tJeir lftlndmtl ~rQt ~ UPfll" ~P~JP T. A standard 11a1e is a particular atate of a apeciea at tamperablre T and at pecllled eonclitJona of prnau-.,composftiOf and physical condiflon1e-.e.g.,,ps, u.,.ld~ or ecdkL A mrJJ1JtJJTI-s~pre.uUR df l !i'Umdard atmosphere {UU,Jl:S h ) was mue for DWIJ' ~ :md ddrr ttat. Qlbolari compounds traklu_,g,pun wlht ftaCtiou an toown. A /onnt~Jfon reac1ionis.defined as a reaaioo whidl form-s~ asingleromptKJrtdftvm ita cmuti.tw!tll t~.Fmram. Fnrexampb:, k ~em C ~~~ + 2lb ObOH is the formmoo ~on for mdllaool 11:te reactioo H:a-0 -t S03 --7 Hl~ is ttor a fonmuloo re~c:m.. ~ it I~ $Uitmio ~ QOl fJoniiJ dlC' .clmJmts tNt from ocl:lcr ~. fwirmllioo reactioos .ue un- derstood to produce t mo1 of~ mebem ofI~ ics iberef(ll't basedM Jl1rD/ ofthe fXIII~fo'fflfb__-t Heats ef ~lion ~ uny ~:tmperatwc CaD be ~~cutaxed from bc111~ity cilia if dJe vltmoe for one t.etnpaarure Is kiirtowo~ lhe tabubli0n of dala cu 1tJeR'f(lr ~ m'JIJCI"d w the Jmpillticm of S1111144111l h't't~U' fl/fofiJftflion ar a Jingle t~ftilllw~ The usual reltoice for this ~~ iJ :l98, ~S K (If zsoc. Tb~ ~ bca.t of ~(JQ af a oompouod this hmlpemnre ~ represenmd by 1Im &ytnbo1 il.Hj.,., . The ~ syrmbd ~ the ~tmdud val~ ~pi I identities 01 hem of fonmaon. and lhe :298 i:s the ~ximme absolu-m tent~ iftttelfins. ntlJts, of~ vtl~ foreummoo~ !MYbefound instandald lmodboo~ but ~he lllOrSteneasive t"'Dpil:aliODS no.rllB.hle ate mr~iml mf~tiCC wodcs.9 An altlridged tiM,ofv.aTues i:S given inThbJe C.4 ofApp. C. Wbco clteinical cqaatioMare combined by addilion. the :Stal:ldaro beats ofreaction may also be added 'to gi-e tfle standard beal of lbt: malring :I"CCiCtioo~ Tid$ is possilllc ~en lhalpy l$ a 513te fl::ma~ .and it1; chan~ for giwn initial and 1inaJ states are r~ of pd~ m~Lllar, formation t_Wlti(ms and~ be1n1 of r~ may~ be~ ~ wprod]Jec any cksired eqwuioo (not ilse:1f a {ormation equaliml) and its ~ying Slllfid3n!III:Jicat of~- - .. G..-aJioo~ iWri-.- f-'- thioS. ~ -A . L .a- !-~! '~"i: tlo..- - OIQ """"~"" - "' '"'"'4'1UodJ. 1,11,11 - p....l-~ 11,.1!~ IDCUJ~ liD ~!OIY.Ciill! V1. """"' pbysieid M* of each reacmm and pmdoct. i.e.. thl: ldler 1~ f, m 1 pJ~ kl ~ ~ ~ d'.J.m:licaJ fotmu.la te show whelher il is a gas.. a tiquid, m a solid. 