Prcess Engineering Thermdynamics 42434 E (4 sp) Exam 9-3-29 ll supprt material is allwed except fr telecmmunicatin devices. 4 questins give max. 3 pints = 7½ + 7½ + 7½ + 7½ pints Belw 6 questins are given, hand in answers fr nly (i.e. mre than) 4 questins. Chse as yu wish. In all questins, use fr ambient cnditins temperture T = 293 K, p = 1 bar = 1 5 Pa if nt stated therwise. 11. Cld water is heated up and used in a shwer. It is transprted in a well-insulated thinwalled duble-pipe cunter-flw heat exchanger, wherein it is heated frm 1 C t 4 C by ht water that enters the heat exchanger at 1 C. The mass flw f the cld and ht water are.25 kg/s and 3 kg/s, respectively. Fr the water, use specific heat c p = 4.18 kj/kgk. Calculate: a. The rate f heat transfer Q (W) and the utlet temperature f the ht water ( C) b. The exergy destructin rate (W) c. The exergy efficiency f this heat exchanger (%) (2+3½+2 p.) 13. In nature (p = 1 bar, T =298 K) magnesium carbnate MgCO 3 (M=84 g/ml) and calcium carbnate CaCO 3 (M=1 g/ml) react t prduce slid slutin mineral dlmite MgCO 3 CaCO 3 (M=184 g/ml). a. Calculate the exergy lsses, -Δex (kj/ml). Fr the Gibbs energy f frmatin fr the species, use the values Δ f G 298 = -122.1 kj/ml fr MgCO 3, Δ f G 298 = -1259.4 kj/ml fr CaCO 3, Δ f G 298 = -2415.1 kj/ml fr MgCO 3 CaCO 3. See curse material sectin 1.8 fr mre infrmatin. b. What is the cntributin f mixing exergy, Δ mix ex (kj/ml)? c. Is this a spntaneus prcess in nature? If nt, what wuld be necessary? (5+1½+1 p.)
21. Tw rectangular surfaces 1 and 2, arranged as shwn in the Figure, are lcated in a large rm whse walls are black and kept at 3 K. Determine the net radiative heat exchange between these tw surfaces when 1 is kept at 1 K and 2 is kept at 5 K,, and give als the crrespnding equivalent netwrks fr the fllwing tw cases: a. Bth surfaces are blackbdies: ε 1 = ε 2 = 1 b. Bth surfaces are gray bdies: ε 1 = ε 2 =.9 The radiatin frm the rm may be neglected. (3+4½ p.) 31. mixture f n-hexane (n-c 6 ) and n-ctane (n-c 8 ) is fed int a distillatin clumn at atmspheric pressure (11.3 kpa). The cmpsitin and the liquid-t-vapur rati (r q-value) fr the feed F are unknwn. distillate is recvered frm a ttal cndenser at a rate D = 5 ml/min, cntaining 95 %-mle (x D = y D =.95) n-c 6. This distillate is a sub-cled liquid at 18 C, having enthalpy h D = 4.2 kj/ml. The cndenser heat duty Q c = 57.8 MJ/min. Frm the rebiler with heat duty Q b = 45.4 MJ/min a bttm prduct cntaining 5 % n-c 6 is btained as a saturated liquid at a rate B = 727 ml/min. See the Figure t the right. See als the enclsed h-x,y diagram fr n-c 6 /n-c 8 at 11.3 kpa: hand it in with yur answer. F ml/min x F =? Q c D = 5 ml/min x D =.95 Q b B = 727 ml/min x B =.5 a. Based n the infrmatin f the distillate and bttm prduct, 1) calculate the ple pints M and N fr the Pnchn-Savarit methd (see curse material part 3 p. 38) in the h,x diagram, and 2) draw the line cnnecting N and M. b. Calculate r determine therwise 1) the flw rate f the feed F (ml/min), 2) the cmpsitin f the feed x F (ml/ml), 3) the fractin f the feed that is liquid (i.e. q), and 4) the temperature f the feed. c. Estimate the number f theretical stages fr the clumn. (2+4+1½ p.)
