15-69C Under the conditions of complete combustion with stoichiometric amount of air.

Transcription

1 15-43 Adabatc Flame emperature 15-68C Fr the case f stchmetrc amunt f pure xy snce we have the same amunt f chemcal energy released but a smaller amunt f mass t absrb t C Under the cndtns f cmplete cmbustn wth stchmetrc amunt f ar [Als slved by EE n enclsed CD] Hydr s burned wth 0 percent excess ar durng a steadyflw cmbustn prcess. he ext temperature f prduct gases s t be determned. Assumptns 1 teady peratng cndtns exst. Ar and cmbustn gases are deal gases. 3 Knetc and ptental energes are neglgble. 4 here are n wrk nteractns. 5 he cmbustn chamber s adabatc. Analyss Adabatc flame temperature s the temperature at whch the prducts leave the cmbustn chamber under adabatc cndtns ( 0 wth n wrk nteractns (W 0. Under steady-flw cndtns the energy balance E E E appled n the cmbustn chamber reduces t n ut system ( h h ( h h he cmbustn equatn f H wth 0% excess ar s 7 C Cmbustn rducts chamber H ( 0.6 O 3.76 H O 0.1O.56 Ar Frm the tables, 0% excess ar 7 C H ubstance h 80 K h 98 K kj/kml kj/kml kj/kml H O H O (g -41, (( 1 41,80 h 9904 ( 0.1( 0 h 868 (.56( 0 h 8669 H O O ( 1( ( 0.6( (.56( It yelds h 0.1h.56h H O O 70,116 kj he adabatc flame temperature s btaned frm a tral and errr slutn. A frst guess s btaned by dvdng the rght-hand sde f the equatn by the ttal number f mles, whch yelds 70,116/( ,488 kj/kml. hs enthalpy value crrespnds t abut 400 K fr. tng that the majrty f the mles are, wll be clse t 400 K, but smewhat under t because f the hgher specfc heat f H O. At 300 K: h H ( 1( 98,199 ( 0.1( 79,316 (.56( 75,676 O ho h 76,856 kj ( Hgher than 70,116 kj At 50 K: h H ( 1( 95,56 ( 0.1( 77,397 (.56( 73,856 O ho h 69,91 kj ( Lwer than 70,116 kj By nterplatn, 51.4 K

2 EE rblem s recnsdered. hs prblem s t be mdfed t nclude the fuels butane, ethane, methane, and prpane as well as H; t nclude the effects f nlet ar and fuel temperatures; and the percent theretcal ar suppled. Analyss he prblem s slved usng EE, and the slutn s gven belw. Adabatc Cmbustn f fuel CnHm enterng at _fuel wth tchmetrc Ar at _ar: eactn: CxHy (y/4 x (he_ar/100 (O 3.76 <--> xco (y/ HO 3.76 (y/4 x (he_ar/100 (y/4 x (he_ar/100-1 O _prd s the adabatc cmbustn temperature, assumng n dsscatn. he_ar s the % theretcal ar. " "he ntal guess value f _prd 450K." rcedure Fuel(Fuel$:x,y,ame$ "hs prcedure takes the fuel name and returns the mles f C and mles f H" If fuel$'ch6' then x;y6 ame$'ethane' else If fuel$'c3h8' then x3; y8 ame$'prpane' else If fuel$'c4h10' then x4; y10 ame$'butane' else f fuel$'ch4' then ] x1; y4 [K ame$'methane' d else f fuel$'h' then pr x0; y ame$'hydr' endf; endf; endf; endf; endf end {"Input data frm the dagram wndw" _fuel 80 [K] _ar 80 [K] he_ar 00 "%" Fuel$'H'} Call Fuel(fuel$:x,y,ame$ rduct temperature vs % theretcal ar fr hydr Calculated pnt he ar [%] Henthalpy(Fuel$,_fuel (y/4 x *(he_ar/100 *enthalpy(o,_ar3.76*(y/4 x *(he_ar/100 *enthalpy(,_ar HH "Adabatc" Hx*enthalpy(CO,_prd(y/*enthalpy(HO,_prd3.76*(y/4 x* (he_ar/100*enthalpy(,_prd(y/4 x *(he_ar/100-1*enthalpy(o,_prd Mles_O(y/4 x *(he_ar/100-1 Mles_3.76*(y/4 x* (he_ar/100 Mles_COx; Mles_HOy/ [1]_prd; xa[1]he_ar "array varable are pltted n lt Wndw 1" he ar [%] prd [K]

