CH05.pdf

Chapter 5 Solutions Engiering nd Chmical Thermodynamics Wyat Tenhaef Milo Kortsky Department of Chemical Engiering Org Sta University koretsm@engr.ost.edu pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 2 5.1 (a) Folwing the xample given by Equation 5.a in the txt dPPudTTudu TP ?????????????????? (b) dssudTTudu Ts ?????????????????? (c) dssudhhudu hs ?????????????????? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 3 5.2. The internal enrgy can be writen as folws dvvudTTudu Tv ?????????????????? Substiuting Equations 5.38 and 5.40 vvcTu????????? and ?????? ?????????????????? PTPTvu vT into the above xpresion yields dvPTPTdTcdu vv ?????? ??????????? From the ideal gas law, e have vRTPv????????? Therfore, dvPvRTdTcdu v ????????? whic upon oting that vRTP? for an ideal gas, becomes dTcdu v? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 4 5.3 The at capcity at constant presure can be dfined mathematicaly as folws ?? PvPPP TvPTuTPvuThc ?????????????????????????????????????? For an ideal gas: PRTvP????????? Therfore, RTuc vP ?????????? One mathematical definiton f duis dPPudTTudu TP ?????????????????? We can ow rerite vTu????????: vvTvPv cTPPuTTuTu ??????????????????????????????????????????? For an ideal gas: 0????????? TPu so PvTuc????????? Substiuting this result into ur expresion for Pc gives RccvP?? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 5 5.4 In terms of P, v, and T, the cylic equation is TPv PvvTTP ??????????????????????????1 For the ideal gas law: RTPv? so the drivatives become: vRTPv????????? RPvTP????????? PvPTPv T ???????????? 2 Therfore, 1?????????????????????????????????????????????? PvRPvRPvvTTP TPv The ideal gas law folws the cylic rule. pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 6 5. For apure specis two indepndent, intesive proerties constrains the stae of the sytem. If we specify ths varibles, al othr prortis ar fixd. Thus, if we old T nd P constant h canot change, i.e, 0,?????????PTvh pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 7 5.6 Expansion f the nthalpy term in the numerator esults in ss TPvsTTh ??????????????????? ss TPvTh ?????????????????? Using aMaxwel relation Ps vsvTh ????????????????? PPs vTTsvTh ?????????????????????????? We can show that TcTs PP????????? (use thermodynamic web) ?????? ??????????? 3221 vabvabvRTRvTP (diferntiate van der Wals EOS) Therfore, ?????? ??????????????? ??????????? vbvRTabvvcvabvabvRTRTvcTh PPs 12223 pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 8 5.7 :TPh???????? vPsTPvsTPh TTT ????????????????????????????? ? ?2''1 PCPBPRTvPs PT ?????????????????????? ? ? vvvPCPBPRTPhT ???????????????? 2''1 0?????????TPh :sPh???????? vPvsTPh ss ???????????????????? ? ?2''1 PCPBPRTPhs ??????????? :PTh???????? PPcTh????????? (Definiton f cP) : sTh???????? sss TPvTPvsTTh ???????????????????????????? ? ? 2''1 PCPBRTcvTTcsPTsTP PPPTPs ?????????????????????????????????????? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 9 ? ?? ?? ?222 ''1 ''1''11 PCPBcPCPBRTPvcTh Ps ???????????????? PscTh????????? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 10 5.8 (a) A sketch of the proces is provide below ?mwel insulated ?s = 0T1 P1 T2 P2 The diagram shows an ifinitesimal mount of mas being placed on top f the piston f apiston-cylinder asembly. Th increse i as cus the s in the istn to b cmpresd. Because th ms increase ifiitsimaly nd the piston is wel isulated, the rsion is rvrsibl and aibati. For arevrsible, aibatic rces th chang in tropy is zer. Therfore, the compresin chngs th intrnl enrgy of te gs t costat entropy as the prsur incras. (b) To detrmine the sign of the rlation, consider an ergy balnce on the piston. Neglcting ptntial d kintic ergy chges, we bti WQU??? Since the proces is adibatic, the nergy balnce rduces to WU?? As the presure increase on the piston, the piston compress. Positve work is done on the sytm; hnc, th hng i itrnal ergy is psitv. W have justifd the stamt 0?????????sPu pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 1 5.9 (a) By definiton: PTvv??????????1 and TPvv???????????1 Dividing, we gt: TPTP vTvPvTv ???????????????????????????? ?????????? wher derivative inversion was used. Aplying the cylic rule: vTP PTvTv ???????????????????? ??????1 Hence, vTP??????????? (b) If we rite T = T(v,P), we gt: dPPTdvvTdT vP?????????????? ???? (1) From Equations 5.3 and 5.36 dPTvdTTcdvTPdTcds PPvv ???????????????? ???? We can solve for dT to get: pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 12 dPTvccTdvTPccTdT vPvvP ???????????????? ???? (2) For Equations 1 and 2 to be qual, each term on the lft hand side must be qual. Hence, vvPP TPccTvT ?????????????? ???? or PPvvP TvTTvTPTcc ????????????????????? ???????? wher the rsult from part awas used. Aplying the dfiniton f the thermal expansion coficnt: ?????? 2TvTvTPTcc PvvP ??????????????? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 13 5.10 We ned at for acetone, benzen, and coper. A table of values for the molar volume, thermal xpasion cefint ad isothrml mrsibilty r tken frm Tabl 4.: Specis ???????mol 1036v ??1-3K 10?? ??1-10Pa ?? Acetone 73. 1.49 12.7 Bz 86.9 .2 9.4 Coper 7.1 0.486 0.1 We can calulate the difernce in heat capcity use the rsult from Problem 5.9b: ??2vTccvP?? or ?? ??? ??? ????????? ??????? ????????? ? ?? KmolJ 6.37Pa 107.12 K 1049.1K 293mol 103.7 1-10 21-336vpcc Specis ????????KmolJ vpcc ???????KmolJ pc % difernce Acetone 37.6 125.6 30% Bz 41. 3. 1 Coper 0.5 2.6 2% We can compare values to that of the at capcity given i Apendix A2.. While we often asume that c P nd cv ar equl fr condensed hase, this may ot be the case. pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 14 5.1 We know from Equations 4.71 and 4.72 PTvv?????????1? and TPvv??????????1? Maxwel relation: vTTPvs ????????????????? Employing the cylic rule gives PTv TvvPTP ?????????????????????????? whic an be rwriten as TPvT vvTvvTPvs ??????????????????????????????????? 11 Therfore, ???????????Tvs Maxwel Relation: PTTvPs ?????????????????? From Equation 4.71: vTv P?????????? Therfore, vPs T??????????? