ME 300 Exam 2 November 18, :30 p.m. to 7:30 p.m.

Transcription

1 CICLE YOU LECTUE BELOW: Frst Name Last Name 1:3 a.m. 1:3 p.m. Nak Gore ME 3 Exam November 18, 14 6:3 p.m. to 7:3 p.m. INSTUCTIONS 1. Ths s a closed book and closed notes examnaton. You are provded wth an equaton sheet and all the needed property tables.. Do not hestate to ask the nstructor f you do not understand a problem statement. 3. Start each problem on the same page as the problem statement. Wrte on only one sde of the page. Materals on the back sde of the page wll not be graded. 4. ut only one problem on a page. Another problem on the same page wll not be graded. 5. Identfy your system(s), lst relevant assumptons, and start wth basc equatons. 6. If you gve multple solutons, you wll receve only a partal credt although one of the solutons mght be correct. Delete the soluton you do not want graded. 7. For your own beneft, please wrte clearly and legbly. Maxmum credt for each problem s ndcated below. 8. After you have completed the exam, at your seat put your papers n order. Ths may mean that you have to remove the staple and re-staple. Do not turn n loose pages. 9. Once tme s called you wll have three mnutes to turn n your exam. onts wll be subtracted for exams turned n after these three mnutes. roblem ossble Score Total 1 1

2 Frst Name Last Name roblem 1 (5 ponts) Gven: Lqud ethanol (C H 5 OH) enters a combuston chamber at 1 atm and 5ºC and reacts wth 1% theoretcal ar also enterng at 1 atm and 5ºC. roducts of complete combuston (neglect product dssocaton) ext from the combuston chamber at 1 atm and 17 ºC. Fnd: (a) Wrte the balanced chemcal reacton for complete combuston of lqud ethanol wth 1% theoretcal ar. (b) Does condensaton occur n the products? You must provde quanttatve justfcaton to support your answer. (c) Calculate the heat transfer (/kg fuel) durng the chemcal reacton. Indcate whether t s nto the combuston chamber or out of the combuston chamber. Molecular Weght of Ethanol = 46.7 kg/kmol Identfy your system(s), lst relevant assumptons, and start wth basc equatons. C H 5 OH 1 atm, 98 K 1% Theoretcal Ar 1 atm, 98 K Combuston Chamber +1 Complete Combuston roducts 1 atm, 4 K Assumptons - Steady state - One-dmensonal flow - Ignore KE and E changes - No work nteracton W CV - eactants and products exhbt deal gas behavor - Ntrogen s nert - Dalton s model s applcable Basc Equatons de CV e Q CV W CV m h gz me he gze Q CV me he m h dt e e

3 roblem 1 (contnued) Frst Name Last Name Q n h n h Dvdng by molar flow rate of fuel Q n h n h CV CV Soluton (a) For complete combuston wth 1% theoretcal ar (stochometrc = 1) C H 5 OH + a(o N ) xh O + yco + zn erformng atom balances: H: 6 = x x = 3 C: = y O: a + 1 = x + y a = 3 N: 3.76 a = z z = 11.8 C H 5 OH + 3(O N ) 3H O + CO N +4 for 1% ar moles For complete combuston wth 1% theoretcal ar C H 5 OH + (1. 3)(O N ) xh O + yco + zn + wo erformng atom balances: H: 6 = x x = 3 C: = y O: = x + y + w w =.6 each for moles of H O, CO, O, and N N: = z z = C H 5 OH + 3.6(O N ) 3H O + CO +.6O N (b) artal pressure of water vapor n products: nho 3 vapor 1 atm.1568 atm.1589 bar + ntotal Usng Table A-: Tdp Tsat vapor 55 C + Snce the product temperature of 17ºC s hgher than the dew pont temperature of product mxture, no condensaton occurs n the product mxture.e. all water s vapor. + (c) Consderng energy balance, heat transfer durng the chemcal reacton: Q n h n h h T h h ;,, CV f s nh 1 hchohl ho h N98 K 1hf h98 Kh98 K 3.6hf h98 Kh98 K CHOH 5 (l) hf h 98 K h 98 K Stable Elements N Usng Table A-5: nh 77, O