3 E Hydr s burned wth 0 percent excess ar durng a steady-flw cmbustn prcess. he ext temperature f prduct gases s t be determned. Assumptns 1 teady peratng cndtns exst. Ar and cmbustn gases are deal gases. 3 Knetc and ptental energes are neglgble. 4 here are n wrk nteractns. 5 he cmbustn chamber s adabatc. Analyss Adabatc flame temperature s the temperature at whch the prducts leave the cmbustn chamber under adabatc cndtns ( 0 wth n wrk nteractns (W 0. Under steady-flw cndtns the energy balance E E E appled n the cmbustn chamber reduces t n ut system ( hf h h ( hf h h he cmbustn equatn f H wth 0% excess ar s 40 F Cmbustn rducts chamber H ( 0.6 O 3.76 HO 0.1O.56 Ar 0% excess ar Frm the tables, 40 F H h 500 h 537 ubstance Btu/lbml Btu/lbml Btu/lbml H O H O (g -104, (( 1 104,040 h 458 ( 0.1( 0 h (.56( 0 h H O O (( ( 0.6( (.56( It yelds h H O 0.1hO.56h 116,094 Btu he adabatc flame temperature s btaned frm a tral and errr slutn. A frst guess s btaned by dvdng the rght-hand sde f the equatn by the ttal number f mles, whch yelds 116,094/( ,593 Btu/lbml. hs enthalpy value crrespnds t abut 4400 fr. tng that the majrty f the mles are, wll be clse t 4400, but smewhat under t because f the hgher specfc heat f H O. At 400 : h H ( 1( 40,740 ( 0.1( 3,989 (.56( 31,503 O ho h 115,110 Btu ( Lwer than116,094 Btu At 4100 : h H ( 1( 41,745 ( 0.1( 33,7 (.56( 3,198 O ho h 117,756 Btu ( Hgher than 116,094 Btu By nterplatn, 4054

4 Acetylene gas s burned wth 30 percent excess ar durng a steady-flw cmbustn prcess. he ext temperature f prduct gases s t be determned. Assumptns 1 teady peratng cndtns exst. Ar and cmbustn gases are deal gases. 3 Knetc and ptental energes are neglgble. 4 here are n wrk nteractns. Analyss he fuel s burned cmpletely wth the excess ar, and thus the prducts wll cntan nly CO, H O,, and sme free O. Cnsderng 1 kml f C H, the cmbustn equatn can be wrtten as C ( O 3.76 CO HO 0.3athO ( 1.3( 3.76 ath H 1.3a th where a th s the stchmetrc ceffcent and s determned frm the O balance, 1.3a a a.5 th th th ( O 3.76 CO HO 0.75O C H Under steady-flw cndtns the energy balance E E E appled n the cmbustn chamber wth W 0 reduces t ut n ut system ( hf h h ( hf h h C H 30% excess ar 7 C 75,000 kj/kml 5 C Cmbustn rducts Ar chamber Assumng the ar and the cmbustn prducts t be deal gases, we have h h(. Frm the tables, ubstance h 98 K h 300 K kj/kml kj/kml kj/kml C H 6, O H O (g -41, CO -393, ,000 ( ( 393,50 hco 9364 ( 1( 41,80 h 9904 HO ( 0.75( 0 h 868 ( 1.( 0 h 8669 (( 1 6,730 O ( 3.5( ( 1.( It yelds hco hh O 0. 75hO 1. h 1, 31184, kj he temperature f the prduct gases s btaned frm a tral and errr slutn. A frst guess s btaned by dvdng the rght-hand sde f the equatn by the ttal number f mles, whch yelds 1,31,184/( ,79 kj/kml. hs enthalpy value crrespnds t abut 500 K fr. tng that the majrty f the mles are, wll be clse t 500 K, but smewhat under t because f the hgher specfc heats f CO and H O. At 350 K: h At 300 K: h By nterplatn, h 0.75h 1.h CO HO O h 0.75h 1.h CO HO O 301 K ( ( 1,091 ( 1( 100,846 ( 0.75( 81,43 ( 1.( 77,496 1,35,961 kj ( Hgher than 1,31,184 kj ( ( 119,035 ( 1( 98,199 ( 0.75( 79,316 ( 1.( 75,676 1,30,517 kj ( Lwer than 1,31,184 kj

5 A mxture f hydr and the stchmetrc amunt f ar cntaned n a cnstant-vlume tank s gnted. he fnal temperature n the tank s t be determned. Assumptns 1 he tank s adabatc. Bth the reactants and prducts are deal gases. 3 here are n wrk nteractns. 4 Cmbustn s cmplete. Analyss he cmbustn equatn f H wth stchmetrc amunt f ar s ( O 3.76 HO H he fnal temperature n the tank s determned frm the energy balance relatn E E E fr reactng clsed systems under n ut system adabatc cndtns ( 0 wth n wrk nteractns (W 0, ( h h v ( h h v H, AI 5 C, 1 atm nce bth the reactants and the prducts behave as deal gases, all the nternal energy and enthalpes depend n temperature nly, and the v terms n ths equatn can be replaced by u. It yelds ( h h u ( u 98 K snce the reactants are at the standard reference temperature f 5 C. Frm the tables, ubstance h 98 K kj/kml kj/kml H O H O (g -41, (( 1 41,80 h ( 1.88( 0 h HO ( 1( ( 0.5( ( 1.88( It yelds h H 188. h O 59, 648 kj he temperature f the prduct gases s btaned frm a tral and errr slutn, At 3050 K: h H ( 1( 139,051 ( 1.88( 103,60 ( 3.94( 3050 O h 60,163 kj ( Hgher than 59,648 kj At 3000 K: h H ( 1( 136,64 ( 1.88( 101,407 ( 3.94( 3000 O h 55,089 kj ( Lwer than 59,648 kj By nterplatn, 3045 K