32. In a standard cntinus distillatin (tray) clumn, an equi-mlar mixture (x F =.5 ml/ml) f n-pentane (n-c 5 ) and n-ctane (n-c 8 ) is separated at atmspheric pressure. Temperatures and heat flws t/frm cndenser and rebiler are shwn in the Figure t the right. Fr simplicity, assume that the tp and bttm prducts are pure n-c 5 and n-c 8, respectively. The feed is a saturated liquid (q = 1). a. With the infrmatin that the relative vlatility α =12.5 at 7 C, shw that the heat f vaprisatin Δ vap H 3 kj/ml. b. Fr reflux rati s r min =.1, r real =.15, estimate the minimum and real heat inputs Q min and Q real fr the rebiler, per mle f feed F, and the minimum wrk W min per mle f feed needed fr the separatin with the ideal clumn. c. Calculate the exergy lsses fr clumn, rebiler and cndenser f the real clumn, and frm that the ttal thermdynamic efficiency f the real clumn. d. What wuld be the results f questins b.) and c.) fr a feed with x F = 1/3? (1 +1½ + 2½ + 2½ p.) 41. n isthermal gas phase mass transfer prcess invlves ne-dimensinal binary diffusin (species in medium B) as decribed by Fick s Law, giving a diffusin flux J m = 1-6 kg/(m 2 s) with a Fickian diffusin cefficient Ð = 1-5 m 2 /s. By creating a temperature gradient f -1 C/m (which means +1 C/m but in the directin ppsite t the cncentratin gradient) the mass transfer is stpped. Given a Furier Law heat cnductivity λ =.3 W/(m K) fr the gas, and assuming that the cncentratin gradient dc /dx didn t significantly change: a. Calculate r therwise determine the values fr the cefficients D 11, D 12, D 21 and D 22 as defined belw, and the units fr these. b. Calculate the heat flux J Q (W/m 2 ) (= J U fr a case withut mass transfer; Q = heat, U = internal energy), and cmpare it t the Furier Law heat flux (if there wuld nt be any mass transfer r cncentratin gradient). The flux relatins fr energy U and mass are given in the text bx t the right. Nte (!) that D 12 D 21, but relatins between D 12 and D 21 can be fund using L 12 = L 21. Fr the average values use T = 33 K, c =.1 kg/m 3, and M = 33 g/ml gives R = 8.314 J/(ml K) = 8.314/.33 = 252 J/(kg K). ssume that μ << L and μ << L. 11 21 (5 + 2½ p.) dt dc J = L X + L X = D D and U 11 U 12 m 11 12 dx dx dt dc J = L X + L X = D D m 21 U 22 m 21 22 dx dx 1 μ d d T T where X =,X =, with U m dx dx c chemical ptential μ = μ + RT ln y = μ + RT ln c bulk where μ = chemical ptential fr pure. This gives, nting that L = L (Onsager) : 21 12 L μ dt L R dc 11 12 J = L X + L X = U 11 12 m 2 T dx c dx L μ dt L R dc 21 22 and J = L X + L X = m 21 U 22 m 2 T dx c dx
Exam PET 42434 939 name: 12 n-c 6 - n-c 8 11.3 kpa 11 1 9 8 7 HL, HG kj/ml 6 5 4 3 2 1-1 -2-3.1.2.3.4.5.6.7.8.9 1 x,y, - T C x - HL kj/ml y - HG kj/ml 68.7 1 12.98 1 41.87 69.35.9772 13.22.9963 42.3 7.9546 13.45.9923 42.18 75.817 15.19.969 43.39 8.6684 16.94.9237 44.7 85.5566 18.65.8788 46.14 9.4566 2.36.8235 47.74 95.375 22.5.7572 49.53 1.2917 23.75.6756 51.57 15.2221 25.44.5842 53.8 11.1591 27.13.4754 56.33 115.135 28.8.3525 59.14 12.538 3.46.288 62.33 122.9.262 31.43.196 64.46 125.8 32.39 66.78
Exam PET 42434 939 name: 8 n-c 6 - n-c 8 11.3 kpa 7 6 HL, HG kj/ml 5 4 3 2 1.1.2.3.4.5.6.7.8.9 1 x,y, - T C x - HL kj/ml y - HG kj/ml 68.7 1 12.98 1 41.87 69.35.9772 13.22.9963 42.3 7.9546 13.45.9923 42.18 75.817 15.19.969 43.39 8.6684 16.94.9237 44.7 85.5566 18.65.8788 46.14 9.4566 2.36.8235 47.74 95.375 22.5.7572 49.53 1.2917 23.75.6756 51.57 15.2221 25.44.5842 53.8 11.1591 27.13.4754 56.33 115.135 28.8.3525 59.14 12.538 3.46.288 62.33 122.9.262 31.43.196 64.46 125.8 32.39 66.78