Sample Exam 2 (C) Solutions

Sample Exam 2 (C) Solutions - EML 3100-— Exam 2 — Fall...

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Unformatted text preview: EML 3100 -— Exam 2 — Fall 2012 Wednesday, October 24 t ‘E ‘I Name Problem 1 (28 points): A 50-kg sample of air is heated from an initial state at P1 = 150 kPa, T1 = 400 K to a final state at P3 = 250 kPa, T2 = 900 K. Assume that under these conditions air behaves as an ideal gas. (A) Calculate the total change in internal energy, A U 1- 2, for this process WITHOUT assuming the specific heats of air are constants. (B) Calculate the total change in internal energy, A U 1-2, for this process assuming the specific heats of air are constants. (C) (Bonus 8 points) Calculate the total change in entropy, 1181-2, for this process assuming the specific heats of air are constants. (A) «14.: aatsq @7ch ua 2 67% 3;; yer/g AU“; = mtusvm®= (50 @‘(swaa ~128Cottict mMa) : \Ot.‘[email protected]\T : ($0 ngnW/xykflqoo kv H00 k) : nqa‘mT ** QC v 53?; «.m ( cm E—ME )@ C it it i l' if T (51) @anw aiming?) Qtamlflat’g» 2 33.38 “I/KQ") @ (A)AU1_3= {C(Ha W13 ® <B)AU1-2=_flW‘—3__ (01151-2: 3‘35 kj/K Problem 2 (20 points): Consider the steady-state operation of the following device. The device accepts two inlet streams ofwater at m = 35 kg/s, P1 = 100 kPa, T1 = 275 °C and m2 = 25 kg/s, P2 = 200 kPa, T2 = 400 °C. The water exits the device at P3 = 1000 kPa. The device requires 50 MW of power to operate and loses 10 MW to the environment through heat loss. (A) Calculate the mass flow rate at the exit, Thg. (B) Determine the enthalpy at the exit [’23. (A) “0%? vvsi+ ma :. VH3 v33 ~_ (:55 “3/5) +095 Meg 2 66 Vél/;® 053 My; VCli/u‘i'wgl’lg +w 3 Q + ””3143 Problem 3 (20 points): Water in a piston—cylinder device undergoes the following two-step process: 1—2: constant volume heating with P1 = 200 kPa, T1 = 200 °C, II] = 1.2 m3, and P2 = 400 kPa. 2—3: constant pressure expansion with V3 = 1.4 In3 . Determine the heat transfer during process 1-2, Q 1-2, and the work done during process 2-3, W2-3. ® '5 Q/fl -, v 2 1,0803% ”/13 Q l—a- - F? A U l’& ‘ V ® V W}: ,2: LUDjQ k5 o1 ws‘t- v ® V"' id" {1‘ 2 Qé5‘1.3‘1 I/kj QR; : mfiuarbtl) VJ: 1.080?“ g0 (~0803‘l " (.0056? _ U; -- 3300.;9 f ' mam , 1,06% 3&17735 - 33%;; u; 2 “Primer *3/23 Q._;:(i,uo7o)(3\tlfll atsmq) Problem 4 120 points): A Carnot forward heat engine (F .13.) supplies 1000 kW of power to an old reverse heat engine (R.E.) that is used to provide refiigeration at temperature T L2. The thermal reservoirs are T H1 = 650 K and T0= 300 K and the heat removed from the refrigerated space is Q L2= 1475 kW (A)Determine the heat input and loss in the Carnot heat engine, Q H1 and Q M (B) Calculate the coefficient of performance of the reverse heat engine, C OPL. (C) If the reverse heat engine is replaced by a Carnot reverse heat engine capable of twice the performance, calculate the temperature of the refrigerated space, TL; CAR/“OT Eflffay A Gm TH® qr , ' ' ® h) Tr:__\‘ Lwrwugq QM TQ- élit : FEE Ci“ Gm — CM 1 W T o \i / Tm “ ~ W __ — l GL1 ’ < To > Q5) ‘. W 1 room G’L‘ “- Tm ‘ _Co’S_D —\ 3,3; ._ goo Problem 5 (20 points): Regeneration is often used in power systems to improve the overall thermal efficiency. A portion of an ideal Rankine cycle with regeneration using a closed-feedwater heater is shown in the following schematic. The following operating conditions are known: ml =18.5 kg/s,P1= 150 kPa, x1= 0, m3 = 22.3 kg/s, P3 = 800 kPa, h; = 3125 kJ/kg, T6= 125 °c, h7= 2975 kJ/kg, W: 11.15 kW (A) Determine the enthalpy at state 5, 175, and the required work for pump 1, Wpl. lg” l (C) Calculate the required heat input to the burner, Q H. Uh) {M who" ()9 ins-Ml : vl(?§' PI) wLere (0 'PS : 133: 860 Mom , 3 CD V} 1 Gimme} W/Lfio; = Vt 7.03 ‘5 k G) 60 Mi (9 /.‘3 LB) mass new: a e 6) 3M, +V‘47 ’ ”‘3 \AS 1(qg7,oS’)—}—L.Dolb§3)(360 ’ (Sb) = “$7? kj/tc'j W72w3~ W, M -— 3&3) ‘ ‘85- . a _ y @ - i y/ , =‘Q8,g©) (Vt‘7-3égfie7fi?) - 37 ‘o/wfiy o : ‘- tamed) w ' ‘ ‘ 0 ® , 0 Cum Arum +3” + WA“ +w7|47 - Why) a J/@ r , e (:3 175% cm: Warm. «7&7 “WPFV’PQ ‘ = 19109 kvx/@ ., © WM W = @133 )QaaQ ngSXQWM) ~L33X¥017g> @ PM — tan, — [MS was? M [email protected]
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