6 Octane gas s burned wth 30 percent excess ar durng a steady-flw cmbustn prcess. he ext temperature f prduct gases s t be determned. Assumptns 1 teady peratng cndtns exst. Ar and cmbustn gases are deal gases. 3 Knetc and ptental energes are neglgble. 4 here are n wrk nteractns. 5 he cmbustn chamber s adabatc. Analyss Under steady-flw cndtns the energy balance E E E appled n the cmbustn chamber wth W 0 reduces t n ut system ( h h ( h h ( h h h f snce all the reactants are at the standard reference temperature f 5 C. hen, ( g 1.3a th ( O CO 9HO 0.3athO ( 1.3( 3.76 ath C where a th s the stchmetrc ceffcent and s determned frm the O balance, 8H18 1.3a a a 1.5 th th th C 8H18 ( g 16.5( O CO 9H O 3.75O 61.1 herefre, kml f dry ar wll be used per kml f the fuel. he partal pressure f the water vapr present n the ncmng ar s φ ka 1.90 ( ( ka v, n ar sat@5 C Assumng deal gas behavr, the number f mles f the msture that accmpanes kml f ncmng dry ar s determned t be v,n 1.90 ka v n ttal ttal ka v C 8 H 18 30% excess ar 5 C ( 1.48 kml,,n v,n, 5 C Cmbustn rducts Ar chamber he balanced cmbustn equatn s btaned by addng 1.48 kml f H O t bth sdes f the equatn, ( g 16.5( O HO 8CO 10.48HO 3.75O C Frm the tables, h 98 K ubstance kj/kml kj/kml It yelds 8H C 8 H 18 (g -08, O H O (g -41, CO -393, (( 8 393,50 hco 9364 ( 10.48( 41,80 h 9904 ( 3.75( H O ho ( 61.1( 0 h 8669 (( 1 08,450 ( 1.48( 41, h CO 10.48hH O 3.75hO 61.1h 5,857,09 kj he adabatc flame temperature s btaned frm a tral and errr slutn. A frst guess s btaned by dvdng the rght-hand sde f the equatn by the ttal number f mles, whch yelds 5,857,09/( ,87 kj/kml. hs enthalpy value crrespnds t abut 150 K fr. tng that the majrty f the mles are, wll be clse t 150 K, but smewhat under t because f the hgher specfc heat f H O. At 000 K: 8 hco 10.48h ( 8( 100,804 ( 10.48( 8,593 ( 3.75( 67,881 ( 61.1( 64,810 HO ho h 5,886,451 kj ( Hgher than 5,857,09 kj At 1980 K: 8 hco 10.48h ( 8( 99,606 ( 10.48( 81,573 ( 3.75( 67,17 ( 61.1( 64,090 HO ho h 5,819,358 kj ( Lwer than 5,857,09 kj By nterplatn, 1991 K

7 EE rblem s recnsdered. he effect f the relatve humdty n the ext temperature f the prduct gases s t be nvestgated. Analyss he prblem s slved usng EE, and the slutn s gven belw. "he percent excess ar and relatve humdty are nput by the dagram wndw." {ercentex 30"[%]"} {elhum60"[%]"} "Other nput data:" Fuel$ 'Octane (C8H18' _fuel (573 "[K]" Ex ercentex/100 "[%Excess ar/100]" _ar [ka] _ar1 573 "[K]" H_1 elhum/100 M_ar 8.97 [kg/kml] M_water 18 [kg/kml] M_C8H18(8*118*1 "[kg/kml]" "Fr theretcal dry ar, the cmplete cmbustn equatn s" "C8H18 A_th(O CO9 HO A_th (3.76 " A_th*8*9*1 "theretcal O balance" "nw t fnd the amunt f water vapr asscated wth the dry ar" w_1huma(arho,_ar1,_ar1,h_1 "Humdty rat, kgv/kga" _ww_1*((1ex*a_th*4.76*m_ar/m_water "Mles f water n the atmshperc ar, kml/kml_fuel" "he balanced cmbustn equatn wth Ex% excess mst ar s" "C8H18 (1EX[A_th(O3.76 _w HO]8 CO(9_w HO (1Ex A_th (3.76 Ex( A_th O " "Apply Frst Law F" H_fuel [kj/kml] "frm able A-6" HH_fuel (1Ex*A_th*enthalpy(O,_ar1(1Ex*A_th*3.76 *enthalpy(,_ar1_w*enthalpy(ho,_ar1 H8*enthalpy(CO,_prd(9_w*enthalpy(HO,_prd(1Ex*A_th*3.76* enthalpy(,_prdex*a_th*enthalpy(o,_prd "Fr Adabatc Cmbustn:" H H "hs slutn used the humdty rat frm psychrmetrc data t determne the mles f water vapr n atmspherc ar. One shuld calculate the mles f water cntaned n the atmspherc ar by the methd shwn n Chapter 14, whch uses the relatve humdty t fnd the partal pressure f the water vapr and, thus, the mles f water vapr. Explre what happens t the results as yu vary the percent excess ar, relatve humdty, and prduct temperature. " elhum [%] prd [K] ] [K d pr Adabatc Flame emperature fr 30% Excess ar elhum [%]

