Cheical Reactins 14-14 rpane is burned wi 75 percent excess during a cbustin prcess. The AF rati is t be deterined. Assuptins 1 Cbustin is cplete. The cbustin prducts cntain CO, H O, O, and N nly. rperties The lar asses f C, H, and are 1 kg/kl, kg/kl, and 9 kg/kl, respectively (Table A-1). Analysis The cbustin equatin in is case can be written as CH + 175. a O + 3.76N 3CO + 4HO+ 0. 75a O + ( 175. 376. ) a N 3 8 where a is e stichietric cefficient fr. We have autatically accunted fr e 75% excess by using e factr 1.75a instead f a fr. The stichietric aunt f xygen (a O ) will be used t xidize e, and e reaining excess aunt (0.75a O ) will appear in e prducts as free xygen. The cefficient a is deterined fr e O balance, O balance: 175. a 3+ + 075. a a 5 Substituting, CH + 875. O + 376. N 3CO + 4HO+ 375. O + 39. N 3 8 The - rati is deterined by taking e rati f e ass f e t e ass f e, AF ( 8.75 4.76kl)( 9kg/kl) ( 3kl)( 1kg/kl) + ( 4kl)( kg/kl) 7.5 kg/kg 14-15 Acetylene is burned wi e stichietric aunt f during a cbustin prcess. The AF rati is t be deterined n a ass and n a le basis. Assuptins 1 Cbustin is cplete. The cbustin prducts cntain CO, H O, and N nly. rperties The lar asses f C, H, and are 1 kg/kl, kg/kl, and 9 kg/kl, respectively (Table A-1). Analysis This is a eretical cbustin prcess since C H is burned cpletely wi stichietric aunt f. The stichietric cbustin equatin f C H is CH + a O + 376. N CO + HO+ 376. a N O balance: a + 05. a 5. Substituting, C H 100% eretical rducts CH + 5. O + 376. N CO + HO+ 94. N The - rati is deterined by taking e rati f e ass f e t e ass f e, AF (.5 4.76kl)( 9kg/kl) ( kl)( 1kg/kl) + ( 1kl)( kg/kl) 13.3 kg/kg On a le basis, e - rati is expressed as e rati f e le nubers f e t e le nubers f e,.5 4.76 kl AF 11.9 kl / kl 1kl 14-3
Cheical Reactins 14-19 Octane is burned wi 50 percent eretical during a cbustin prcess. The AF rati and e dew-pint teperature f e prducts are t be deterined. Assuptins 1 Cbustin is cplete. The cbustin prducts cntain CO, H O, O, and N nly. 3 Cbustin gases are ideal gases. rperties The lar asses f C, H, and are 1 kg/kl, kg/kl, and 9 kg/kl, respectively (Table A-1). Analysis (a) The cbustin equatin in is case can be written as C H +.5a O + 3.76N 8CO + 9H O + 1.5a O + (.5 3.76) a N 8 18 where a is e stichietric cefficient fr. It is deterined fr C 8 H 18 O balance: 5. a 8+ 45. + 15. a a 15. Substituting, 5 C CH + 315. O + 376. N 8CO + 9HO+ 18. 75O + 117. 5N 8 18 Air Cbustin chaber 1 at rducts AF ( 31.5 4.76kl)( 9kg/kl) ( 8kl)( 1kg/kl) + ( 9kl)( kg/kl) 37.8 kg/kg (b) The dew-pint teperature f a gas-vapr ixture is e saturatin teperature f e water vapr in e prduct gases crrespnding t its partial pressure. That is, T v dp N N T v prd prd sat@5.951 ka 9 kl 153.5 kl 35.7 C ( 101.35 ka) 5.951 ka 14-7
