Exam 3 Solutions

# Exam 3 Solutions - Problem 1 116 points A spark—ignition...

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Unformatted text preview: Problem 1 116 points}: A spark—ignition automobile engine can be modeled as an Otto cycle with compression ratio 1“,, = 9 and displacement volume Vd = 0.002 m3. For operation at full throttle the following conditions are found: T1=330K, T2=795K, T3=2400K. Assume that the air-standard model is valid and that the constant speciﬁc heats of air are taken at 300 K. The heating value of the fuel is FHV = 43,000 kJ/kg-fuel. Determine the minimum volume of the cycle, me, the maximum volume of the cycle, Vmax, and the air-to-fuel ratio AF. v (v: )7: *3; M-Jo’a \L / V V VJ O-OOQ . _ l ‘ _( V-i‘ ‘6’)“ 7;” ' '75 re};- 3' (‘V -\/’= ’03,,” = 0.00225 M3 V, 000995 V” E q ‘ Mug—33 VF’v/m‘ Mom M3 .7 Q”: Ma (v (B’TJ) QH : W116 FHV \‘NMWW: WSW Wm P/boess.’ AF - W FHV - ”39‘” "7-9 0 Cv (T3 ~12) h (ommwoo "795) A? = 37.3; Vmin = 0000.15 m3 Vmax : 0,009.25 m3 Problem 2 118 points}: A fossil-fueled steam power plant operates on the ideal Rankine cycle shown in the schematic. The following operating conditions are known. P1= 10 kPa,v1 = 0.001010 m3/kg, P2 = 15000 kPa, 123 = 3310 kJ/kg, Determine the exhaust pressure, P4, the exhaust quality, x4, and the entropy at the exit of the turbine, s4. 034W ﬂuke out/ms a (‘mdP/IW‘ P. : F4 : to kPA Side 3? P3: Pg: 19,000 W01 1,33; 3310 W713 a 93: SB}! q: (peep/MP1? +ur9N) s5: 3:! = 0.3% 553; P4: (0 k?“ X4: 05—75%? a 163‘ S4: G. 590 ’3‘ K Problem 3 116 points): A refrigerator operating on a vapor-compression cycle is shown in the diagram below. The working ﬂuid is R-134a and the following conditions are known: P1: 60 kPa, P2 = 1600 kPa, x1=1,x3 = O, QH = 95 kW, Assuming the compressor operates isentropically, determine: (A) The temperature exiting the compressor, T 2, (B) The mass ﬂow rate of R—134a through the system, m, Ass {sz com:w: ’ ; 90 W ? O —> 93,: Ho “(I/13¢ Y, 1 l 819-: S1 : 7:1: 73-“1 0C, a —._————_——_——————_ Pl: [560 W0. h; 1 4458 VJ/rj X3 ' 0 9/\ 1M {or Maser 52H : w ( K2443) M: ﬁ— \$36.; : 0.58%qc Vii/s T2: 73.14 0C 3%.QOIK Problem 4 116 points}: Consider the steady-state Brayton cycle shown in the schematic below. The air-standard model holds and the following operating conditions are known: Assuming the constant speciﬁc heats of air are evaluated at a mean effective temperature of 600 K, calculate the exhaust temperature, T4, and the exhaust’s P3=900 kPa, T3=850 K, P4: 150 kPa, 77C=80%, m~=85% isentropic temperature, T43. [)4 600k: 3(7- 1370 [\$145,991 +Urblhe‘. b. P3 : <73 >‘C‘l Pkf 17.45 Mal thm‘ pit " T3- TV a B~T~(s T, 570- 3 K T4, 9020,01 K :4 [:i l (\P ‘1 ’\ Cl l {A tn v ~. 851) i (o.gs)(a’sb \$220.9) 74: 570,30 k Problem 5 116 points): The real (non-ideal) turbo-j et engine shown in the diagram below contains a diffuser section at the inlet to slow the ambient air before entering the compressor. Assume the air-standard model holds, that cold properties are used for the constant specific heats of air (300 K), and that the following conditions are known: m =1kg/s, T1= 250 K, T2 = 450 K, T3 = 1200 K, T4 = 765 K, P3/P4 = 6 =1500 k Calculate the rate of entropy generation in the turbine, 39,7134, and the rate of entropy generation in the combustion chamber, Sgen,2_3, if the equivalent heat of combustion comes from a reservoir at TH = 1500 K. PWOM'PS of Ar a} 300 k Cp; Loos “3/ng CV: 0/7’2 W/ks,“ k1 L000 Sean} Low , ”"NW’LQI O = M53 ‘VJ'Sq + 5904,34 ‘ ~ ~ 774 El 53,,“ : Mar—say = M cm ,3 ~ M F3) , , 7(08 1 — Q )(0-005 > m ~(0,337) L (a )> ' . KW was/J [044/ W W: 5.9/5), 'co/hJSJMW (/LW r 0 ~ 0 : W] S}; ‘W’lss + T:L 4. 336%,2'3 Off-H : WO’B‘ba) - ' F l W) (T ~Ta) 53%,95 3 W(S>'Sg) ‘ if], C10 3 ’H = UHLWSXth/oovysv) (Imyﬂl‘ ”‘30 _0>~E£ - (H (V ) [500 : 753375— kw kw SI‘gen 3-4:.ﬂLL Mhmr WW ' M55 {neer » . W 8%,, = Aussies 5‘2— E Problem 6 118 points): A compression-ignition, internal combustion engine operating on the ideal Diesel cycle operates with a compression ratio of rv = 16 and a cutoff ratio of rC = 3. Assume the air-standard model holds with a mean effective constant speciﬁc heat ratio of k = 9/7. The following operating conditions are known: P, = 150 kPa, T, = 350 K, V, = 0.0015 m3 ® @ (9 Determine the speciﬁc heat at constant pressure, cp, the thermal efﬁciency of the Diesel cycle, 11,;,, and the mass of air used in the system during each cycle. I r k _ l ____ c @ a: 2: ® ”2W0: I~ viii-“Wm ] k" ‘ 3‘17 | . (‘7/7)(0 187) _ ) ‘ F) q/7(3’))] Q/7- 1 C10 ‘ 1.951’5 %K [bmmr O #59059 k cp l-MR kw 77th = (DJ-[530 ma= 0.0094“! ’53 q I ll ...
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