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 15 5.12 (a) An isochor n aMolier diagram can be rpresnted mathematicaly as vsh???????? This can be rwriten: vvv sPTsPvsTsh ????????????????????????????? Employing the apropriate Maxwel relation ad cylic rule rsults in Tvv vssTvTsh ?????????????????????????? We know vvcTsT????????? and vTTPvs ????????????????? For an ideal gas: vRTPvs vT ?????????????????? Therfore, ?????????????????? vvv cRTRcTTsh 1 (b) In Part (a), we found vvv TPcTTsh ?????????????????? For avn der Wals gas: pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 16 bvRTPv?????????? Therfore, ????????????????? bvvcRTTsh vv pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 17 5.13 (a) The cylic rule can be mployed to give TPs PssTPT ?????????????????????????? Substiution f Equations 5.19 and 5.31 yields PPs TvcTPT ????????????????? For an ideal gas: PRTv P????????? Therfore, PPs cvcPRTPT ?????????? 1 (b) Separtion f varibles provides PcRT??? Integration provides PcRPT ????????????? 1212lnln whic an be rwriten as PcRPT???????1212 The ideal gas law is now employed pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 18 PcRPvPv ???????1212 111212 vPvP PP cRcR ??????????????? wher kcccRccR PvPPP 11 ????? If we raise both sides of the quation by apower of k, we find kkvPvP12? .constPv k?? (c) In Part (a), we found PPs TvcTPT ????????????????? Using the drivative inversion rule, we find for the van der Wals equation ????2332bvaRTvbvvTv P ???????????? Therfore, ???? 23321 bvaRTv bvTvcPTPs ???????????? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 19 5.14 The dvelopment of Equation 5.48 is anlogus to the dvelopment of Equation E5.3D. We want o knw h the t capcity ches wit prsur, s cosider TPc???????? whic an be rwriten as PTTPTP PhTThPc ?????? ????????????????? ??????????????????? Consider the TPh????????term: v TvTvPsTPvsTPh PTTT ???????????????????????????????????????? Substiution f this expresion back into the quation for TPc????????results in PPTP vTvTTc ?????? ?????? ????????????????????? PPPTP TvTvTTvTc ?????????????????????????????????????? 22 PTP TvTc ?????????????????? 22 Therfore, ?? ?????? ?????????? realidealrealPidealP PP PccP dTvTc 22 and ? ?????? ??????????realidealPP PidealPrealP dTvTcc 22 pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 20 5.1 In order to slve this problem we ned to relate the change in etropy from 10 to 12 bar to the chag in mlar olume (fr hic w hav complt dta). First, we can rewrite the chng in entropy as ?? ??????????? bar 12bar 1012 dPPssss T Aplying aMaxwel relation, we can relate the above quation to the change in molar volume: ?? ????????????????????? bar 12 bar 101bar 12bar 1012 dPTvsdPPsss T As 10 bar: ????????????????????????? ?Kkgm 1060.5 34 PPTvTv At 12 bar: ????????????????????????? ?Kkgm 1080.4 34 PPTvTv To integrate the above ntropy equation, we ned an expresion that relates PTv????????to presure. Thus, we il fit aline to the dat. We obtain ??????????????? ??????????????????? ?? Kkgm106.9PaKkgm 100.4 34310 PTvP Now integrate the quation to find the ntropy: ? ?? ? ????????????????????????? ?? KkgkJ 392.5KkgkJ 104.4960.5106.9100.4Pa 101.2Pa 100.1 41012 66 dPPss pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 21 5.16 A schematic of the proces folws: Propane inv1 = 60 cm3/ol T1= 350 oC Turbine P2 = 1 atmwsPropaneout We also know the ideal gas heat capcity from Table A.2.1: 263 10824.10785.2213. TTRcP ?? ????? Since this proces is ientropic (?s=0), we can construct apth such tat he sum of ?s i zero. (a) T, vas indepndent varibles Chosing T a vas th idepndnt varibles, (and changi T under ideal gas conditons), we get: Temperature volume Ideal Gs step 1step 2 v1,T1?s=0v2,T ?s?s2 or in mathematical terms: 0??????????????????? dvvsdTTsds Tv Howevr, From Equation 5.3: pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 2 ds?cvTd??P?T????????vd To get ?s1 P?RTv?bav 2 so ?P?T????????v?Rv?b and ?s1?d?s??P?T????????vdv 1v2? ?Rv?bdv?Rln1v2? v2?bv1b?????????? or, using the ideal gas law, e can put ?s1 in terms of T2: ?s 1?RlnRT2P2?bv1?b??????? ??????? For step 2 ? ? ?? ??????? 21 2K 15.623 2632 10824.10785.2213.0TT Tv dTT TRdTcs Now ad both steps ? ? ? ?? ?22623212221 K 15.623210824.K 15.62310785.215.63ln213.0ln 0 ???????????????????????? ?????? ?? TTTbvbPRTsss Substiute K 15.623 1?T ? ?/molc 6031?v atm12P ????????? Kmolatmc 06.823R pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 23 and solve for T2: ??K 3.482?T (b) T, P as indepndent varibles Chosing T and P as the indepndent varibles, (and changi T under ideal gas conditons), we get: Temperature Pressure Ideal Gs step 1step 2 P1,T?s=0P2,T ?s1?s2 Mathematicaly, the ntropy is defined as folws 0??????????????????? dPPsdTTsds TP Using the apropriate rlationships, the xpresion can be rwriten as 0??????????? dPTvdTTcdsP For the van der Wals equation ???? ?????? ??????????????????? 322vabvRTbvRTvP Therfore, pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 24 ???? 022121 32 ??????? ????????????? ?? dPvabvRTbvRdTTcs PPTP We can?t integrate the scond term of the xpresion as it is, o we ned to rewrite dP in terms of th othr vribls. Fr th van der Wals quati t cnstant mpratur: ??dvbvRTvadP ????????? 232 Substiuting this into the ntropy expresion, we gt ??010824.10785.2213. 2121 263 ????????? ?? ?? dvbvRdTT Ts vvTT Upon substiuting ???????????????? ??? Kmolatmc 06.82molc 91b atm) 1atidealy acts (gs cm 60K 15.62333222 311RPRTvvT we obtain oe quation for ne unkown. Solving, we gt K 3.482?T pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 25 5.17 (a) Atractive forces dominate. If we xamine the xpresion for z, we se that t any absolute tempertur an presur, .1?z Th itrolcular tractins caus t molr volume t dviat negtively from ideality and are strnger thn the rpulsive interactins. (b) Energy balnce: qhh??12 Alternative 1: path trough ideal gas tae Bcuse th gs i not ideal nr thes conditons, we have to creat ahypothetical path tat oncts te inital finl staes trugh tre stps. On hypthticl at is hown below: P [bar] T [K] P,T1step 1 step 3 step 2ideal gas30 q = ?h 50 0 50 P,T2 ?h 1 ?h2 ?h3 Chosing T and P as the indepndent proerties: dPPhdTThdh TP ?????????????????? or using Equation 5.46 dPvTvTdTcdh PP ?????? ???????????? The given EOS can be rwriten as ???????? 