8 15-50 Entrpy Change and ecnd Law Analyss f eactng ystems 15-77C Assumng the system exchanges heat wth the surrundngs at 0, the ncrease-n-entrpy prncple can be expressed as s s 0 ut 15-78C By subtractng ln(/ 0 frm the tabulated value at 1 atm. Here s the actual pressure f the substance and 0 s the atmspherc pressure C It represents the reversble wrk asscated wth the frmatn f that cmpund Hydr s burned steadly wth xy. he reversble wrk and exergy destructn (r rreversblty are t be determned. Assumptns 1 Cmbustn s cmplete. teady peratng cndtns exst. 3 Ar and the cmbustn gases are deal gases. 4 Changes n knetc and ptental energes are neglgble. Analyss he cmbustn equatn s H 0.5O H O. he H, the O, and the H O are at 5 C and 1 atm, whch s the standard reference state and als the state f the surrundngs. herefre, the reversble wrk n ths case s smply the dfference between the Gbbs functn f frmatn f the reactants and that f the prducts, snce the W 0 0 rev g f, g f, H g f,h O g f,o HO g f,ho HO g f,ho ( 1 kml( 37,180 kj/kml 37,180 kj (per kml f H g f f stable elements at 5 C and 1 atm s zer. herefre, 37,180 kj f wrk culd be dne as 1 kml f H s burned wth 0.5 kml f O at 5 C and 1 atm n an envrnment at the same state. he reversble wrk n ths case represents the exergy f the reactants snce the prduct (the H O s at the state f the surrundngs. hs prcess nvlves n actual wrk. herefre, the reversble wrk and exergy destructn are dentcal, X destructn 37,180 kj (per kml f H We culd als determne the reversble wrk wthut nvlvng the Gbbs functn, W rev ubsttutng, W ( hf h h 0s ( h h h 0s f ( hf 0s ( h 0s f H ( h 0s O ( h 0s H O( h 0s f H f O f H O (( ( 0.5( ( 1( 85, ,04 kj rev whch s almst dentcal t the result btaned befre.

9 Ethylene gas s burned steadly wth 0 percent excess ar. he temperature f prducts, the entrpy eratn, and the exergy destructn (r rreversblty are t be determned. Assumptns 1 Cmbustn s cmplete. teady peratng cndtns exst. 3 Ar and the cmbustn gases are deal gases. 4 Changes n knetc and ptental energes are neglgble. Analyss (a he fuel s burned cmpletely wth the excess ar, and thus the prducts wll cntan nly CO, H O,, and sme free O. Cnsderng 1 kml f C H 4, the cmbustn equatn can be wrtten as ( g 1.a th ( O 3.76 CO HO 0.athO ( 1.( 3.76 ath C where a th s the stchmetrc ceffcent and s determned frm the O balance, H4 1.a 1 0.a a 3 th th th C H4( g 3.6( O 3.76 CO HO 0.6O Under steady-flw cndtns, the ext temperature f the prduct gases can be determned frm the steadyflw energy equatn, whch reduces t ( h h h f, ( h f C H 4 snce all the reactants are at the standard reference state, and fr O and. Frm the tables, h 98 K ubstance kj/kml kj/kml C H 4 ubsttutng, 393,50 h r, C H 4 (g 5, O H O (g -41, CO -393, % excess ar 5 C ( ( CO 9364 ( ( 41,80 h 9904 HO ( 0.6( 0 h 868 ( 13.54( 0 h 8669 (( 1 5,80 h O h 0.6h 13.54h CO HO O 1,484,083 kj By tral and errr, 69.6 K (b he entrpy eratn durng ths adabatc prcess s determned frm s s 5 C Cmbustn rducts Ar chamber he C H 4 s at 5 C and 1 atm, and thus ts abslute entrpy s kj/kml K (able A-6. he entrpy values lsted n the deal gas tables are fr 1 atm pressure. Bth the ar and the prduct gases are at a ttal pressure f 1 atm, but the entrpes are t be calculated at the partal pressure f the cmpnents whch s equal t y ttal, where y s the mle fractn f cmpnent. Als, s, s, 0 ln y ( ( ( ( he entrpy calculatns can be presented n tabular frm as u y s (,1atm uln( y m m s C H O kj/k CO H O O kj/k kj/kml K and (c X ( 98 K( kj/kml K C H 390,760 kj ( per kml C H destryed 0 4 4