4 Frst Name Last Name roblem 1 (contnued) nh 3h h.6h h HOg CO O N 4 K nh 3h h4 K h98 K h h4 K h98 K f f H O ( g ) CO.6h h 4 K h 98 K h h 4 K h 98 K f f O N +4 Stable Elements Usng Table A-3: nh 3 41,8 13,356 9,94 393,5 13,37 9, ,7118, ,64 8,6691,45,95 +8 QCV nh nh 1,6,583 77,691,174,45 + 1,174, 45 Heat transfer durng the chemcal reacton: Q Q 5,49 kg 46.7 kg-fuel Q heat rejected from the combuston chamber to the surroundngs + 4

5 Frst Name Last Name roblem (5 ponts) Gven: Consder the reacton NO NO + O relevant to the producton of oxdes of ntrogen. Followng data s known for the gaseous speces. h f (/kmol) O 49,173 NO 9,91 NO 33,95 h ( K) - h (98 K) s ( K) (/kmol) (/kmol-k) 35, , , Fnd: (a) Calculate the equlbrum constant for the reacton at K. (b) At K, the equlbrum composton conssts of.5 moles each of NO, NO, and O. Calculate the pressure (atm) of the system. (c) At constant temperature, what s the effect of ncreasng pressure on the number of moles of NO n the system? You must justfy your answer wth an equaton. (d) At constant pressure, what s the effect of ncreasng temperature on the number of moles of NO n the system? You must justfy your answer wth an equaton. Unversal Gas Constant = /kmol-k Lst relevant assumptons and start wth basc equatons. Assumptons - eactants and products exhbt deal gas behavor - Dalton s model s applcable Soluton (a) ln K T p +5 GT T where G g g 1g 1g 1g T NO O NO, K K K K 98 K g T h T Ts T h h Ts T f, s gno hno TsNO hf,no hno hno TsNO K gno 9, 91 57,859 K ,16 kmol kmol kmol-k kmol 5

6 Frst Name Last Name roblem (contnued) K K K K 98 K K g h Ts h h h Ts go 49,173 35, 713 K , 68 kmol kmol kmol-k kmol O O O f,o O O O K K K K 98 K K g h Ts h h h Ts NO NO NO f,no NO NO NO gno 33, 95 87, 59 K , kmol kmol kmol-k kmol G T 7,58 kmol 7,58 ln K K kmol p K kmol-k K K.191 Equlbrum constant for the reacton at K: p n roducts nno n O p 1 atm 1 n n total ref ntotal ref 1 atm n NO eactants K atm (b) K T K p ressure of the equlbrum product mxture at K: (c) At constant temperature: K T p.5736 atm nno n O 1 n n NO total ref Wth ncreasng pressure, the second term ncreases number of moles of NO ncrease snce K p does not change at constant temperature Le Chateler rncple: Snce number of moles ncrease durng the forward reacton, the reacton proceeds to a drecton wth lower number of moles when pressure ncreases.e. towards more moles of reactant NO for explanaton usng K p equaton 6

7 roblem (contnued) (d) Frst Name Last Name H h h 1h 1h 1h NO O NO hno 9, 91 57, ,15 kmol kmol kmol ho 49,173 35, ,886 kmol kmol kmol hno 33, 95 87, 59 1,354 kmol kmol kmol H 31,68 reacton s endothermc kmol K At constant pressure: p T H 1 1 ln +5 for explanaton usng van t Hoff equaton Kp T1 T1 T Wth ncreasng temperature, snce the reacton s endothermc K p ncreases number of moles of NO decrease Le Chateler rncple: Snce heat s absorbed (endothermc) durng the forward reacton, the reacton proceeds to a drecton where heat s released when temperature ncreases.e. towards products NO and O 7