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exam 1 solution - AERO 489-502: Thermodynamics for...

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Unformatted text preview: AERO 489-502: Thermodynamics for Aerospace Engineers 1” Mid-term examination Feb. 22, 2006 Make sure that your copy of the exam has 5 numbered pages. While checking, please write your name and UIN on the first page, and your name at the bottom of each page in the exam. Read the problems carefully before starting. Some problems are easier than others, and you may want to approach these first (or last). While solVing the problems, try to write as cleanly as possible. If you find that you need more space for any problem, please write on the reverse of the page. Note: Feel free to use any notes or books you may consider useful. You have 120 mins. Good luck! “An Aggie does not lie, cheat, or steal, or tolerate those who do.” Name & UID Problem 1 (30%): Using the tables of properties of superheated water vapor (pp. 764-767 of the class text), calculate k of water vapor at P = 3 bar and T = 500° C (k=c,,/c..) (Hint: use the original definition of 6,, and 0,). Next, calculate k for water vapor assuming it is an ideal gas (use Table A-21; if you’re pressed for time, use Fig. 3.13). Compare the two k’s, and comment briefly. ~ falméflz 2%/2 9.1.4.. ASSWM ' "’aT/vv AT v ET P AT 9 61mm 4: Rngow‘ J fi=509°¢ .3,> U7¢4_18.Z 7% M4: 380 iii/{SD 241: 3486 KT/kf‘ mil” (2.) ms 2:235” : (java 76,144006 Val/was Z w "247, Kg 6m¢¢ro+Zfiz2¥$ l4 s, , L3 Cy 3 3 2 Urus } AT V2V: «7: v 3 l /% T j Vs~w a 580,255,333 \CT/go M7 12:17.5? (Cu/r Ll W’IZO +28~273 K W” ( We 21mm - Q7 1155 —3 l ’6 ,0, 3 lde 3% Cr/é: 40:54 tosxio 11-14mm 7-2%qu 1+ "" l2 ’3 Q” 4613552383 E; , +080th TA a was: 63* Q: QO%W2=3§.E E3; ,3 18 KKK swam».- ‘ ( aloowl’ . The Ohm,” Nazi/{,1 / 1 A , ‘t MW 033:: "iii/vet 351'? a? CV a x- Problem 2 (30%): The chamber shown schematically in the figure below has adiabatic walls and is divided by a thin diaphragm into two compartments A and B. Both compartments contain water vapor (which CAN NOT be assumed to be an ideal gas). Compartment A has a volume of l m3 and the initial conditions in it are PA=lO bar, TA=600°C. Compartment B has a volume of 2 m3 and the initial conditions in it are PB=l bar, TB=200°C. Suddenly, the diaphragm is ruptured and the tw0 quantities of vapor mix until a final state is reached. What is the final pressure and temperature in the chamber? (Hint: if you need to interpolate between table values, assume that property numbers that differ by less than 1% are identical, i.e. if lbl—bgl/b. or lbl‘bzllbg < l%, then b.=b3) //////// // pA: 10W // // TA:QOQ°C > l%.