10 Lqud ctane s burned steadly wth 50 percent excess ar. he heat transfer rate frm the cmbustn chamber, the entrpy eratn rate, and the reversble wrk and exergy destructn rate are t be determned. Assumptns 1 Cmbustn s cmplete. teady peratng cndtns exst. 3 Ar and the cmbustn gases are deal gases. 4 Changes n knetc and ptental energes are neglgble. Analyss (a he fuel s burned cmpletely wth the excess ar, and thus the prducts wll cntan nly CO, H O,, and sme free O. Cnsderng 1 kml C 8 H 18, the cmbustn equatn can be wrtten as C ( l 1.5a th ( O CO 9HO 0.5athO ( 1.5( 3.76 ath 8H18 where a th s the stchmetrc ceffcent and s determned frm the O balance, 1.5a a a 1.5 th th th ( l 18.75( O CO 9HO 6.5O C 8H Under steady-flw cndtns the energy balance wth W 0 reduces t E E E n ut system appled n the cmbustn chamber ut ( h h ( h h h f, h f snce all f the reactants are at 5 C. Assumng the ar and the cmbustn prducts t be deal gases, we have h h(. Frm the tables,, ubstance kj/kml C 8 H 18 (l -49,950 O 0 0 H O (l -85,830 CO -393,50 C 8 H 18 (l 0 98 K 5 C Ar 50% excess ar 5 C & Cmbustn chamber rducts 5 C ubsttutng, (( 8 393,50 (( 9 85, ( 1( 49, ,470,680 kj/kml f C8H18 ut r ut 5,470,680 kj/kml f C8H18 he C 8 H 18 s burned at a rate f 0.5 kg/mn r & m & & M ut & ut [(( 8 1 ( 18( 1 ] 0.5 kg/mn kg/kml 3 ( kml/mn( 5,470,680 kj/kml 11,997 kj/mn 3 kml/mn he heat transfer fr ths prcess s als equvalent t the enthalpy f cmbustn f lqud C 8 H 18, whch culd easly be de determned frm able A-7 t be h C 5,470,740 kj/kml C 8 H 18.

11 15-53 (b he entrpy eratn durng ths prcess s determned frm ut s s surr he C 8 H 18 s at 5 C and 1 atm, and thus ts abslute entrpy s s C 8 H 18 ut surr kj/kml.k (able A-6. he entrpy values lsted n the deal gas tables are fr 1 atm pressure. Bth the ar and the prduct gases are at a ttal pressure f 1 atm, but the entrpes are t be calculated at the partal pressure f the cmpnents whch s equal t y ttal, where y s the mle fractn f cmpnent. Als, s ( (, s (, 0 ln( y he entrpy calculatns can be presented n tabular frm as and u y s (,1atm uln( y m m C 8 H O ,097.3 kj/k CO H O (l O , ,531 kj/k & & surr surr 5,470,53 17,531 18, K kj 17,798 kj/kml K 3 ( kml/mn( 17,798 kj/kml K kj/mn K (c he exergy destructn rate asscated wth ths prcess s determned frm X & destryed ( 98 K( kj/mn K 11, kw & kj/mn 0 s

12 Acetylene gas s burned steadly wth 0 percent excess ar. he temperature f the prducts, the ttal entrpy change, and the exergy destructn are t be determned. Assumptns 1 Cmbustn s cmplete. teady peratng cndtns exst. 3 Ar and the cmbustn gases are deal gases. 4 Changes n knetc and ptental energes are neglgble. Analyss (a he fuel s burned cmpletely wth the excess ar, and thus the prducts wll cntan nly CO, H O,, and sme free O. Cnsderng 1 kml C H, the cmbustn equatn can be wrtten as C ( g 1.ath ( O 3.76 CO HO 0.athO ( 1.( 3.76 ath H where a th s the stchmetrc ceffcent and s determned frm the O balance, ubsttutng, 1.a a a.5 th th th ( g 3( O 3.76 CO H O 0.5O C H 11.8 Under steady-flw cndtns the ext temperature f the prduct gases can be determned frm the energy balance E E E appled n the n ut system cmbustn chamber, whch reduces t ut C H 0% excess ar 5 C ( h h h f, ( h h ( h f snce all the reactants are at the standard reference state, and 300,000 kj/kml 5 C Cmbustn rducts Ar chamber C H 0 fr O and. Frm the tables, ubstance h 98 K kj/kml kj/kml C H (g 6, O H O (g -41, CO -393, ubsttutng, r, 300,000 ( ( 393,50 hco 9364 ( 1( 41,80 h 9904 HO ( 0.5( 0 h 868 ( 11.8( 0 h 8669 (( 1 6,730 O h CO hh O 0.5hO 11.8h 1,086,349 kj By tral and errr, 06.1 K (b he entrpy eratn durng ths prcess s determned frm ut s s surr he C H s at 5 C and 1 atm, and thus ts abslute entrpy s ut surr s CH kj/kml K (able A-6. he entrpy values lsted n the deal gas tables are fr 1 atm pressure. Bth the ar and the prduct gases are at a ttal pressure f 1 atm, but the entrpes are t be calculated at the partal pressure f the cmpnents whch s equal t y ttal, where y s the mle fractn f cmpnent. Als, s ( (, s (, 0 ln( y u m