Cheical Reactins 14-4 The vluetric fractins f e cnstituents f a certain natural gas are given. The AF rati is t be deterined if is gas is burned wi e stichietric aunt f dry. Assuptins 1 Cbustin is cplete. The cbustin prducts cntain CO, H O, and N nly. rperties The lar asses f C, H, N, O, and are 1 kg/kl, kg/kl, 8 kg/kl, 3 kg/kl, and 9 kg/kl, respectively (Table A-1). Analysis Cnsidering 1 kl f, e cbustin equatin can be written as (0.65CH + 0.08H + 0.18N + 0.03O + 0.06CO ) + a (O + 3.76N ) xco + yh O + z N 4 The unknwn cefficients in e abve equatin are deterined fr ass balances, C: H: O: 0. 65 + 0. 06 x 065. 4+ 008. y 0. 03 + 0. 06 + a x+ y/ æææ æææ æææ x 0. 71 y 138. a 131. N : 018. + 376. a z æææ z 5106. (. 0 65CH4 + 0. 08H + 018. N + 0. 03O + 0. 06CO) + 131. ( O + 376. N) 071. CO + 138. H O + 5106. N The - rati fr e is reactin is deterined by taking e rati f e ass f e t e ass f e, and AF ( 1.31 4.76 kl)( 9 kg/kl) 180.8 kg ( 0.65 16 + 0.08 + 0.18 8 + 0.03 3 + 0.06 44) kg 19. kg, 180.8 kg 19. kg 9.4 kg / kg 14-11
Cheical Reactins 14-6 The cpsitin f a gaseus is given. It is burned wi 130 percent eretical. The AF rati and e fractin f water vapr at wuld cndense if e prduct gases were cled are t be deterined. Assuptins 1 Cbustin is cplete. The cbustin prducts cntain CO, H O, O, and N nly. rperties The lar asses f C, H, N, and are 1 kg/kl, kg/kl, 8 kg/kl, and 9 kg/kl, respectively (Table A-1). Analysis (a) The is burned cpletely wi excess, and us e prducts will cntain H O, CO, N, and se free O. Cnsidering 1 kl f, e cbustin equatin can be written as (0.60CH + 0.30H + 0.10N ) + 1.3 a (O + 3.76N ) xco + yh O + 0.3a O + z N 4 The unknwn cefficients in e abve equatin are deterined fr ass balances, C: H: O: 060. x 060. 4+ 030. y 13. a x+ y/ + 03. a æææ æææ æææ x 060. y 150. a 135. N : 0. 10 + 3. 76 13. a z æææ z 6. 70 (0.60CH + 0.30H + 0.10N ) + 1.755(O + 3.76N ) 0.6CO + 1.5H O + 0.405O + 6.7N 4 The - rati fr e is reactin is deterined by taking e rati f e ass f e t e ass f e, and AF ( 1.755 4.76 kl)( 9 kg/kl) ( 0.6 16 + 0.3 + 0.1 8) kg 13.0 kg 4.3 kg, 4.3 kg 13.0 kg 18.6 kg / kg (b) Fr each kl f burned, 0.6 + 1.5 + 0.405 + 6.7 9.05 kl f prducts are fred, including 1.5 kl f H O. Assuing at e dew-pint teperature f e prducts is abve 0 C, se f e water vapr will cndense as e prducts are cled t 0 C. If N w kl f H O cndenses, ere will be 1.5 - N w kl f water vapr left in e prducts. The le nuber f e prducts in e gas phase will als decrease t 9.05 - N w as a result. Treating e prduct gases (including e reaining water vapr) as ideal gases, N w is deterined by equating e le fractin f e water vapr t its pressure fractin, N v v 15. N w.339 ka N w 13. kl N 905. N 101.35 ka prd, gas prd w since v sat @ 0 C.339 ka. Thus e fractin f water vapr at cndenses is 1.3/1.5 0.88 r 88%. 14-7 EES slutin f is (and er cprehensive prbles designated wi e cputer icn) is available t instructrs at e Instructr Manual sectin f e Online Learning Center (OLC) at www.hhe.c/cengel-bles. See e reface fr access infratin. 14-13
