Sample Exam 3 (A) Solutions

Sample Exam 3 (A) Solutions - Problem 1(20 points A...

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Unformatted text preview: Problem 1 (20 points): A spark-ignition automobile engine can be modeled as an Otto cycle, with compression ratio l/l/Vz = 9. For operation at full throttle the following conditions are found: P, = 100 kPa, T; = 320 K, T3 = 2400 K. Assume that the effective constant specific heat ratio is k = 4/3 and that the heating value ofthe fuel is FHV= 43 000 kJ/kg—fuel. The combustion process is modeled as an equivalent input ofheat given by QH = m FHV. I Determine the constant pressure specific heagp, the pressure after the compression stroke, P2, and the air to fuel ratio AF @na/mf. ‘ - '~// (5287 ) (D Q k R 3 iv: erect/+26 r—a CPZT’" “ q/3—i / CV} H L be S L‘ \ é" l 7: CP ® mates“: HQ f5 gawk/1330,31 _~ @% ~04)“ ‘4 be m ‘13; ' Va 3 3 3:2: mm M @ TL: mwas’ea From) 3 a3 prowi ’3 3'3 3 W ’V .— , : Nifty“ Q‘n— “‘46:! : AU:'3\ I A W W» WV 0 . R3960 __________._—e———-———-————--’ A? 2 Mr CV03 .712) I - (5,8bl)(&‘tt)0 ‘=— (40519) @ 0 II ("3? KM» 90‘ 0“: 53:75 5; {F l 7 Ha? Weak M ®33 “HM T y x: ©AF=__9_3~__8§___ '. 3H 4 @ SP n . Problem 2 §20 points): Consider the steady—state operation ofthe ideal vapor compression cycle shown in the schematic below. Theworking fluid is R—l34a. ' . smother; (A) Derive anlexpression for the coefficient ofperformance, COPL, in terms ofonly the variables M, 172, and 173. (B) Calculate the specific heat loss in the condenser il‘P; = 800 kPa and T2 = 60°C. ___Jit;; 12 1 ‘ l ‘ WC l {:3 K ! l \I fie (El zoo «771.0 M; ~ W; 76; M Z 2387 (5—710 * M “3 'WM Problem 3 g20 points): Consider the steady-state operation ofthe ideal Rankine cycles shown in the schematic below. The working fluid is water with a mass flow rate ofm = l kg/s. The following operating conditions are known: P1: 10 kPa, P2 =15000kP‘a I72: 206 9 kJ/kcy g, s; —— 0 6492 kJ/kg -K T3 = 600 °C W (13 l Calculate the amount ofheat transferred to the fluid 1n the boiler, QH the exit quality X4,c and the amount of enti‘aopy Oenei‘ation across the boiler and turbine SW71 2 4. ii the boile1 1eceives heat from a constant temperatme 1‘ese1‘voi1‘at 900 0c. 9 LC) (/1 ’" Ti?” ~ \ \ _ « ,. _ 4 lag: 352391.30 Wig " ~fiL—fi \ 1111 621—1111131117w a fi:_m~v__ \ Q)§35a2(3~ma) :3?” A) \ \ / i W (31”; 8%75/MV/ \i \\ i i ® ® ’ L ‘ ”—‘ X (B) £3.34 (019775 ”I’M . 1'01 @543; ‘ g,c775‘~10,o‘4m® 53.54: i 8.185;. Wm To 1» ~ 1331,; , _ 5. ~13 .. __ $391 3M4 ' Vi“ T a) T15} Problem 4 (20 p, oints): An air—breathing turbojet engine operating in steady-state is shown in the schematic below. The work generated by the turbine is just sufficient to drive the compressor. in addition to, m = 70 kg/s, 175 = 85. %. I77‘= 85 %, rm = 95 %, 0p = L292 l<.l/l<g~l,<. and k = 9/7, the following conditions are known: P, = 50 kPa, ‘7} = 1200 K, :0 = 900 K, P4 = 400 kPa, W 93" CC? on Determine WC, P3, and the exit velocity, V_,-. 7;=5841<, ‘ 0. wt = $5796 WV i M T 7 9 g ’33:” M w - 3 “l _ 3 ' ‘4 T - T — ‘ i" T ' _ A ”((7 ‘ ‘ ff?” a ‘iS ‘3 ”1c ’35 3’ y 9CF(T‘F J 1 WC — @1701?) ”M W P5: lcll3 kl)“ V]: nose “/5 Problem 5 (20 points): An ideal Brayton cycle with reheat is shown in the schematic belowhAssume that the air—standard model is valid and that the following operating conditions are known: 3", = 300 K T3: 550 K, 73- = l lSO K, [35/136 = 3, m = l kg/s ‘ C4) ~ Q33 W (P) Determine the compression ratio, PZ/Pl, the required compressor work, WC, and the temperature To. Plot the cycle on the T—S coordinates provided. Clearly label each state and darken the process line between each state. . t w .. , - . 5'; GE lLQHi llQ (A) F9 To? M 550) A 1 A7.-_:l.2. _, 1 m 1 ______ ' ”g l— l— ’ Jl_“ a Til 3‘” Zl ____ s l l\~ {l/ //[ . lift 6) W / l K E was: 9“ ltd, @ 1% a CC) TL "& K - « 3 A ’ i ; A) ~59 (9 1 QED) 3 lb : 8‘40’; k 75 l7§ - ...
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