Process Engineering Thermodynamics E (4 sp) Exam

Transcription

1 Prcess Engineering Thermdynamics E (4 sp) Exam 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 = kj/ml fr MgCO 3, Δ f G 298 = kj/ml fr CaCO 3, Δ f G 298 = 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.)

2 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.)

3 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 = J/(ml K) = 8.314/.33 = 252 J/(kg K). ssume that μ << L and μ << L (5 + 2½ p.) dt dc J = L X + L X = D D and U 11 U 12 m dx dx dt dc J = L X + L X = D D m 21 U 22 m 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) : L μ dt L R dc J = L X + L X = U m 2 T dx c dx L μ dt L R dc and J = L X + L X = m 21 U 22 m 2 T dx c dx

4 Exam PET name: 12 n-c 6 - n-c kpa HL, HG kj/ml x,y, - T C x - HL kj/ml y - HG kj/ml

5 Exam PET name: 8 n-c 6 - n-c kpa 7 6 HL, HG kj/ml x,y, - T C x - HL kj/ml y - HG kj/ml