Handout Problems with Solutions - Engineering Thermodynamics | MAE 301, Study notes of Thermodynamics

Download Handout Problems with Solutions - Engineering Thermodynamics | MAE 301 and more Study notes Thermodynamics in PDF only on Docsity! CUM (3 H ILL ltV /0 s ec ) JA q. 8' $ce;.l. ~O(X) "" ~ \ r, M ~ So;VI : qg~ too ·IJM IJSu.'l. 2-3<­ \cPt' i .e\ ~ ~ <'f.fl Sc."" 30° !t,. ,. a., w- W T/tr11l2. :J"oulC- ='8 I~O W I b) VI':: f'i1/,~t..0 Vz.. ':. '30 Iftl. ) 100 ~~_o 2. 1.. Vz. - V; -::. <1 tV I 00{) IJ 1-'1 b,(,,-s \ -:: fY) -:. zeoo " ~ I~ iJ ~<c.~2.1 c, 2~ 'II: IJJ/J I. oQt> AlItA IO~ ~:: 3'5 ",,(~ vl.~ 5 M/5':('" L(/'.'t"I ~ ZoftJO" ~ '2.5 ;;:... - \"2.:£.1$ M '1sec. '" -= -) 200 000 ) ) jJ,.,.. 2* I '"'i M IJ~"" • W':: '0 sa. J VI";..\,) o /0 ". /'U/TO 'J \..v"l- r'l, ....i. ~ :l: -+ .1 ~~.11+ ~\ +W (Ib~,-L):' -~ f + 1"~e- 1c.. .HtIJ r l.3'" v 2._ V 2- I ()O M"Y1.I.(. l_ 0 '2- I /J'M vJ ( '1>£4 L) -::. 5>0-r:,w . 2.,,, Lit- (~ ':: ~ JJ $c.t..... , • ~ tV'\ Wr:.1tNWr:MJ M3 ~ ~ ~M f V -- (.,g M'J, ~ Lf -Sec.. ': t.t ,ry 2- ~ 1 V -::. 2. rY\ lsec :t el«.-h-,c,'"T ~ctk~ rr,c E ~ 0,09 !Ij:W ~ 41~,--h-1"~ oer = l 0.03 / )c:l.Nh rrrrrrrtr» 1, PV.N'P TlMo!t :., 0 tv. I d4'1Pv,ttr -1V'I.~r e+.C- =o. "5 -+v.r~,ne. ,,~t)~"o.~r'" e~-:: 0.,7'> ~rb,ne 1l"o'Z. -= \ 0 """'- I dtJ."t W-M- f IY/l- El£ c. CoS.T =: IV.jAIt- AC.iLiA L i"'t,..(RBIAJE: Wt"(~~A-L) = 0.?511­ ?'B-z.·Y I'-w ': Sgt,,8 "w ~ S\3(..el(....uJ ... 'OM a:a.." ~ 3l. S da.'1 '10-..... -:: ¥'lr J'3'ic./ylt­ 114 t.~ '7 ( ~ .., p\ ": t~"1-4-q.f Sec­ -+ 88\(J:lO ~ '- _ ~ (o,,";I\Il)~ _ #J f\ ~ "DJ !,r.. -;-l.. T \'00c. 2~.1, 0" 7 TABLE A-13 SUoerheated refrizerant-I T °C Sat. -20 01.- 1 -10 0 1-\ > 10p\l -:; ." 20 30 40 50 60 70 80 90 100 34a v u h s m3/kg kJ/kg kJ/kg kJ/kg . K v u h s m3/kg kJ/kg kJ/kg kJ/kg' K P = 0.05 MPa (Tsat = -35.95°C) P = 0.10 MPa (Tsat = -25.37"C) 0.31121 209.12 227.79 0.9544 0.19254 215.19 234.44 0.9518 0.33508 220.50 240.75 1.0174 0.19841 219.56 239.50 0.9721 0.35048 227.55 248.58 1.0477 0.20743 226.75 247.49 1.0030 \ 0.36476 234.56 256.54 1.0774 0.21630 233.95 255.58 1.0332 0.37893 241.92 264,66 1.1066 0.22506 241.30 263.81 1.0628 0.39302 249.35 272.94 1.1353 0.23373 248.79 272.17 1.0918 0.40705 256.95 281.37 1.1636 0.24233 256.44 280.68 1.1203 0.42102 264.71 289.97 1.1915 0.25088 264.25 289.34 1.1484 0.43495 272.64 298.74 1.2191 0.25937 272.22 298.16 1.1762 0.44883 280.73 307.66 1.2463 0.26783 280.35 307.13 1.2035 0.46269 288.99 316.75 1.2732 0.27626 288.64 316.26 1.2305 0.47651 297.41 326.00 1.2997 0.28465 297.08 325.55 1.2572 0.49032 306.00 335.42 1.3260 0.29303 305.69 334.99 1.2836 0.50410 314.74 344.99 1.3520 0.30138 314.46 344.60 1.3096 I • /0 - • (;> (..10 - .ClCf01.l Cl-t p::. .10 T::..