1lti.s mi@ibt ieeiD UDrl~. ~a porecbemic:al ~ lit a panicular ttm~~ a1Jd l hatCLIJ ~y emCJofy in ol'lle pb)'1iea1 stat~. Uowem-, littnioo:s states an: oflen~ usurned for CO!Weftie:oce. CoMickf the reactiOllll C~(g) + H1(g) --+ CO(,) + ltlO(r) m~C. T.b.is wuter--ps.. llift reaction ~ ro.mmooly enooum~ hllhe cbemi.I!Jd indosll)'. thoogb it wms ptace oo]yItt lt~~ ~u above2S&C. H~. medata used~ for l:Sq~ aDd lheinitial Slepin any. caleulauoo,of held t-fl~ for this R'lH:tiDQ is.cva.Jualion lbt ~~of rcaetioo .at 25e.c. The peninefl[ fonnation 1'e31:1ioo~ m1ld ~.heir hem off~~ &urn~~ C4 ~; c~~): C(J) +Ozf$~ ...... CO!(s) 6Hf:.. ~ --393..1091 J fi2Cr:t Bccara.~ ~m an dc~nt 4Hia ~ 0 CO(g): C(1) .f. ~02f.g)-.. CO(g) bHf: == -110,525 J H~): Rz(g}t + ~Oz(g) .-. th()fs) Hh. = -241~UI J Ike~ Ebe ~ i adualb carried out QlliJe'ly in tbe gas phase at big)) temper1mll"e-, ron- ~ diaal.'e!l lhw. tlbe smnd:mt &tateS of aU pliOdJlcu.and traJctaJIIS at "2S~ be talco as lht: ~For cumple, see UC ~ Tabl~ IIJd TIC ~- f'itbUp.-/l'(NP- 11~~ ~ 11'1~ of~ il'benDu;lJIIlllllfe~ ~ C'.cJC~ 1'tu5. A & M Ubiv. ~ ~P' s.a.~"'1"kNDS1!liblayte~~"*u.:,~;J.~-~~~~ "01. ll, ~~~pp. %. I 8ft also. T. E. .D.mbcrl fC02: pl~ l mol ofH:! ~ 4.1 166.1 Wb.en eacb prodnct and n!.amm.is ~ IS t:be pure gas at 25'lC in its~ fllate at J. bar. ln tbi:s eumpk the 5lmldald be rof.mm.atioa of rH,O is avai~AtJlt for j1$ h~tical ~ ~ ~ a12C OacnMigbt s~t me v-all& oflhe ~bent mlfo.rmm.ion ofwa:tn 110 be IH&t.d b its aanaJ stale u a liquid at 1 bar and ~ As a ~r of fDa, ~oes for lbodt are given m'lbbk C.4 ~ ~beN am:0011 fmpmtly UKfi"l'his i liW rornmuy compouods that oortttaDydi$hI liquids lid.2JC:C :and J bat. C..ses dn ame, howe!~.w. in which a 'Yilb1e given oru1 for ~be &mDclard hUe as a lliqp:kl or u :m tdeal gas ~1leo wbat iB oeededl is die odmr value:. s~ tms ~ tiJe cawfor IDe~ CIC~T l!f'ilfl only me $1andard kat offo:rn:J;:W:on,offiquld J.~O av-dilable... lle 'OOkldin.inelwte ,aft equation for the pbysicaJ dDm!J= lhat t:rruKfonm water from it& standard state as a liquid i!l'ltD its standmd Sl:ft as an Jdea1 Them~~ for thi. physical~ is tk dl~noe between 'the lbm.ts of fonnatiuu of-~ wits l10 #lindatd ~ -l4m.JJ8- (-285.830)- 44.0121 1bi.s iJ appi(J~}y llbe latml beat ofvapOrlt.ati~ of ~at 25~C. 1ibe ~ence of~ . oo-w: rOO~(g) ~ 1Qs) +0%(1) C(.rJ + ~{}z(g} ._. ~) H2(g) + ~Oi(g) _, tbO(I) H!O(fJ ....... H20(s) Example4.5 4 Hi9S =393..500 J a~ - - tl0..52SJ AR9 - :285't830J AlfM :e: 44-.0ll J Calculafe the.S1andatd heat at 259C fOr the follo'Wing reaction: 4HC1(#) +~(g) ..., 2H10(g) +2C~(9} Obras protegidas par d1reitos de autc 151. RC(g); -92.