2/11aTPRv pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 26 Taking the drivative gives: 5.05.0??????????? aRTPRTvP so ? ?dPaRTdTcdhP 5.05.0?? For step 1 ? ? ???????????? molJ 255.05.00bar 50 5.015.011 PaRTdPaRTh For step 2 ? ? ????????????? ?? molJ 7961875.01002.358.3K 50 K 30 5.032 dTTTRh For step 3: ? ? ???????????? molJ 325.05.0bar 50 0 5.025.023 PaRTdPaRTh Finaly suming up the thre terms, we gt, ????????????? molJ 78321 hhhq Alternative 2: real heat capcity For rel gas realPch?? From Equation 5.48: ? ?????????? real ideakPP PidealPrealP dTvTcc 22 For the given EOS pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 27 ???????? 2/11aTPRv Therfore, 5.122 25.0??????????? aRTTv P and ??? ?5.01/2bar 50bar 0 5.022 K 875.025. ??? ???????????? ?? RTdPaRTdPTvT real ideakrealideak PPPP P We can combine this result with te xpresion for realPc nd find the nthalpy change. ? ?dTTTRh? ???????K 50K 30 5.03875.01002.358.3 ????????? molJ 78hq The answers i equivalent o that calulated in alternative 1 pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 28 5.18 (a) Clculate the tmperature of the gas using the van der Wals equation. The van der Wals eqtion is givn by: 2vabvRTP?? First, we ned to find the molar volume and presure of stae 1. ??? ???? ??? ? ????????? mol 016.mol 250 4.0 1.0 3211 nAlnVv ??? ??? ?? ??Pa 1008.1Pa 1001325.m 1.0 sm 81.9kg 100 65221 ?????????? ?????????atmPAmgP Substiuting thes equations into the van der Wals equation above gives ?? 233353 16 mol 016. molJ .50mol 104mol 016. KmolJ 314.8Pa 1008.1 ?????? ???????????????????????????? ?????? ????????? ?T K 5.2971?T Since the proces is iothermal, the folwing path can be used to calulate internal enrgy: v Tv1,T1 v2,T2= T1?u ?s Thus, we can write the change in iternal enrgy as: pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 29 dvvudvvudTTudu TTv ??????????????????????????? Using Equation 5.40 ? ? ????? ???????????21vv vdvPTPTu For the van der Wals EOS: 2vabvRTP?? so bvRTPv?????????? Therfore, ???2 12vvdvau We can sume the gas in stae 2 is an ideal gas ince the final presure is atmospheric. Therfore, we calulate 2v, ???????? mol 024. 3222PRTv and ????????????????? molJ 5.3104molJ 5.0024.016. 23dvvu or ??kJ 1.76??U pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 30 (b) From the dfiniton f entropy: sursyunivs ????? First, let?s olve for sy? using the thermodynamic web. dvvsdTTsds Tvys ?????????????????? Since the proces is iothermal, dvvsds Tys ????????? ???????????? 21vvvsy dTP Again, for the van der Wals equation, bvRTPv?????????? Substiution f this expresion ito the quation for entropy ields ? ???21vvsy dvbR ???????????????? ?????????? ? KmolJ 17.4mol 104KmolJ 314.8024.016. 35dvvsys KJ 5.1042????????syS The change in etropy of the suroundigs wil be calulated as folws sursursurTQ?? wher pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 31 QQsur?? (Q is the at ransfer for the sytem) Aplication f the first law provides WUQ??? We know the change in iternal enrgy from part a, so let?s calulate W using ???2 1vvPdvnW Since the xternal presure is constant, ??? ? ??? ? ?????? ???????????????? mol 016.mol 024.Pa 1001325.mol 250 335W ??J 61403??W Now calulate hat ransfer. ???? ?? ??J 1039.1J 61403J 7610 6????Q Therfore, ???? ???????????? KJ 4672K 5.297J 1039.16surS and the ntropy change of the univers is: ?????????????????????? KJ 5.6370KJ 4672KJ 5.1042univS pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 32 5.19 First, calulate the inital nd final presure of the sytem. ?? ??? ???? ??? ??Pa 1092.4m05. /s81.9kg 200Pa1010 6225 ?????iP ?? ??? ???? ??? ??Pa 1089.6m05. /s81.9kg 300Pa1010 6225 ?????fP To find the final temperature, we can perform an ergy balnce. Since the sytem is wel-insulate, al of th work don by dig the third block is covrted ito intrnal nergy. The ergy blnce is wu?? To find the work, we ned the inital nd final molar volumes, whic we can obtain from the give EOS: ? ?/mol 1037.8 34??? iv ? ? ? ?/mol 103.22511089.6314.8 35-6 ??????????? fff TTv Now, calulate the work ? ?? ?? ? ?????????? ?????????????????? ?45-66 1037.8103.22511089.6314.8Pa 1089.6 ffiff TTvvPw We also ned to find an expresion for the change in iternal enrgy with only one varible: Tf. To find th chage i itrnal ergy, w crat ahypothtical pat sw blow: v T vi,Ti v f,Tf step 1 step 3step 2ideal gas 50 Tf ?u = -Pf (vf -vi) pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 3 For step 1, we calulate the change in iternal enrgy as folws dvPTPTdvvuu lowilowi PRTvv vPRTvv T ?? ?? ?????? ?????????????????? //1 ?????? ?????????????????????? bvbPRTaTaRTbvdvaTaRTu ilowi iiPRTvv iilowi /ln22/ 221 Similarly, for step 3: dvPTPTdvvuu f lowf low vPRTv vvPRTv T ?? ?? ?????? ?????????????????? //3 ?????? ?????? ??????????????? ? bPRTbvaTaRTbvdvaTaRTu lowffffvPRTv fff low /ln22/ 223 Insert he xpresion for the final molar volume into the quation for3u?: ??? ?? ?? ?? ????? ?????? bPRTTTaTaRTu lowfffff //2511089.6 314.8ln 6223 Since the presure is low (molar volume is big) during the scond step, we can use the ideal heat capity to callat the change in itrnal enry. ? ??? ?? ????? fifi TTTTv dTRdTcu K 50K 502 05.2 ? ? ? ?222 50025.5068.1 ????? ff TTu If we st he sum of the thre steps in the internal enrgy calulation equal to the work and chos an rbitray valu for P low, 10 Pa for xmple, we obti tin ith e unkw: pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 34 ?? ? ? ? ???? ?? ?? ?? ?? ? ?????????? ?????????????? ??????? ???? ?????????????? ?45- 66 622 2222 1037.8103.22511089.6314.8Pa 1089.6 //2511089.6 314.8ln 50025.5068.1/ln ff lowfffff ffilowiii TT bPRTTTaTaRT TTbvbPRTaTaRT Solving for Tf we gt K 2.536?fT The piston-cylinder asembly is wel-insulated, so syunivs??? Since the gas in the cylinder is not ideal, we must construct ahypothetical path, such as one show blow, to alulat th chag in tropy durig this prces. P T Pi,Ti Pf,Tfstep 1 step 3 step 2ideal gas50 536Plow 4.96.9 For steps 1 and 3 ?? ?????????????????????????? lowilowi PP PPPT dTvdPss1 pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 35 ?? ?????????????????????????? flowflow PP PPPT dTvdPss3 We can diferntiate the given EOS as required: ? ??? ? ??? ?????????????????????? ilowiiiPP i ii PTaTaRTdPPTaTaRTslowi ln22 221 ? ??? ? ??? ?????????????????????? lowffffP f ff PTaTaRTdPPTaTaRTsf low ln22 223 For step 2 ??? ??????????????????? fififi TTTTPTTP dTTdTcdTTss 05.202 ? ?ifif TTTTs ?????????? 