13 15-55 he entrpy calculatns can be presented n tabular frm as y s (,1atm uln( y m s C H O kj/k CO H O O kj/k surr surr 300,000 kj kj/kml K 98 K (c he exergy destructn rate asscated wth ths prcess s determned frm X destructn 0 ( 98 K( kj/kml K 578,835 kj ( per kml C H

14 CO gas s burned steadly wth ar. he heat transfer rate frm the cmbustn chamber and the rate f exergy destructn are t be determned. Assumptns 1 Cmbustn s cmplete. teady peratng cndtns exst. 3 Ar and the cmbustn gases are deal gases. 4 Changes n knetc and ptental energes are neglgble. rpertes he mlar masses f CO and ar are 8 kg/kml and 9 kg/kml, respectvely (able A-1. Analyss (a We frst need t calculate the amunt f ar used per kml f CO befre we can wrte the cmbustn equatn, v &m CO CO CO 3 ( ka m /kg K( 310 K 110 ka 3 V& CO 0.4 m /mn kg/mn v m /kg hen the mlar ar-fuel rat becmes AF ar fuel m& m& ar fuel / M / M ar fuel m ( 1.5 kg/mn /( 9 kg/kml ( kg/mn /( 8 kg/kml 3 /kg CO 37 C 110 ka rducts Ar 900 K 5 C 3.03 kml & ar/kml fuel 800 K hus the number f mles f O used per mle f CO s 3.03/ hen the cmbustn equatn n ths case can be wrtten as ( O 3.76 CO 0.137O.40 CO Under steady-flw cndtns the energy balance En Eut Esystem appled n the cmbustn chamber wth W 0 reduces t ut ( h h ( h h Assumng the ar and the cmbustn prducts t be deal gases, we have h h(. Frm the tables, ubstance h 98 K h 310 K h 900 K kj/kml kj/kml kj/kml kj/kml CO -110, O , ,890 CO -393, ,405 ubsttutng, ut (( 1 393,50 37, ( 0.137( 0 7, (.4( 0 6, ( 1( 110, ,99 kj/kml f CO hus 08,99 kj f heat s transferred frm the cmbustn chamber fr each kml (8 kg f CO. hs crrespnds t 08,99/8 746 kj f heat transfer per kg f CO. hen the rate f heat transfer fr a mass flw rate f kg/mn fr CO becmes & & ( kg/mn( 746 kj/kg 3567 kj/mn ut mqut 0

15 15-57 (b hs prcess nvlves heat transfer wth a reservr ther than the surrundngs. An exergy balance n the cmbustn chamber n ths case reduces t the fllwng relatn fr reversble wrk, ( h h h s ( h h h s ( W / rev f 0 f 0 ut 1 0 he entrpy values lsted n the deal gas tables are fr 1 atm ka pressure. he entrpy f each reactant and the prduct s t be calculated at the partal pressure f the cmpnents whch s equal t y ttal, where y s the mle fractn f cmpnent, and m 110/ atm. Als, s ( (, s (, 0 ln( y he entrpy calculatns can be presented n tabular frm as u m y s (,1atm uln( y m s CO O kj/k CO O kj/k he rate f exergy destructn can be determned frm where X& destryed & 0 m& 0 ( / M ut res 08,99 kj kj/kml K 800 K ( 98 K( kg/mn( 316.5/8 kj/kml K 1610 kj/ mn X & destryed

16 E Benzene gas s burned steadly wth 95 percent theretcal ar. he heat transfer rate frm the cmbustn chamber and the exergy destructn are t be determned. Assumptns 1 teady peratng cndtns exst. Ar and the cmbustn gases are deal gases. 3 Changes n knetc and ptental energes are neglgble. Analyss (a he fuel s burned wth nsuffcent amunt f ar, and thus the prducts wll cntan sme CO as well as CO, H O, and. he theretcal cmbustn equatn f C 6 H 6 s C6H6 a th ( O CO 3HO 3.76ath C 6 H 6 where a th s the stchmetrc ceffcent and s 77 F Cmbustn rducts determned frm the O balance, chamber a th hen the actual cmbustn equatn can be wrtten as Ar 95% theretcal ( 0.95( 7.5( O 3.76 x CO ( 6 CO 3HO C 6H6 x 6.79 he value f x s determned frm an O balance, ( 0.95( 7.5 x ( 6 x C / 1.5 x 5.5 ( O CO 0.75CO 3H O 6H Under steady-flw cndtns the energy balance En Eut Esystem appled n the cmbustn chamber wth W 0 reduces t ut ( h h ( h h ( h h h f snce all f the reactants are at 77 F. Assumng the ar and the cmbustn prducts t be deal gases, we have h h(. Frm the tables,, ubstance h 537 h 1500 Btu/lbml Btu/lbml Btu/lbml C 6 H 6 (g 35, O , ,648.0 H O (g -104, ,551.4 CO -47, ,711.1 CO -169, ,576.0 ut ( 5.5( 169,300 14, ( 0.75( 47,540 10, (( 3 104,040 1, ( 6.79( 0 10, (( 1 35,680 1,001,434 Btu/lbml f C 6 H 6 0 0