-J0f7 J 4H0lr) -. 2H.1(g) + 2CJ;z~} h.H~ e (4)(92,307) 2H2{J) +~(g) - 2~0(g) ilH~ ;,;;; (2){-24118Ul) 4-HCI{R) + O~Jg), - :!H20(g) + 2Qb(g) 4H!9s = - ~ ~4,408 J Tb.is. n;sul~ Is fQur~~ lie $18~ ltc'-.1t orc;qmbgsuonof4HC1(g) sa below). 4.5 STANDARD,KEAT OF COMBUSTION Onl}' a fewfomWiDIJ readim)&, CIIII actual~)' be ~ed out at the cwditions of intcn:st~ :md Lhae:f~ dma for these .reactions IDUSl Ui5iWJ.l'y be dele~ ~>'- One kind or~ Lhld rem:lilyleJids itself10 ~mcnt is lhe C 298..15. ,lafl ~t/OOZ the le5Uit mthe ~~ QQUa.tion. Thh )nidd.ll u 1CCW walue of T fat whim (Cp)8 is Ee!W'..d.liared The pt'OC'ftlute corWrn.Jes ro C0JM9'1,ence on lbe ftoaJ vafw. or Obras proteg1das por direitos de autc 157. &xample4.8 One method tor1M m~ Of ~nJheSis gas. 1(a mixtUre Df CO and H:!) is lhe catalytic reforming[ofauwlh steam ,at high tempem.tum and ab'nOSpheric iPfessur&: Cll.(9) +H~O(Jl .....,. CO(I) +lh~(R} The oo1y dJlet reaction to be considered is1he Qer-gas-Stlift reattion: CO(Q) +H10(gJ ~ c:D.!{g) + K1(9} lllf th& ~s 818 suppled i.Q lhe ratio.. 2 md steam to 1 md CH.t~ and f meat is suppled to lhe reactor$& mar me pmducts nta:dl a tP'Ipctwabe rof 1.300 I(. ilaJ eM& is tomplefett OOI'MJfled and the PJOdUct stream contains 17.4 rncl-% en Assuntlng the treactant~ to be preheated to SOD 11t gh~ !by f dQIT ev.tl:nnlat for 11x: irrei."'NSI"'Me pli'OOC'S'S itsdl became llh.~ .caJculation of e.nrropy dmnp by dW in~gDl must m~neat be: aiong ~wble patm.. Obras proteg1das por direitos de autc 181. )69 D ~.5.5: T""Fe~patfis joiningequilibrium ~ alB. The ernrqpy change of i:l hmJ R!Unwir, ib(lla"evef., i$ ~~ ~ by QIT~ w~ Q is the quamdy ofbeatllmSfared to or from ~he rescn'Oif' d tempera1IJ:IIe T. Wi'betller~ m:uW'cr is f'C1:1'SJ!1Jle ~"bk. 1beRaWn i!i that the effcet ofbtal ftmiSfr:.r on a be ~iris me:Salllle llqi.b'dles!! oftbe l~pemute cf llte SI)U(lle or ink or~he heaL Ifa p:moess is re't~ "MIIIldfabarfe~ d ~ ~ ~ menby Eltt. (5.ll1), d~ ~ il "l1::ns llbemtropyof.a.systnlll u00115~ dlll'ins a~u adiabmic ~! and dE proce:ssismid ro-be i.smnvple. '".Ibis di...~ on ,Df,~ can be SUilliDarizedu tOollmw: Einrn;,py cm.