05.ln202 Sum al of the steps to btain the change in etropy for the ntire proces 321 sssss ysuniv ????????? ? ??? ? ? ? ??? ????????????????????????????? lowffffififilowiiiuniv PTaTaRTTTTTPTaTaRTs ln205.ln20ln2 22 Arbitraily chose P low (try 10 Pa), substiute numerical values, and evalute: ?? ????????????? ????????? ????????? KJ 76.0KmolJ 38.0mol 2 KmolJ 38.0 univunivSs pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 36 5.20 A schematic of the proces is given by: V = 1 LT = 50 Kwel insulated VacumV = 1 LnCO=1 mole Stae i V = 2 LT = ?nCO=1 mole Stae f (a) The folwing equation was devloped in Chapter 5: dv TPTcc vv videalvrealv ideal? ?????? ?????????? 22 For the van der Wals EOS 0 22?????????TP Therfore, idealvrealvcc? From Apendix A.2: ?? ??????????????? ???? ? KmolJ 0.250310501057.376. 24 RRcrealv (b) As the diaphragm ruptres, the total internal enrgy of the sytem reains constant. Because the volum vilble to th molculs icrs, th averag distanc btwe mlecules lso increase. Du t te increase in itermoleculr distnces, the potential nergis inrase. Since th totl internal enrgy dos ot chang, th kinetic rgy must cmpesat by decrsing. Terfr, th tmprature, whi is manifestaion f oleclar kintic nerg, rease. pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 37 (c) Beause the at capcity is ideal under thes cirumstances we can creat a two-step hypothtical pth to nect h iital nd final staes. O hypothtil pth is hown below: v Tvi,Ti vf,Tfstep 2 step 1 50Tf ?u2 ?s2 ?u1, ?s1 For the first ection f the path, we have ?? ??? fifi TTidealvTTrealv dTcdTcu1 ? ?? ??? 4.10574.257375.191032. 3101057.376.2231K 50 241 ?????? ?????? ????? ? ?? fffT TTTu dTTTRufi For the scond step, we can use the folwing equation ???????????fivvTdvvuu2 If we aply Equation 5.40, we can rewrite the above quation as ? ?????? ???????????fivv vdvPTPTu2 For the van der Wals EOS, 2vabvRTP?? , pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 38 bvRTPv?????????? Therfore, ????????????????? ?? ???? molJ7.302.01. 202.01.1 fifi vvvv dvvadvPbvRTu Now set he sum of the two internal enrgies qual to zero and solve for Tf: ? ? 07.34.10574.257375.191032. 23 21 ?????????? ? fff TTTuu K 497?fT (d) Since the sytem is wel-insulated syunivs??? To slve for the change in etropy use the folwing devlopment: dvvsdTTsds Tvys ?????????????????? Using the thermodynamic web, the folwing relationships can be proven TcTsv v????????? vTTPvs ????????????????? For the van der Wals EOS ??bvRTPv?????????? Now e can combine verything and calulate the change in etropy pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 39 ???? ???? 02.01.K 497K 50 dvbvRdTTcs vys ? ? ? ? ??????????? ?????? ????????? ????? ?? ??KmolJ 80.5 1095.33101057.376.2 02.01. 5K 497K 50 34syunivsys vdvdTTTR pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 40 5.21 A schematic of the proces is given by: V = 0.1 m3T = 30 Kwel insulated VacumnA=40 moles Stae i T = ?Stae f V = 0.1 m3 nA=40 molesV = 0.2 m3 Energy balnce: 0??u Because the gas i not ideal under thes conditons, we have to creat ahypothetical path tat oncts t inital finl stas trugh tre stps. On hypthticl at is hown below: v [m3/ol] T [K]vi,Ti vf,Tf step 1step 3 step 2ideal gas 30Tf ?u 0.2/400.1/40 For the first ection f the path, we have ????????????vv T i dvvuu1 If we aply Equation 5.40, we can rewrite the above quation as ??? ?????? ??????????v v vi dvPTPTu1 pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 41 For the van der Wals EOS 2vTabvRTPv ??????????? Therfore, ?????????????? ????? ?? ???????? ?? molJ120244 105.2105.2 21 vv ivv ii dvvTadvPTvabvRTu Similarly for step 3: ???????????????? ????? ?? ?? ???????? KmolJ1680244 105 2105 23 fvv fvv TdvvTadvPTvabvRTu ff For step 2, the molar volume is infiite, so we can use the ideal heat capcity given i the prblm stant callat the chang in itral nrgy: ? ?K 30232 ???fTRu If we st sum of the changes in iternal enrgy for each step, we obtain oe quation for ne unkon: ? ? 01680K 30 KmolJ314.823molJ 120321 ?????????? ???????????????????? ff TTuuu Solve for Tf: K 6.21?fT pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 42 5.2 A schematic of the proces is hown below: Ethane3 MPa; 50K Initaly: vcumTsur = 293 K (a) Consider the tank as the sytem. Since kinetic and potential enrgy efcts are ngliible, the pe sytm, ustedy-sta nrgy balc (Equti 2.47) is ?? ?????????? out soutoutinininsy WQhnhdtdU ???? The proces is adibatic and o shaft work is done. Furthermore, ther is one inlet stream and o outlt stram. The nergy balnce rduces t ininsyhdtdU???????? Integration must now be prformed ??? t ininUU dthd021 ? ininintinin hnnhdthunun )(120122 ??????? Since the tank is initaly a vcum, n1=0, and the rlation reduces to: inhu?2 pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 43 As i typical for problems involing the thermodynamic web, this problem can be solved in sevral osible ways. To ilustrate w prsnt wo lternativs belw: Alternative 1: path trough ideal gas tae Substiuting the dfinitn f nthlpy: inininvPuu??2 or ? ?? ? ininin vPuTu ?? K 50 MPa, 3at MPa, 3at2 (1) From the quation f stae: ? ? ?? ? ?? ? ???????????????? ?????????? ? molJ 80,3Pa 103108.21K 52KmolJ 314.8'1 68PBRTvPinin (2) The change in iternal enrgy can be found from the folwing path: Plow Tstep 1 step 3step 2ideal gas50 K T2?u1 3 MPa ?u3 ?u2 P For steps 1 and 3, we ned to detrmine how the internal enrgy changes with presure at cnstant emperatur: Frm th fudantal prorty rltio and t aproriat Mxwel reltio: TPTTT PvTvTPvPsPu ????????????????????????????????????????????? From the quation f stae ? ? RTBPRTPB'PPRTPu 'T ????????????????????? 21 pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 4 So fr step 1: [J/mol] 3490 '0'1 ???????????????? ? inPin PinT PRTBRTdPBdPPuu (3) and for step 3: TPRTBRTdPBdPPuuP PT 7.0220 '20'3 ???????????????? ? (4) For step 2 ??dTRcdTTPvThdTTuu TPT PPT P ??? ???????? ???????????????????????????? 