(5T~ rS ~ ~ 'ZJ, '3. e' or 'Z.'1't..(1 2­ ~ ~ 1.~1."'" 3-31 (~r,) , f" ,o"Z.I01,7 - • o'Z-oi'l.3 • , _ • 0 "to Y • f - ,(;) I. • 0'20 e.l./ ,0 q<?y 11;'- ,'l.,O'7t.JJ ,IIJ- .oqCJ"t .1_ ,DC, 11:- • 2417 I ) /:} V -e, o.~;; Jr (. to$: '" 4 - . 1-"50 'L-) ':" 19, /) ZJ) IS? m -- , . , , , , ( , ~ I SUfERt4E.AT£.D ~'j1:...Jt. I , \If' pol ra ,PI :: 18D r&)Q. I I I Ti": S t/(.lI F' / r=t 3 II 1lj ~ ~. 0" 3 '$ l"b:;", I , TAJ3LE I't-t.,. E Mf z: (/-"')(z.-) 'Vf +:XL -zr; -:: ('-Xz,.) (.Ol?) -+ ;KL (, 'l,6It) z: (3,f.J1./33- ,0/7) f (1'3.'61' - .(lI?) = O..Z/cr~ J {;-Jl.J --R f + 7*2- ~1 - . ~~ -+ 'Z./!.(.J-t O,Z'Clfjl * <f4!t,VI _ TABLE A-4E Saturated water-Temperature table Specific volume, Internal energy, Enthalpy, Entropy, ­ ft3/lbm Btu/Ibm Btu/Ibm Btu/Ibm· R -Sat. Sat. Sat. Sat. Sat. Sat. Sat. Sat. Sat. Temp., press., liquid, vapor, liquid, Evap., vapor, liquid, Evap., vapor, liquid, Evap., vapor, T of Psat psia v, n, hvg uf ufg "« hfg g Sf Sfg Sg 210 14.136 0.01670 27.798 178.15 898.68 1076.8 178.20 971.35 1149.5 0.30922 1.45046 1.7597 212 14.709 0.01671 26.782 180.16 897.24 1077.4 180.21 970.09 1150.3 0.31222 1.44427 1.7565 220 17.201 0.01677 23.136 188.22 891.43 1079.6 188.28 965.02 1153.3 0.32414 1.41980 1.7439 230 20.795 0.01684 19.374 198.31 884.10 1082.4 198.37 958.59 1157.0 0.33887 1.38989 1.7288 240 24.985 0.01692 16.316 208.41 876.70 1085.1 208.49 952.06 1160.5 0.35342 1.36069 1.7141 250 29.844 0.01700 13.816 218.54 869.21 1087.7 218.63 945.41 1164.0 0.36779 1.33216 1.6g.~9 260 35.447 0.01708 11.760 228.68 861.62 1090.3 228.79 938.65 1167.4 0.38198 1.30425 1.6862 I I ~u I>! Il.l-+E.A-r'e.p V/ATE.-,.. VAf'<J 2 1\ ": Z SO 0,,­ '7 • TABLE A-6 Superheated water v u h 5 m3/kg kJ/kg kJ/kg kJ/kg' K P = 0.05 MPa (81.32°C) Sat.! I 3.2403 2483.2 2645.2 7.5931 50 100 3.4187 2511.5 2682.4 7.6953i 3.8897 2585.7 2780.2 7.9413150 200 250 300 400 500 600 700 I 800 : 900 1000 1100 1200 1300 Sat. 200 250 300 350 400 500 ' 600 4.3562 2660.0 2877.8 8.1592 4.8206 2735.1 2976.2 8.3568 5.2841 2811.6 3075.8 8.5387 6.2094 2968.9 3279.3 8.8659 7.1338 3132.6 3489.3 9.1566 8.0577 3303.1 3706.0 9.4201 8.9813 3480.6 3929.7 9.6626 9.9047 3665.2 4160.4 9.8883 10.8280 3856.8 4398.2 10.1000 11.7513 4055.2 4642.7 10.3000 12.6745 4259.9 4893.7 10.4897 13.5977 4470.8 5150.7 10.6704 14.5209 4687.3 5413.3 10.8429 P = 0.60 MPa (158.83°C) 0.31560 2566.8 0.35212 2639.4 r..