-es its exi'Sieoce ro lbe ~oond ilnw~ from w.bicll k ~ in l:fil:dJ lbe ~ 'lq}' a inttmal ~ ~~ IJQm t.bc fiP1 law. Bqua.tion (S.II) is 1be ultimate S01lliCe of,all ~_o:ttion:s ibm ~~me the cotliOpy to ~a5lllabk qiJalJiitin It does I'IOt.n:pi'C;5mt.a ddinllicm or emro;py; mere is nooe io the. ~ of c~ l:bermodyoatnics. Wba1: i~ [I)WVi~ iJ lbc IJICaD.'Ii fur cakWIIing drwJgeJ io lhis property. llB eMelltia1 mture u ~ b)' 11mftdlG-..-ing Hiom:: 'There exfats properly called enlropy SiF whllcb I .am !Intrinsic proptfty IJfa "~ ~ltr' ~ to'Ual measurablecoor- diMIH whfcb ChlracteriD the spt8m. For a~ PNsiR.. 1.rtd the~ OODiiDt~a. mL~f!~ oo o liDaJ "~orr~ ~ 411.34 K- 51.8 MATHBtA11CAL STATEMENT OFTHE SECOND LAW ~two heal l'eSlef.-u~ 0ne at umtpec-arure TR Dnd a.W"J-,nd at'lhcl~ ~ Tc. Let a qUUtity of bAt 1Qt ~ tmJsfaml &om ~ botter 1t0 lbe cooec la9Wir.. n.e e~~~ropY c:bangt"S of lbe ~ i TB W1d.41 T(.' (ll'e: Asln e -IQi Tn 'lbese two mJropy ~me added m ~~ .0.~ = A.f. .~ =-IQ~ + lru =IQI (TB_-Tc)~ B c TJ!J T~ TyTc . &a-. TH > Tl"t tbc tOial 1lll'O(lY~hqe ~ a~m of1Im~btc PllXl!a . pusltiVL AlSO. ~~ beoome.s ~llliillrer M Che dlfl'~-e TIJ - Tc &~ oWlet. Wben. TH ~ on)y inliDitc:simaby ~~lxr dwJJ Tc.. the lb.cn ~ ~ l!a'em"ble. and~ appoacha ~ ~ for d'le p~ of i~ible beat lniMfct. ASr.uw is ahva)'$ ~~ ~ng ~m the~ beecmes J'ecremhl~ 8D Co.Midn' DOW IDIrrre~ process in :IIekud5j51m1.wheJ:cln ItO heat l!miSfeJrOCCUlS.. Such a pmce&S i ~ted an tbe I' V,~ diagJam afFig~ !i..6. wb.jd) bows I'm ~~. Obras proteg1das por direitos de autc 186. 174 ~Jdlatic expansion of 1 mut of ftuid fAMD an ini1ial eqc;ilihrium stan: at point A 110 .a in.aJ equilibrium t~~eal po.im B.. Now ~me hid ~ M inkiild ~b) al'l!l~enibk ~ t~ 0( t'Wtt trp ~ ~ lht ~miMe-. adiabatic (aan1lttint-etttmp)l) comp;ressiM arme ll1liidJ mme iniWd pressu:rre.. and seooBL a ~itde. ~step th:d restores me U.icial ''Otmne. ]f die mnw plfJCe$S ~ ill m entropy change of tho fiuid. ~n dae must~ bcattnmsfer d'uliinglbc revasib~ to- tam+P Ste.OBdi q> sud~ lbaa: A ~~ = ~ "" -= ('A ,cJQn.w ~" ..... "'"" - "'B ..... JIJ T 1'be original Jmwem"'ble pll'QC and 1he mcui~ nsrom1iwl ~ ~titJUte a cycle rw w&Wb AU -;;;:; 0 and fur whidlJ tbt 'tXk is tbcrd"~= -IV~ Q,.. "'LAJQ,.. u_ __s:_ o il 1a f lthe -~~ -- ~ ll ......,. ..:........ted .........nuWe-". ao:::ll.IIU!D~ IL BWemtll. .t _ 0. _ .. ~~1111!! ~w. ~l'l:'' ~ ~ U-Jl..l~. __ 11'd6 11,11!1;;: y .,. 1r.m,. for ~ cyd~ would ahen.be a proce$& fOt fie oompk':te com-ersioo inm cwart of lhe beat m~ l:llm.. f aCl~ is neptive, udl it ro~ t1m1 ~. - s~ is also ,oegam~ w.beN:e. S'#j > ~- &cause oriiBmJ ~"We~~ adimtic (AS~ -=O),lbe ~ mtrOpy ~of mesyStemmu1 surnmndiap. 