Exam 1 Solutions

# Exam 1 Solutions - EML 3007 — Exam 1 — Spring 2015...

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Unformatted text preview: EML 3007 — Exam 1 — Spring 2015 Thursday, February 5 K51 Name Materials allowed: - Basic calculator and/or graphing calculator - Supplied formula and data sheets — OPEN BOOK - OPEN NOTES - OPEN LAPTOP 0 may use any local software or documents 0 may NOT use ANY online resources; no browsers; no messaging; no googling Problem 1 {20 points): A piston-cylinder device containing an unknown ﬂuid undergoes a thermodynamic cycle that consists of the following three processes: 1-2: constant pressure process 2-3: linear p-V process 3-}: polytropic process with n = 1.35 The following operating conditions are also known: P1 = 500 kPa, V] = 005 m3, V2 = 0.09 m3, and V3 = 012 m3. Determine the unknown pressures, P 2 and P3, the work done in each process, the net work of the cycle, and the net heat transfer of the cycle. P[kPa] 1 2 1:3: 00551. P f‘ = pg : 500 WA OR‘Wria’i 34- WWII L35 L35 \ -—' 1’0 {34/3 P, V, v '3‘ P3 - PW Vi) 05 L35 3 i 5‘” §.—f-.; 73‘- 15334 hoot V[m3] ﬂ v.4: RWxV.) = (soovtaoavO—osi Wm: a1) KHZ t “*3 : gcﬁtfﬁl (*5 ”I 1(sue H95HX012~ 0001) 04.800 k5 r r . -l - — {LL- Us-: ~ In: (P,¥.- 135/3) = ”Sf—IKE) 0.3(005) -asz.v)(°m\) W:H 48.85 k7 (AIM/f: Unra+w&'3 +L‘J3W{ WM; = [0,015 It: (3) P2: 900 W © MM th (a ./ 3 W]_2= 9.0 “I w _ AU 0 ‘ {if CYLzl/t QCY: " Cyc ya 3 W23: 9.200 MT @ W3_4= 43-35 MT Qcye‘ chc, @Wm- MS N am- w as N @Qm- 10,03 kr Problem 2 (16 points}: The piston—cylinder device shown in the ﬁgure below-contains 2 kg of water. Initially the water is at P,= 200 kPa and T1= 500 °C. The device is then exposed to frigid temperatures while a shaft holds the piston in place. If the ﬁnal pressure of the water is 75 kPa, calculate the amount of heat extracted from the system. WEN/:1 R: 9011 Wu P; : ‘73 Ma T, = 5mm (13- , @l gm hpu 500C --> 1/, =l‘78HQ M/@ “1 = 3131.4 “3/9 W}: SWW moor V1: H9! 111%: V,‘- Va N <9 [Sink ui ' . 75m. 1.75% ”3/65 ‘9 M X : ‘4‘ VP ‘ ua— Up HJ’WQ- 0.001037 2 u&- 2,314.39, ‘1 1/349 US- 0115 3.917; — 0.0011137 Mam-384.39 Q‘_l: mturw) = (2161(3080-85' 313W) H SQ'CW alwé' leol“ ~ 940) k7 m -9400 “I T H143 News 9'0) chN‘ Med I 13 ex+mde&i Q: QiOi RI +_ £1» be pox/941,2! lh Problem 3 {16 points): The piston-cylinder device, shown in the ﬁgure below, contains refrigerant R-134a whose volume is constrained to a maximum volume of VHW = 0.893 In3 by a set of stops ﬁxed to the cylinder walls. Initially the ﬂuid is in the following state: P, : 180 kPa, V; = 0.290,m3, x, = 0.4 ? The ﬂuid is heated until the temperature reaches 70 °C. Sig—Z. é (A) Calculate the mass of R-l 34a contained within the piston—cylinder device. (B) Determine the temperature at the point when the piston just hits the stops. (C) Determine the ﬁnal pressure, Pf, in kPa. V, - Cl—x,)\/p + x, v3 -. (O‘BXowowmﬁ (o,v)(o.uow) LA) ﬁupmlx,;ov ——» ~. 0.0446139; n3”; @ V, 0. mo v.3 v, o.owuw"’/Ig m = 0500 QC? G . me ‘ 0.3613 ; O I q V's/1L (By ‘3: lgo M:Q) \/a_- —— - \$0 .37 .l To; {deco 5a) «3 5318.531 Problem 4 116 points): A fan is used to accelerate air through a nozzle to a jet velocity of Vj. The required fan power is described by the equation, W}: = pj Aj Vj3 /(2nan), where pj is the density of the air in the jet, Aj, is the cross-sectional area of the jet, W is the efﬁciency of the fan, and 771v is the efﬁciency of the nozzle. (A)Determine VJ- given Wp = 2.5 kW, pj = 0.0751bm/ft3, Aj = 1.0 ftz, m = 70%, and 771v = 90%. Express your answer in m/s. (B) Express the given fan power, W}: = 2.5 kW, in units of hp. (C) If the unit cost of electricity is \$0.09/kW—h, and assuming that the fan operates continuously, what is electrical cost of operating the fan for three days? ' / 3 . We act”? w (A) \¢:< ‘ N F < JujAJ' 30AM V} = m ”/5 Wp- 3.353 Lip cost: I}? {6.520 Problem 5 116 points}: A piston-cylinder device containing C02 at a pressure of 100 kPa, a volume of 1.0 m3, and a temperature of 127 °C is heated to a ﬁnal pressure of 200 kPa and a ﬁnal temperature of 627 °C. (A) Determine the ﬁnal volume in m3 . (B) Calculate the change in speciﬁc enthalpy in the C02 during this process assuming constant speciﬁc heats and evaluating the speciﬁc heats at 300 K. (C) Calculate the change in speciﬁc enthalpy in the C02, again assuming constant speciﬁc heats, but evaluating the speciﬁc heat at the average process temperature. DO NOT use software in solving this problem! ASM (M 3% WM Q9 LA) R )5 _ {>02 V; 4; = v! E '2 ; (LOWS )(200 > %) ’— - .—-—'— . Pa T} T: TQ k) ~_ (0,349 E5: )(qoo-LLW) CP‘ own. [25% @zsow km Aim; (Hog ﬁKKQWWO) " .M 99W Says: Aw 5%.0 “3/9 I Problem 6 116 gointsl: A U—tube manometer is a connected between the two-tanks as shown and is ﬁlled with mercury (p = 13580 kg/m3) and oil (,0 = 920 kg/m3). Both tanks are' rigid and contain air that may be assumed to behave as an ideal gas. The following conditions are also known: PA = 200 kPa, T3 = 50 °C, h] = 0.45 m, h; = 0.10 m Determine the pressure in tank B, P3, and the density of the air in tank B, p B. (3/1 71— PA "Mi mm mm Pg, 1 290,000 + (Q303(q.80(0,3y) —(13580)(7.8))(0H5) P3: Msaawu Pa PB ~_ Mafl Wm F NS Q de ‘ k3 — _ — ,S 3 w ' ...
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