5050502 or ? ?? ? ?? ?????21K 50 2632 1056.1025.1913.TT dTTTRu (5) Substiuting Equations 2, 3, 4, and 5 into 1 and solving for T gives: K 522?T Alternative 2: real heat capcity Startig with: inhu?2 The above quation is equivalent o inhvPh??22 22 vPhhin? To calulate the nthalpy difernce, we can use the ral heat capcity dPTvTcc PP PidealPrealP ideal? ?????? ?????????? 22 For the truncated viral equation, pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 45 022?????????PTv Therfore, idealPrealPcc? Now, e can calulate the change in ethalpy and equate it o the flow ork term. ? ? ?21 K 50 2TTidealP vPdTc ? ? ? ??? ?? ???????2 1K 50 2222263 '11056.1025.1913.TT PBRTvPdTTTR Integrate and solve for T2: K 522?T (b) In order to slve the problem, we il ned to find the final presure. To d so, first we ned to calulat the molar vlu. Using th ifrmatio from Prt (a) nd the truncated viral eqtion to d this ? ? ?? ? ?? ?Pa 103108.21 Pa 103 K 52KmolJ 314.8'1 686 ?????????? ?????????? ?PBPRTv ???????mol 014. 3v This quantiy wil not change as the tank cols, o nw e can calulate the final presure. ??? ?2832 108.21K 293KmolJ 314.8 mol 014. PP ?????????? ??????? ?????? ?????? Solve for 2P: pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 46 Pa 106.162??P The ntropy change of the univers can be xpresd as folws: sursyuniv SSS ????? To slve for the change in etropy of the sytem start with te folwing relationship: dPPsdTTsds TPys ?????????????????? Alternative 1: path trough ideal gas tae Usig th proer elatinsips, th bove quation can be rwriten as dPTvdTTcds PPys ?????????? We can then use the folwing solution path: Plow Tstep 1 step 3step 2ideal gas50 K T2?s1 3 MPa ?s3 ?s2 P 1.6 MPa Chosing avlue of 1 Pa for Plow, for step 1: ? ??? ????????????? Pa 1 MPa 6.1 'Pa 1MPa 6.11 1dPBRdPTvs P For step 3, ? ??? ????????????? MPa 3Pa 1 'MPa 3Pa 11 1dPBPRdPTvs P pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 47 For step 2: ?? ?????? ??????? ??K 293 K 52 63K 293K 522 1056.1025.1913. dTTTRdTTcs P Ading togethr steps 1, 2 and 3: ?????????? KmolJ9.46sy __________________________ Alternative 2: real heat capcity Usig th pror ltionshis, the above quation can be rwriten as dP TvdTTcdsrealPys ?????????? For the truncated viral equation ???????????????? '1BPRTv P Now, substiute the proer values into the xpresion for entropy and integrate: ?? ???? ?????????????? ????? Pa 106.1Pa 103K 293K 52 63 6^ '11056.1025.1913. dPBPRdTTTRsys ?????????? KmolJ9.46sy __________________________ In order to calulate the change in etropy of the suroundigs, first perform an ergy balnce. qu?? Rewrite the above quation as folws ??qPvh???? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 48 Since the ral heat capcity is equal to ideal heat capcity and the molar volume does not change, w obtain te folwing equation ? ?? ??? fiTT ifidealP qPPvdTc ? ? ? ??? ? ?? ????????? ???????????K293K 52 663263 Pa 103-Pa 106.1mol 014.1056.1025.1913.fiTT qdTTTR ????????molJ 15845q Therfore, ???????molJ 15845surq and ????????? KmolJ 08.54sur Before combinig the two entropies to btain the ntropy change of the univers, find the numbr f oles in t tak. ?? mol 7.5mol 014. m 05. 33????????n Now, calulate the ntropy change of the univers. ? ? ?????? ?????????????????? KmolJ 9.46KmolJ08.54mol 7.5univS ???????? KJ 54univS pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 49 5.23 First, focus on the numerator f the scond term of the xpresion given i the problem staemnt. We ca rwrit the numratr as flws: ? ?? ?idealvTidealvTidealvTvTidealvTvT rrrrrrrrrrrr uuuuuu ???? ????? ,,,,,, For an ideal gas, we know 0,, ????idealvTidealvT rrrr uu Therfore, idealvTvTidealvTvT rrrrrrrr uuuu ????? ,,,, Substiute this relationship into the xpresion given i the problem staemnt: cidealvTvTcidealvTvTcdepvT RuuRuuRu rrrrrrrrrr ??????? ,,,,, Now, e ned to find an expresion for idealvTvT rrrr uu ???,, . Note that he tmperature is constant. Equation 5.41 reduces to the folwing at constant emperature: dvPTPTdu vT ?????? ?????????? The presure can be writen as vzRTP? and substiuted into the xpresion for the diferntial internal enrgy dvTzvRTdvvzRTvRTTzvRTTdu vvvT ?????? ??????????????? ??????? ?????????? 2 Aplying the Principle of Corespondig Staes pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 50 rvrrrcT dvTzvTRdu rr ?????? ?????????2 If we integrate the above xpresion, we obtain ?? ???? ?? ?????? ?????????? r rvrrrr vv rvrrrvv cidealTvTcT dvTzvTRuuRdu 2, , Therfore, ????? ?????? ????????????? r rrrrrrrrrrr vv rvrrrcidealvTvTcidealvTvTcdepvT dvTzvTRuuRuuRu 2,,,,, pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 51 5.24 We write nthalpy in terms of the indepndent varibles T and v: dvvhdTThdh Tv ?????????????????? using the fundamental proerty relation: vdPTdsdh?? At constant emperature, we gt: dv vPvTPTdh TvT ?????? ?????????????????? For the Redlich-Kwong EOS ??bvTabvRTP v ???????????? 2/321 ?? ?? ??22/12/12 bvTabvvTabvRTvPT ??????????????? Therfore, ?? ?? ??dvbvTabvTabvRTvbvRTdhT ?????? ??????? 22/12/1223 To find the nthalpy departure function, we can itegrate as folws ?? ?? ???? ???? ?????? ??????? vvvvTdep dvbvTabvTabvRTvbvRTdhh 22/12/1223 Since tmperature is constant, we obtain ??bvTabvvbTabvRTbhdep ????????????? 2/12/1ln23 To calulate the ntropy departure we ned to be careful. From Equation 5.64, we have: ? ?? ?gas ideal0,gas ideal,gas ideal0,,gas ideal,, ?? ????? PTPTPTPTPTPT ssssss pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 52 Howevr, since we have a P explict equation f stae, we ant o put his equation i terms of v. Let?s lok at onvrting ch stae. Th first wo sts ar stright -forward vTPTss ,,? and gas ideal,gas ideal0, ????vTPT ss For the third stae, howevr, we must realize that he ideal gas volume v? at he T and P of the sytm is ifernt frm the vole of th sytem, v. In order t s this w ca compare t equation f sta for an idal gas t T and P 'vRTP? to areal gas t T and P ??bvTabvRTP ??? The volume calulated by the ideal gas equation, v?, is clearly difernt from the volume, v, calulated by the Rlic-Kwon qution. Hece: ?????? ???? gas ideal,gas ideal,gas ideal,gas ideal,gas ideal, '' vTvTvTvTPT sssss Thus, ? ?? ? ?????? ??????? ???? gas ideal,gas ideal,gas ideal,gas ideal,gas ideal,,gas ideal,, ' vTvTvTvTvTvTPTPT ssssssss Using aMaxwel relation: vTTPdvds ??????????????? Therfore, dvTPds vT????????? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 53 For the Redlich-Kwong EOS ??bvTabvRTPv ???????????? 2/321 so ? ? ??????? ?????? ???? vvvTvT dvbvTabvRss 2/3gas ideal,, 21 For an ideal gas vRTPv????????? so ? ?????? ??????? vvvTvT dvvRss gas ideal,gas ideal, Finaly: PvRTRvvRvdvRss vvTvT lnln'gas ideal,gas ideal, '' ???? ? Integrating and ading togethr the thre terms gives: ?? PvRTRbvvbTavbvRsdep lnln2ln 2/3 ???????????? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 54 5.2 Calculate the rduced temperature and presure: ????34.0bar 48.20K 3.647???wPTcc (Table A.1.2) ????04.1K 647.3 15.673 36.1bar 20.48bar30?? ??rrTP By double interpolation f dat from Tables C.3 and C.4 921.)0(, ???????????cdepPTRh rr 459.1)1(, ???????????cdepPTRhrr From Tables C.5 and C.6: 29.)0(, ???????????RsdepPTrr 405.1)1(, ???????????RsdepPTrr Now e can calulate the dparture functions ???????? ????????????????? )1(,)0(, cdepPTcdepPTcdep RhwRhRTh rrrr ?? ? ?? ????????????????? ????????? molJ 18421459.134.0921.3.647KmolJ 314.8deph ???????? ????????????????? )1(,)0(, RswRsRs depPTdepPTdep rrrr ? ?? ?????????????????? ????????? KmolJ 07.23405.134.029.KmolJ 314.8deps pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 5 To use the steam tables for calulating the dparture functions, we can use the folwing relatinsips. idealPTPTdep hhh ,,??? ideal PTPTdep sss ,,??? From the steam tables ???????kgkJ 0.215,PTh and ???????? KkgkJ 4728.,PTs We ned to calulate the ideal enthalpies and entropies using the steam tables? refrence stae. ? ????? K 673.15K 273.16, C.01? dTchh idealpvapidealPT We can get ???????? molkJ 1.45vaph from the steam tables and heat capcity dat from Table A.2.. Using this information, we btain ? ?????? ?????????? ??????????????? ?K 673.15 K 273.16 253, 101.01045.147.3KmolkJ 08314.molkJ 1.45 dTTThidealPT ???????molkJ 14.59,idealPTh Now, calulate the ideal entropy. ? ? ?????????? ? 12K 673.15K 273.16, lnC.01? PRdTTcss idealpvapidealPT From the steam tables: ? ? ? ???????? KmolkJ 165.0C? 01.vaps Substiute values into the ntropy expresion: pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 56 ?????? ????????????? ?????????? ????????? ? ? 0613.30ln1012.01045.147.3KmolkJ 08314. 165.0 K 673.15K 273.16 353, dTTTsidealPT ???????? KmolJ 107,idealPTs Now, calulate the dparture functions: ? ?? ? ??????????????????????? molkJ 4.20molkJ 14.59kg/mol 0180148.kgkJ 0.215deph ? ?? ? ?????????????????????????? KmolkJ 0264.KmolkJ 107.kg/mol 0180148.KkgkJ 4728.deps Table of Results Genralized Tbls Steam Tables Percnt Difernce (Basd o stam tabls) ???????molkJ deph -18.62 -20.4 9. ????????KmolkJ deps -0.231 -0.264 12.5 pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 57 5.26 Stae 1 is at 30 K and 30 bar. Stae 2 is at 40 K and 50 bar. The rduced temperature and prsures re ???? 982.0K 305.4 30 61.0bar 74.48bar30,1,1 ?? ??rrTP ????31.K 305.4 40 026.1bar 74.48bar50,2,2 ?? ??rrTP and 09.?? By double interpolation f dat in Tables C.3 and C.4 825.0)0(, ,1,1 ???????????cdepPTRhrr 79.0)1(,,1,1 ???????????cdepPTRhrr 71.0)0(, ,2,2 ???????????cdepPTRhrr 196.0)1(,,2,2 ???????????cdepPTRhrr Therfore, ? ?904.79.009.825.0,1,1 ???????????????cdepPTRhrr ? ?730.0196.009.71.0 ,2,2 ???????????????cdepPTRhrr The ideal enthalpy change from 30 K to 40 K can be calulated using ideal cP dat from Table A.2.1. RdTTTRhidealTT 39.711056.1025.1913. 2K 40K 30 6321 ??????? ? ??? The total entropy change is pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 58 depPTidealTTdepPT rrrr hhhh ,2,221,1,1 ???????? ? ??? ?CC TRh 730.039.7904. ????? ? ? ? ?? ?K 4.3057.0K 39.71K 4.305904.KmolJ314.8 ???????? ?????????h ???????? molJ 2.6406h Using the dat in Table C.5 and C.6 ? ?67.0756.009.601.,1,1 ???????????????RsdepPTrr ? ?416.024.009.394.0 ,2,2 ???????????????RsdepPTrr Substiuting heat capcity dat into Equation 3.62, we gt ?????? ????????????? ? ?? bar 30bar 50ln1056.1025.1913.K 40K 30 263 dTT TRsideal Rsideal 542.1?? Therfore, ? ?416.0542.167.0,2,2,1,1 ??????????? Rssss depPTidealdepPT rrrr ????????? KmolJ 98.14s pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 59 5.27 The turbine is ientropic. Therfore, we know the folwing 0 ,2,2,1,1 ????????? depPTidealdepPT rrrr ssss Using the van der Wals EOS, we can fid P1,r whic leaves one unkown i the above equation: T2. ? ? 232353331 molc 60molcat 109molc 19molc 60 K 15.623Kmolatmc 06.82 ?????? ?????? ??????????????? ????????????? ?????? ?????????P ?? ??bar 19.76at 19.751 ??P Calculate rduced temperature and presures using dat from Table A.1. ????8.1bar 4.2bar19.76,1 ??rP ????024.bar 2.4bar013.,2 ??rP 68.1K 370. 3.156,1 ??rT Also, 152.0?? From Tables C.5 and C.6: ? ?34.0102.152.0327.0,1,1 ???????????????RsdepPTrr Substiuting heat capcity dat into Equation 3.62, we gt ?????? ????????????? ? ?? atm 5.197at 1ln10824.10785.2213.2K 23.156 263 dTT TRs Tideal Therfore, pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 60 sRsdTT TR depPTT rr ?????????? ????????????? ?? ,2,22K 23.156 263 32.410824.10785.2213.34.0 We can solve this using a gues-and-check method K 602?T: 62.1,2?rT ????????? KmolJ 84.3s K 4502?T: 2.1,2?rT ????????? KmolJ 7.0s K 6.42?T : 21.,2?rT ?????????KmolJ 0s Therfore, K 6.42?T pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 61 5.28 A revrsible proces requires the minium aount of work. Since the proces is revrsible and adibatic 0??s whic an be rwriten as 0,2,2,1,1 ????????? depPTidealdepPT rrrr ssss Calculate rduced temperature and presures using dat from Table A.1. ????0217.bar 0.46bar1,1 ??rP ????217.0bar 6.04bar10,2 ??rP 57.1K 190.6 3,1 ??rT From Tables C.5 and C.6: ? ?046.028.08.0457.,1,1 ???????????????RsdepPTrr Substiuting heat capcity dat into Equation 3.62, we gt ?????? ????????????? ? ?? bar 1bar 01ln10164.21008.9702.12K 03 263 dTT TRs Tideal Therfore, ???????? ?????????????? ? ?? RsdTT TRs depPTT rr,2,22K 03 263 30.210824.10785.2213.046. We can solve using a gues-and-check method K 402?T: 10.2,2?rT ????????? KmolJ 98.4s K 3852?T: 02.,2?rT pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 62 ????????? KmolJ 42.1s K 3792?T: 9.1,2?rT ?????????? KmolJ 018.s Therfore, K 3792?T An ergy balnce rveals that swhhh ????12 We can calulate the nthalpy using departure functions. From Tables C.3 and C.4: ? ?096.01.08.0965. ,1,1 ???????????????cdepPTRhrr ??0613.015.089.0614. ,2,2 ??????????????cdepPTRhrr Ideal heat capcity dat can be used to detrmine the ideal change in ethalpy ?????? ?????? ? ?? dTTTRhideal K 379K 03 263 10164.21008.9702.1 Therfore, ? ?? ? ?????? ???????????? ????????? ? ?? dTTTh K 379K 03 263 10164.21008.9702.10613.096.K 6.190KmolJ 314.8 ????????? molJ 2.304hws? and W1.10molJ 2.304smol 30/1 ??????? ???????????? ??????? SW? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 63 5.29 Equation 4.71 staes PTvv?????????1? PTvv??????????? This can be substiuted into Equation 5.7 to give ?? PJTcTv1???? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 64 5.30 For an ideal gas PRTvP????????? Therfore, ??0??????????? PPJT cvvcvRT? This result could also be rasoned from aphysical rgument. pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 65 5.31 The van der Wals equation is given by: 2vabvRTP?? (1) The thermal expansion coeficent is given by: PP vTvTvv ???????????????????? ????? 11 (2) Solving Equation 1 for T: ??????????????? RbvvaPT2 Diferntiating by aplying the chain rule, 3332 221 RvabavPvvaRbvRvaPvTP ??????????????????????????? (3) Substiution ito Equation 2 gives abavPvRv2 32???? Substiuting Equation 1 for P gives b in terms of R, T, v, a ,and b: ???? 2322bvaRTvbv???? The isothermal compresibilty is given by: TT vPvPvv ?????????????????????? ????? 11 From the van der Wals equation: ?? ???? 23 2332 22 bvbvaRTvvabvRTvPT ????????????????? so pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 6 ????23 222bvaRTvbvv???? For the Joule-Thomson coeficent, we can use Equation 5.7: ? ????????????? ?????? ????????realidealPP PidealP PJT dTvTc vTvT22????? Substiuting the van der Wals equation ito Equation 3 gives ???? ???? 3323 22 RvbvabvTRvbv bvaRTvvTP ??????????????? (4) Thus, the scond erivative bcomes: ?? ?? 43222 621 RvbvaRvavTbvbvTvT PP ???????????????????? ???? or simplifying using Equation 4, ?? 422 32RvbvavTP ?????????? (5) Substiuting Equations 5 and 4 into Equation 5.7 gives: ??????? ?????????????realidealPPidealPJT dPbvaRTvc bvaRTv bvabv 3222423 23? At agiven temperature the integral in presure can be rwriten i terms of volume using the van der Wals quation to giv: pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 67 ?????? ????? ?????????? ?????realidealvvidealPJT dvbvbvaRTvbvaRTvc bvav bvabRTv 22323 23 23222? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 68 5.32 We can solve this problem by using the form of the Joule-Thomson coeficent given i Equation 5.7. Th folwing aproxiatio can be ad PPTvTv ???????????????? ?? At 30 ?C, ? ?? ?C? 250350 ,1MPa?250?C,1MPa?350?? ????????? vvTv P C? 250350 kgm 2368.0kgm 2847.0? 33? ?????????????????????PTv ????????????????????????? K kgm 05.C? kgm 05.? 33PTv A similar proces was folwed to find cP. PPP ThdThc ???????????????? ??? At 30 ?C, ? ?? ?C? 250350 ,1MPa?250?C,1MPa?350?? ????????? hhTh P C? 250350 kgkJ 6.2942kgkJ 7.315? ? ?????????????????????PTh ? ??????????????????????????????? K kgkJ 15.2C? kgkJ 15.2??? PPP ThdThc Now, JT?can be found. pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 69 ? ? ??????? ?????? ?????????? ?????????????? ?????????? K kgkJ 15.2 kgm 25794.0K kgm 05.K 15.573??? 33PPJT cvTvT? ???????? kJK m 013. 3JT? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 70 5.3 At he inversion lie, the Joule-Thomson coeficent is zero. From Equation 5.7: 022 ?????????????? ?????? ?????????realidealPP PidealP PJT dTvTc vTvT????? This i true when the numerator is zero, i.e, 0?? ????? ??????? vTvTP?? For the van der Wals equation, we have 2vabvRTP?? Solving for T: ??????????????? RbvvaPT 2 so 3332 221 RvabavPvvaRbvRvaPvTP ??????????????????????????? Substiuting for P: ???? 3232Rvbv bvaRTvvTP ??????????? Hence, ???? 23 23220 bvaRTv bvabvvTvTP ?????????????? Solving for T: ?? 322bRvbvaT?? (1) pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 71 Substiuting this value of T back into the van der Wals equation gives ?? ? ? 223 322 bvbvavabvbvaP ????? (2) We can solve Equations 1 and 2 by picking a vlue of vand solving for T and P. For N2, the critl tempratre d presure are give by Tc = 126. [K] ad Pc = 3.84 [bar], respectivly. Thus, w can fid th van dr Wls constants a nd b: ????????????? 232 molJ 0.137=6427ccPRTa ???????? mol 103.8=8 35- ccPRTb Using thes values in Equations (1) and (2), we gt he folwing plot: Joule-Thomson iversion lie 020 4060 8010 0 10 20 30 40T [K] pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 72 5.34 We can solve this problem using departure functions, o first find the rduced temperatures and prsures. ????9.0bar 0.365bar50,1 ??rP ????2.0bar 0.365bar10,2 ??rP 967.0K 28.4 15.27,1 ??rT Since the thylen is in two-phase quilbrium when it leaves the throtling device, the tempratur is costraied. From the vapor-liquid om in Figur 5.: 6.21476.02,2???TTr The proces is ienthalpic, so the folwing expresion holds 0 ,2,221,1,1 ????????? ?depPTidealTTdepPT rrrr hhhh Therfore, idealTTdepPTdepPT hhh rrrr 21,1,1,2,2 ?????? From Table A.2.1: ? ?? ?? ? ?????? K 6.214K 15.273 263 10392.410394.1442.21 dTTTRhidealTT From Tables C.3 and C.4 ? ?085.??: ??976.351.3085.678.3 ,1,1 ???????????????cdepPTRhrr Now e can solve for the nthalpy departure at stae 2. pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 73 ?????? ???????? ? ??K 6.214K 15.273 263, 10392.410394.1442.K 4.281976.3,2,2 dTTTRThcdepPTrr 01.3,2,2 ???cdepPTRhrr We can calulate the quality of the water using the folwing relation ?? cvapdepPTcliqdepPTcdepPT RhxRhxRh rrrrrr ,,,,, ,2,2,2,2,2,2 1 ?????? wher x represnts the quality. From Figures 5. and 5.6: ??068.55.085.6.4,,,2,2 ???????cliqdepPTRhrr ??46.075.00859.4.0,,,2,2 ???????cvapdepPTRhrr Thus, 47.0?x 5.3% of the inlet stream is liquefid. pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 74 5.3 Density is calulated from olar volume as folws: vMW?? Substiute the above into the xpresion for 2soundV: ??s ssound vPMWvMWPV ????????????????? ??????? /112 The folwing can be shown using diferntials: 21vvv?????????? Therfore, sssound vPMWvPV ??????????????????? 