17 15-59 (b he entrpy eratn durng ths prcess s determned frm ut s s surr he C 6 H 6 s at 77 F and 1 atm, and thus ts abslute entrpy s s CH Btu/lbml (able A-6E. he entrpy values lsted n the deal gas tables are fr 1 atm pressure. Bth the ar and the prduct gases are at a ttal pressure f 1 atm, but the entrpes are t be calculated at the partal pressure f the cmpnents whch s equal t y ttal, where y s the mle fractn f cmpnent. Als, s ( (, s (, 0 ln( y he entrpy calculatns can be presented n tabular frm as u y s (,1atm uln( y m m ut surr C 6 H O Btu/ CO CO H O (g Btu/ 1,001, Btu 537 ut / surr hen the exergy destryed s determned frm X destryed 0 ( 537 ( Btu/lbml 1,179,306 Btu/ ( per lbml C H s 6 6

18 [Als slved by EE n enclsed CD] Lqud prpane s burned steadly wth 150 percent excess ar. he mass flw rate f ar, the heat transfer rate frm the cmbustn chamber, and the rate f entrpy eratn are t be determned. Assumptns 1 Cmbustn s cmplete. teady peratng cndtns exst. 3 Ar and the cmbustn gases are deal gases. 4 Changes n knetc and ptental energes are neglgble. rpertes he mlar masses f C 3 H 8 and ar are 44 kg/kml and 9 kg/kml, respectvely (able A-1. Analyss (a he fuel s burned cmpletely wth the excess ar, and thus the prducts wll cntan nly CO, H O,, and sme free O. Cnsderng 1 kml f C 3 H 8, the cmbustn equatn can be wrtten as C ( l.5a th ( O CO 4HO 1.5athO (.5( 3.76 ath 3H8 where a th s the stchmetrc ceffcent and s determned frm the O balance, ubsttutng,.5a 3 1.5a a 5 th th th ( l 1.5( O CO 4HO 7.5O C 3H8 47 he ar-fuel rat fr ths cmbustn prcess s m AF m & ar fuel & ( kml( 9 kg/kml ( 3 kml( 1 kg/kml ( 4 kml( kg/kml 39. kg ar/kg fuel m ( AF( m ( 39. kg ar/kg fuel( 0.4 kg fuel/mn 15.7 kg ar/mn ar fuel (b Under steady-flw cndtns the energy balance En Eut Esystem appled n the cmbustn chamber wth W 0 reduces t ut ( h h ( hf h h Assumng the ar and the cmbustn prducts t be deal gases, we have h h(. Frm the tables, (he f lqud prpane s btaned by addng the g at 5 C t f gaseus prpane. ubstance kj/kml h 85 K h 98 K h 100 K kj/kml kj/kml kj/kml C 3 H 8 (l -118, O , ,777 H O (g -41, ,380 CO -393, ,848 ut (( 3 393,50 53, ( 4( 41,80 44, ( 7.5( 0 38, ( 47( 0 36, ( 1( ( 1.5( ( ,464 kj/kml f C 3 H 8 118,910 h hus 190,464 kj f heat s transferred frm the cmbustn chamber fr each kml (44 kg f prpane. hs crrespnds t 190,464/ kj f heat transfer per kg f prpane. hen the rate f heat transfer fr a mass flw rate f 0.4 kg/mn fr the prpane becmes & & ( 0.4 kg/mn( kj/kg 173 kj/mn ut mqut 98 h 98

19 15-61 (c he entrpy eratn durng ths prcess s determned frm ut s s surr he C 3 H 8 s at 5 C and 1 atm, and thus ts abslute entrpy fr the gas phase s s kJ/kml K (able A-6. hen the entrpy f C 3 H 8 (l s btaned frm s ut surr 15, C 3H 8 fg ( l s ( g s s ( g kj/kml K C3H8 C3H8 fg C3H8 h he entrpy values lsted n the deal gas tables are fr 1 atm pressure. Bth the ar and the prduct gases are at a ttal pressure f 1 atm, but the entrpes are t be calculated at the partal pressure f the cmpnents whch s equal t y ttal, where y s the mle fractn f cmpnent. hen, s ( (, s (, 0 ln( y he entrpy calculatns can be presented n tabular frm as u y s (,1atm uln( y m m s C 3 H O , kj/k CO H O (g O , kj/k ut surr hen the rate f entrpy eratn becmes & 190,464 15, , kj/ K ( & ( kml/mn ( kj/kml 34. kj/mn K K 44 ( per kml C H 3 8