-----~ <-Q.~9390) 2721.2 0.43442 2801.4 0.47428 2881.6 0.51374 2962.5 0.59200 .q'?R? 2756.2 6.7593 2850.6 6.9683 2957.6 7.1833 3062.0 7.3740 3166.1 7.5481 3270.8 7.7097 ~l1Q~ 11 II f"\f"\~ 1 V u h m3/kg kJ/kg kJ/kg P = 0.10 MPa (99.6P\ 1.6941 2505.6 2675.0 1.6959 2506.2 2675.8 1.9367 2582.9 2776.6 2.1724 2658.2 2875.5 2.4062 2733.9 2974.5 2.6389 2810.7 3074.5 3.1027 2968.3 3278.6 3.5655 3132.2 3488.7 4.0279 3302.8 3705.6 4.4900 3480.4 3929.4 4.9519 3665.0 4160.2 5.4137 3856.7 4398.0 5.8755 4055.0 4642.6 6.3372 4259.8 4893.6 1 6.7988 4470.7 5150.6 1 7.2605 4687.2 5413.3 1 P = 0.80 MPa (170.41°C: 0.24035 2576.0 2768.3 6 ~2631.1 2839.8 6 .29321'2715.9 2950.4 7 0.324162797.5 3056.9 7 0.35442 2878.6 3162.2 7 0.38429 2960.2 3267.7 7 rv .... If")"'")" ,,11"'lr r­ ..... ,...1 .... ~ f-U~ . g *" ,-z.Cl3z..1 -= ,;7..3"/ S c: '2J;j -;. 4. ~ q z,Lj '6 (T,,~{..F- ;4-'"1) 1fj -= -v;. -= O. 3<t, "'" ",' {~ f'V-:. .k* .3'L~O ':' ."l..'3'-3 q T l -=. 2. $.0 0 c, p-,r- .2 311Sf. ~2.3('J4- .'l.!"I$' . 3'" v·IS - . 2952. I . 343qo - . ,q,3 1- J P-V-: ."23 '3/$ 0,£.,0' I (3.841 The specific volume of steam is to be determined using the ideal gas relation, the compressibility ~ and the steam tables. The errors involved in the first two approaches are also to be determined. Properties The gas constant, the critical pressure, and the critical temperature of water are, from Table A-I, R = 0.4615 kPa'm3/kg-K, i: = 647.1 K, Per = 22.06 MPa Analysis (a) From the ideal gas equation of state, 3/kg·K)(673 v = RT = (0.4615 kPa·m K) = 0.03106 m3/kg (17.6% error) P (10,000 kPa) (b) From the compressibility chart (Fig. A-IS), P .s.. 10MPa OA53}R Per 22.06 MPa Z =0.84 T =.I..- = 673 K =1.04 R r.; 647.1 K Thus, v = ZVideaJ = (0.84)(0.03106 m ' /kg) = 0.02609 m3/kg (1.2% error) (c) From the superheated steam table (Table A-6), P = 10 MPa J 00 6 3T = 4000C v = . 2 44 m /kg or l.1r-----,--r----r--...,-------,---r--.,........----r--..,-----;---~--..,-----,---- ./~ 09' 't:I" z/ 1R =1.00 . /w - - - II x Methane - Iso-pentane o Ethylene g n-Heptane '" Ethane to Nitrogen o Propane e Carbon dioxide On-Butane • Water Average curve based on data on hydrocarbons I I Legend: 1R 2.00 ,I I 0.4 I I 0.3 I I I 0.2 I I I 0.1 I 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Reduced pressure PR FIGURE 3-51