22 ? pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 75 5.36 From Problem 5.3: sssound vPMWvPV ??????????????????? 22 ? The thermodynamic web gives: PTTvssPvs TssPvssTTPvTvssPvP ????????????????????????????????????????????????????????????????????????????? PvvPPTTvs vTPcccsvscTvP ?????????????????????????????????????????????????????????????? If we treat ir as n ideal gas consiting of diatomic olecules only 57? vPcc vRTPv????????? RPvTP????????? Therfore, ?????????????????????? vPvP s57 and ???????????????????? MWRTvPMWvVsound 57572 ??m/s 34?soundV The lightenig bolt is 1360 m awy. pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 76 5.37 From Problem 5.3: sssound vPMWvPV ??????????????????? 22 ? The thermodynamic web gives: PTTvssPvs TssPvssTTPvTvssPvP ????????????????????????????????????????????????????????????????????????????? so ?????????????????????????????????????? TcvTTPcTvP PPvvs For liquids vPcc? water at 20 ?C, so Pvs vTTPvP ?????????????????????????? Howevr, the cylic rule gives: TPv vvTTP ??????????????????????????1 So TsvPvP????????????????? From the steam tables, for saturated water at 20 oC: P = 2.34 kPa nd ??????? kgm 0102.? 3v For subcoled water at 20 oC: P = 5 MPa nd ??????? kgm 095.? 3v pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 7 So ????????????????????????????????? 3mkPa g 0102.095. 34.250??? vPvPvPTs and ??m/s 14??2?????????? ssound vPvV pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 78 5.38 (a) The fundamental proerty relation for internal enrgy is revrevWQdU???? Substiuting the proer elationships for work and heat, we obtain FdzTdSdU?? The fundamental proerty relation for the Helmholtz enrgy is ?? SdTTdSdUTSddUdA ????? Substiute the xpresion for the internal enrgy diferntial: SdTFdzdA?? (b) First, relate the ntropy diferntial to temperature and length. dzZSdTTSdS Tz ?????????????????? Now e ned to find expresions for the partial derivatives. zzzz TSTTzFSTTunnc ????????????????????????????? Therfore, ????????????????? bTanTncTSz z The folwing staemnt is true mathematicaly (order of diferntiation does not mater): zTTz ZATTAZ ????????????????????????????????? Furthermore, pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 79 TTz ZSTAZ ?????????????????????????? zzTTFZAT ????????????????????????? ??0zzkTFZS zT ????????????????????? Substiuting the xpresions for the partial derivatives into the xpresion for the ntropy difertial, w obtain ??dzzzkdTbTandS 0?????????? (c) First, start with an expresion for the internal enrgy diferntial: dz ZUdTTUdU Tz ?????????????????? From information given i the problem staemnt: ??bTanTU z ?????????? Using the xpresion for internal enrgy devloped in Part (a) nd information from Part (b) ??? ??000 ???????????????????????? zzkTzzkTFzSTZU TT Therfore, ??? ? ??? ?dTbTandzdTbTandU ????? 0 (d) We showed in Part (c) that 0??????????TUzUF pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 80 Using the xpresion for TzS???????? devloped in Part B, we obtain ??0zzkTzSTF TS ???????????? (e) First, perform an ergy balnce for the adibatic proces. WdU?? Substiute xpresions for internal enrgy and work. ??? ? ?? dzzzkTFdzdTbTan 0???? Rearngemnt gives ????? ?bTanzzkTdzdT???0 The right-and side of the above quation is always positve, so the tmperature increase as the rubr is tretch. pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 81 5.39 The scond law staes that for aproces to be posible, 0??univs To se if this conditon is atisfied, we must ad the ntropy change of the sytem to the ntropy chang of te surudigs. For this iotherl procs, the tropy cang can be writ dvTPdvTPdTcds vvv ??????????????? ???? Aplying the van der Wals equation: dvbvRds?? Integrating ????????? K molJ 5.1ln 12vvRsys For the ntropy change of the suroundigs, we use the value of heat given i Example 5.2: ????????? molJ 60 surqq Hence the ntropy change of the suroundigs i: ???????????? K molJ 6.13760 sursursurTq and ???????????? K molJ 9. sursyunivs Since the ntropy change of the univers is positve we say this proces is posible and that it is irvrsibl. Under thes conditons proane xhibits atractive intermolecular forces (dispersion). The closer thy ar togther, averg, th lower the nrgy. That w ned t put work it this ystm sas tht he work ned to separt t proae molecules i grater than the work we gt out during t irversibl xpansin. pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 82 5.40 A schematic of the proces is given by: Gas A in Pi = 10 bar Ti = 60 KTurbine Pf = 20 bar Tf = 45 KwsGas Aout The nergy balnce for this proces is provide below: Swh?? Because the gas i not ideal under thes conditons, we have to creat ahypothetical path tat oncts t inital finl stas trugh tre stps. On hypthticl at is hown below: P [bar] T [K] Pi,Ti Pf,Tf step 1step 3 step 2 ideal gas 6045 ?h 10 20Plow For the first ection f the path, we have ???????????01 1PPTdPPhh If we aply Equation 5.4 we can rewrite the above quation as ?? ?????? ???????????01P P Pii dPvTvTh For the given EOS: pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA 83 2iPTaPPRTv ?????????? Therfore, ?????????????????????? ????? ?? ?????? molJ 2467201010010101 55 vP iPP i ii dPbTaPdPvTaPPh Similarly for step 3 ???????????????????? molJ 25025102003fPP f dPbTaPh For step 2, the presure is zero, so we can use the ideal heat capcity given i the problem stamnt o callat th nthalpy hge. ? ? ???????????? ?? molJ 627002.30K 45K 602 dTdTchfiTTP Now sum each part o find the total change in ethalpy: ? ?????????????? molJ 847321 hhhh ????????molJ 847sw In other words, for evry mole of gas that flows through te turbine, 847 joules of work are prducd. pdfMachine - is a pdf writer that produces quality PDF files with ease! Get yours now! ?Thank you very much! I can use Acrobat Distiller or the Acrobat PDFWriter but I consider your product a lot easier to use and much preferable to Adobe's" A.Sarras - USA Microsoft Word - CH05 - pdfMachine from Broadgun Software, http://pdfmachine.com, a great PDF writer utility!