8 a.~h mrlbe ~ ~ a~ ~ - ~ > o. In l.lm'iviDg ~ tbJ.s ~ull, 001 ~ is tbd dte oripnaJ ilrra'Cini.ible process :rcso.l.m in 1.11 emmpy dJange .of l.be 1fluid. Iftbe original pme.eu is inrae.:~e. lhen lbe system GlB bli-. HStUJtd lO i inkr..d Wt by simple ~]C acf.iab.aijc ~ This ~"etc t$ ~ ~JICd wllb 110 heM ll'iiM.fer and.lhuefore witb 110 net om. Thus me ysrem is restored witbout lavi:q D)" cbaoge elsevrbere.. md lhis implies that. die original process ilt nJ'>~II!! Rlb:r Df~- Thm ~.tie s:a.memmltlls fou-nd foramabati processes a:s for 0 .J'f5 d't dr 6 - wbefeSa ~-rated'~~ ~r.Jtion- lb. ~ooi:sfbc&t0t'111J~ fwmofthecntl'q1y I ~q:~pJkmle at my instanL Eacb (enD a~DJ lW'f with lime. The mst tenn is simp]) ~ ~- - -"- =m: ,pfifi"'"'tW A 4 --'e ~n ~ i rtb~ .~.~ ~~'Ill. lh ~ , f'r,nftv~-~VI ~~m...,..._...r.r VI QJ. DUWLg-~ ~.~ -~ YJJII!;~~~~ ~ tne ..v~m.al..-,.,.Jt'J k'mipW'led om by exit Rrea~Ds aod the toml emrop,y D'DmipORedl ~n by emmoce ~ The ~ ~ ~ tbe lime tate. of chm,p:. of the tntal ~trOpy mf.ht fluid ~ i.lhin die c:ootioJ wlwoc.. The Wn1 term is the ~ rre o(ch:mge of du= et:dmp)' of~die slllTOilod~ ~ldtin#fNm~~~~gdj~ l.el ra:lm of heat II.J'"anSifcr ai whb -~tt ro a puWu}.ar pmt or lbt conttol wrlate be ~ with r (l.} 'here mbscripl " J delliJ!e~ a [allpeml~De in the. SUDOdndinp. 1'be mte. ofemmp)' dla.nge mtm: :smnmn~gs as a result ofthis rmmfer lis; [ben - OJ/Ttt.l " The minDs ifll eonvertJ OJ.. detioed '5'iib leSJ'Cd to tbe sy~~ to a hal rate w:U!h respet1 tc. the ~ttp. Tilt' dWd rr.rm in Bq. (S..20) i lllerdom iDe sum ofall such quwnitics: dstWJf =-- .... E ~ dt J Toe.} (5..21) Obras protegidas par d1reitos de autc 189. 1?7 'The JimJ:I tmn.. represemmg lhe rat(' pj~tmpy ~ SGtrefteas lht ~law requiniD.teol ttw it be. positie fot me~em"ble ~e&. 1lrere&U'e llwO ~ ofifrevmtibiJ.- i~~ (a) those wi/hiJr lhG- cootml. ~-o!ume. i.e.. ilriUildl. ~~'w:rsibilities, and lb} ~~hose resulting from hem ~fer~ fi:nj~ remperM11R diHt'tellRS between system aod SIJlTOOtldi~ li.e~ aumaJ thermal ~ies. In the bm:!tin~ where 411 is the enthalpy dlam,ge of tbe stea.Jn as it lftotwi tbrongh the ~" rus $nd Q is lhe tfflal hteat 1111Dd'er ~ dta a:ppuattli ud & ~_nd~ Becali.lse no shaft l'll1:11. ooemnpmies me process,. W ::::r 0. 1be m:mmn~ tfiD.. sis~