Cheical Reactins 14-57 Eane gas is burned wi stichietric aunt f during a steady-flw cbustin prcess. The rate f heat transfer fr e cbustin chaber is t be deterined. Assuptins 1 Steady perating cnditins exist. Air and cbustin gases are ideal gases. 3 Kinetic and ptential energies are negligible. 4 Cbustin is cplete. &Q rperties The lar ass f C H 6 is 30 kg/kl (Table A-1). Analysis The eretical cbustin equatin f C H 6 is C H 6 5 C Cbustin chaber rducts Air 800 K CH 6 + a ( O + 3.76N ) CO + 3H O + 3.76a N 1 at 500 K where a is e stichietric cefficient and is deterined fr e O balance, a + 1.5 3.5 Then e actual cbustin equatin can be written as ( O + 3.76N ) 1.9CO + 0.1CO + 3H O + 0.05O C + H 6 + 3.5 13.16N The heat transfer fr is cbustin prcess is deterined fr e energy balance Ein Eut Esyste applied n e cbustin chaber wi W 0. It reduces t Q ut N ( h f + h h ) N R ( h f + h h ) Assuing e and e cbustin prducts t be ideal gases, we have h h(t). Fr e tables, R h f h 500 K h 98 K h 800 K Substance kj/kl kj/kl kj/kl kj/kl C H 6 (g) -84,680 --- --- --- O 0 14,770 868 4,53 N 0 14,581 8669 3,714 H O (g) -41,80 --- 9904 7,896 CO -110,530 --- 8669 3,844 CO -393,50 --- 9364 3,179 Q ut ( 1.9)( 393,50 + 3,179 9364) + ( 0.1)( 110,530 + 3,844 8669) ()( 3 41,80 + 7,896 9904) + ( 0.05)( 0 + 4,53 868) + ( 13.16)( 0 + 3,714 8669) ()( 1 84,680 + h h ) ( 3.5)( 0 + 14,770 868) ( 13.16)( 0 + 14,581 8669) + 98 1, 01, 005 kj / kl C 98 H 6 r Q ut 1,01,005 kj / kl CH6 Then e rate f heat transfer fr a ass flw rate f 3 kg/h fr e eane beces Q& NQ & & Q N 5 kg/h 30 kg/kl ( 1,01,005 kj/kl) 00,170 kj/h ut ut ut 14-33
Cheical Reactins Adiabatic Flae Teperature 14-63C Fr e case f stichietric aunt f pure xygen since we have e sae aunt f cheical energy released but a saller aunt f ass t absrb it. 14-64C Under e cnditins f cplete cbustin wi stichietric aunt f. 14-65 [Als slved by EES n enclsed CD] Hydrgen is burned wi 0 percent excess during a steadyflw cbustin prcess. The exit teperature f prduct gases is t be deterined. Assuptins 1 Steady perating cnditins exist. Air and cbustin gases are ideal gases. 3 Kinetic and ptential energies are negligible. 4 There are n wrk interactins. 5 The cbustin chaber is adiabatic. Analysis Adiabatic flae teperature is e teperature at which e prducts leave e cbustin chaber under adiabatic cnditins (Q 0) wi n wrk interactins (W 0). Under steady-flw cnditins e energy balance Ein Eut Esyste applied n e cbustin chaber reduces t N ( h f + h h ) N R ( h f + h h ) The cbustin equatin f H wi 0% excess is ( O + 3.76N ) H O + 0.1O H + 0.6 +.56N Fr e tables, R H 7 C Air 0% excess 7 C Cbustin chaber rducts T h f h 80K h 98 K Substance kj/kl kj/kl kj/kl H 0 7945 8468 O 0 8150 868 N 0 8141 8669 H O (g) -41,80 996 9904 ()( 1 41,80 + h 9904) + ( 0.1)( 0 + h 868) + (.56)( 0 + h 8669) HO O N ( 1)( 0 + 7945 8468) + ( 0.6)( 0 + 8150 868) + (.56)( 0 + 8141 8669) It yields h + 01. h +. 56h 70, 116 kj HO O N The adiabatic flae teperature is btained fr a trial and errr slutin. A first guess is btained by dividing e right-hand side f e equatin by e ttal nuber f les, which yields 70,116/(1 + 0.1 +.56) 80,488 kj/kl. This enalpy value crrespnds t abut 400 K fr N. Nting at e ajrity f e les are N, T will be clse t 400 K, but sewhat under it because f e higher specific heat f H O. At 300 K: h H 0.1.56 ( 1)( 98,199) ( 0.1)( 79,316) (.56)( 75,676) O + ho + h N + + 76,856kJ ( Higher an 70,116 kj) At 50 K: h H 0.1.56 ()( 1 95,56) ( 0.1)( 77,397) (.56)( 73,856) O + ho + h N + + 69,91kJ ( Lwer an 70,116 kj) By interplatin, T 51.4 K 14-38