20 EE rblem s recnsdered. he effect f the surrundngs temperature n the rate f exergy destructn s t be studed. Analyss he prblem s slved usng EE, and the slutn s gven belw. Fuel$ 'rpane (C3H8_lq' _fuel ( "[K]" _fuel [ka] m_dt_fuel 0.4 [kg/mn]*cnvert(kg/mn, kg/s Ex 1.5 "Excess ar" _ar [ka] _ar ( "[K]" _prd 100 [K] _prd [ka] Mw_ar 8.97 "lbm/lbml_ar" Mw_C3H8(3*18*1 "kg/kml_c3h8" {surrc 5 [C]} _surr surrc73.15 "[K]" "Fr theretcal dry ar, the cmplete cmbustn equatn s" "C3H8 A_th(O CO4 HO A_th (3.76 " *A_th3*4*1"theretcal O balance" "he balanced cmbustn equatn wth Ex%/100 excess mst ar s" "C3H8 (1EXA_th(O CO 4 HO (1Ex A_th (3.76 Ex( A_th O " "he ar-fuel rat n a mass bass s:" AF (1Ex*A_th*4.76*Mw_ar/(1*Mw_C3H8 "kg_ar/kg_fuel" "he ar mass flw rate s:" m_dt_ar m_dt_fuel * AF "Apply Frst Law F t the cmbustn prcess per klmle f fuel:" E_n - E_ut DELAE_cv E_n H "nce EE gves the enthalpy f gasesus cmpnents, we adjust the EE calculated enthalpy t get the lqud enthalpy. ubtractng the enthalpy f vaprzatn frm the gaseus enthalpy gves the enthalpy f the lqud fuel. h_fuel(lq h_fuel(gas - h_fg_fuel" h_fg_fuel "kj/kml frm able A-7" H 1*(enthalpy(C3H8, _fuel - h_fg_fuel (1Ex*A_th*enthalpy(O,_ar(1Ex*A_th*3.76 *enthalpy(,_ar E_ut H _ut H3*enthalpy(CO,_prd4*enthalpy(HO,_prd(1Ex*A_th*3.76* enthalpy(,_prdex*a_th*enthalpy(o,_prd DELAE_cv 0 "teady-flw requrement" "he heat transfer rate frm the cmbustn chamber s:" _dt_ut_ut"kj/kml_fuel"/(mw_c3h8 "kg/kml_fuel"*m_dt_fuel"kg/s" "kw" "Entpy Generatn due t the cmbustn prcess and heat rejectn t the surrundngs:" "Entpy f the reactants per klmle f fuel:" _O_reac 1/4.76*_ar "Daltn's law f partal pressures fr O n ar" s_o_reacentrpy(o,_ar,_o_reac

21 15-63 reac 3.76/4.76*_ar "Daltn's law f partal pressures fr n ar" s reacentrpy(,_ar, reac s_c3h8_reacentrpy(c3h8, _fuel,_fuel - s_fg_fuel "Adjust the EE gaseus value by s_fg" "Fr phase change, s_fg s gven by:" s_fg_fuel h_fg_fuel/_fuel 1*s_C3H8_reac (1Ex*A_th*s_O_reac (1Ex*A_th*3.76*s reac "Entpy f the prducts per klmle f fuel:" "By Daltn's law the partal pressures f the prduct gases s the prduct f the mle fractn and _prd" _prd 3 4 (1Ex*A_th*3.76 Ex*A_th "ttal kml f prducts" _O_prd Ex*A_th/_prd*_prd "atral pressure O n prducts" s_o_prdentrpy(o,_prd,_o_prd prd (1Ex*A_th*3.76/_prd*_prd "atral pressure n prducts" s prdentrpy(,_prd, prd _CO_prd 3/_prd*_prd "atral pressure CO n prducts" s_co_prdentrpy(co, _prd,_co_prd _HO_prd 4/_prd*_prd "atral pressure HO n prducts" s_ho_prdentrpy(ho, _prd,_ho_prd 3*s_CO_prd 4*s_HO_prd (1Ex*A_th*3.76*s prd Ex*A_th*s_O_prd "nce _ut s the heat rejected t the surrundngs per klmle fuel, the entrpy f the surrundngs s:" _surr _ut/_surr "ate f entrpy eratn:" _dt_ ( - _surr"kj/kml_fuel"/(mw_c3h8 "kg/kml_fuel"*m_dt_fuel"kg/s" "kw/k" X_dt_dest _surr*_dt_"[kw]" surrc [C] X dest [kw] ] W [k s t X de surrc [C]