£io()=:ngjQ@lOW W A3) // A // #9 ‘ Jaw // 9 /m/s‘ub/flo{(éaét6/ Egzl loaf Tb: 260% flagfc: Eathwx{/\3\ =5) l/m‘ “*4 : \IA: Mon M}ij , MA: 329sz iii/k5 flat-$358393 “3/5 vg: 2.112 axe/5: , @2263! wt; , beams la3/5» Whasit WA: VAKA :- —: \/ 3 rm 3 e : 2m __ 8 ’45 /2/H2w3/,_5 " 0321 E” H”: A+W8 : 3.414 243 was; Gauqu (335%; Vfim 7: VA “Ink/e, “7" 3 W3 3 fl ,,,, M c? w 61a? Cmmbw -. AffiCrA/Qéa—AU z/QK-W =43 505:0 a; UA+nguflM “WM+W§@=M%fi%W as mflx=@EE:%EE:ZEE§§£&EEA$E§ «4:3 M5”: WA-HMB fa giqlqw We have 1/200 Fwd/ho? (V5.4 MEWS we, Cam HM, mi“ Wyflfirhfiw @ fl 1 5-0 W [nil/w Jomsl of u lg U133l2‘8'4‘ K: I . / C? PinbObour Ala, Cchs‘i' web/30+ u is Mzgfigo . W T211500 C OLA/b SM?” Ufim QW’EUZ “’7 iE'M:W=Tz=/5booc, W ‘2 U “Meme i“? WA Prim ’ (P‘v’Pfl/fiamwhzkfiwwh “ 4%" 4‘2 e3lam=42raz7 WM.) ,1 A , \ “like; W’QQNQ 1% 53:5; assauflplww Wauici 5W9, Ramada +%\C@A+W5\RTPM mam a» vfimzmew MW}. 3 Problem 3 (25%): After graduation you begin working at a rocket company. One of your first tasks is to study DiMethylHydrazine (DMH for short, chemical formula C2H3N2). This is a rather dangerous rocket propellant fluid (not a solid). One day, a colleague brings a sealed container of DMH to your bench, stating that the container holds 1 kg of saturated DMH. You forget to ask if the DMH is saturated liquid or saturated vapor. You leave the container on your bench, next to a l-Liter bottle of your favorite soda (not too close, DMH is really dangerous) and start thinking about the problem: What is the quality x of the DMH in the container? The National Institute of Health (NIH) offers the following information on DMH (amongst numerous warnings): Critical temperature 523 K, critical pressure 5.42 MPa. Atomic Weights of C: l2, of H: l, and of N: l4 (all in kg/kmol). (Hint: drawing what you know on a p-v, or T-v diagram may help.) 5.3 J : i 9:0,? (pair amj guloslmace; 6437M 0+ (ameew Slat/lag at“ Ma M \) i V £03 I? CT MW: (2xl2+8xl+ leél\ :1 Q) «(Z/aw c. ’ “ »—- I .. I” 1.592412% :3 Va: gem; Womw M 7;»5Z3l4m/Afi/ PC MW 3 ’ 3 «*3 vcez 0,2,. YEW “LS/éwxflézé K 3 265m w {3, §lmcb $66241 Dal DMH VDMH 4} )2? K3 3% :20 M ltd, lg M a. Problem 4 (25%): A piston—cylinder assembly contains a two—phase liquid—vapor mixture of Refrigerant 22 initially at 24 0C with a quality of 50%. Expansion occurs to a state Where the pressure is 1 bar. During the process the pressure and specific volume are determined by pv : constant. For the refrigerant, determine the work and heat transfer per unit mass, each in kJ/kg. Sketch the process in a p—v diagram, and consider the question: is the process isothermal? TM; 3:» a «Exijlflook Pmi’fij’q’ asg‘xguzj 0x5 Lfiwemvk‘Tl/u' W was MW Mew/{hail (X,=;OO/o\ I: we, a , s, p /\ Lia 610/33 Camshaft 1 wawpd 05,91? «013 a? % ‘2 A + VJ/M I ‘ flow: A? ‘ U1:U‘R +7<1at 3" (49$ s + 039/2538? ~13 l?» {U1 3153.53 % M ‘2) <_W,n.mw.,uwwwm U21; 0,122 my& "3 7%: w 3 0122/0109Sao 3 1) X2: 055; \»§1“\1§2 0416.2“ 0309 3x10- uz 1“ UfZJt’Xz {(1524452) : ,1,2é, + 0,55%(24125 ~(11,2©\ K375». (Ag/«Mt: “32-1935; 5. -3533 >437} r ~ my a/M=@35.55+22.2Q 5/5 =23 x: x, p c...» try.” / W \ "W ' i z {>110 ,. W >0 “irrwASgis’ was} UJ‘O‘FK mm‘iijw fiOjL ...
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exam 1 solution - AERO 489-502: Thermodynamics for...

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