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ChBE 2120 Summer 07 Exam_001 Solution

# ChBE 2120 Summer 07 Exam_001 Solution - ChBE 2120 Professor...

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Unformatted text preview: ChBE 2120 Professor Gallivan, Summer 2007 i I I Exam 1 1 v /10 ( l) (10 pts) Consider a mass balance on the system shown below. Assume that the mass ﬂow M l is 1 kg/s. Set up mass balances for the system. Clearly state your unknowns. Write this system of equations as a matrix equation. Does this matrix equation have a unique solution, no solution, or inﬁnite solutions? Explain. A, mm) B. ‘l o I 0 M1 ’ W13 0 l —] 0 0 m , - .. 9 ’ o O l l 0 O .1 o l "45 I C. By :‘nspwtﬂn Jr Gut/ifs bﬂ‘m‘naﬁmn) 4.69:3 am? r14, out)? M "Ma M of msi}. 6.15. ML W 19—9. RHWVB,+W I‘M}; iNFW/Tﬁ Nvmﬁék 0F SOLUﬂan/S/ I, ‘i l (2) (30 pts) Solve the matrix equation A x = b for x using Gauss elimination. Show all steps. -—4 2 l 5 A: 2 -1 0,1): 3 1 l 3 —7 o I It “12-3 x: '27.7 gamma Mmﬁﬂm \‘ 4, g u 6X23*13”“233 "/GG ail/A'ng W 't (3) (40 pts) Consider a house in Atlanta on a hot summer day. The interior of the house is T = 65 C and outside the temperature is Tout = 90 C. At time t = 0 hours, the air conditioning fails. Over the next 6 hours the outside temperature decreases linearly from 90 C to 75 C. The energy transferred from the inside to the outside is Q = 1000 (T —- Tout) kW. The thermal mass of the house is (m cv) = 1000 kJ/K. - A. Write an energy balance for the temperature in the house at time t (where t is somewhere between 0 hr and 6 hr). Set it up in a form for use with the Euler method or any other Runge Kutta method. Do NOT solve. B. Now assume that a more detailed heat transfer analysis was performed, resulting- in the equation: ‘57: = 0.047(90e'"21 — T) ‘75 and T(0) = 65C . T is in units of degrees C and t is in hours. Solve for three iterations using a time step of 0.1 hr using the Euler method. i if. 7? f (e, '71-) A Hajj/q o o 65 _ 5.375 ' ~ M375 ' n 0.1 ' 99,59 5,520 0,552.0 7' a7— GG-l‘r’ _ 5.187 _ 05137. 3 lo.3 Geog : - . - Wff Em “swims: Hem): act/700\$ hi“ 7:}; I I 6"“: '1'; I I *Wiﬂiii C. Solve for three iterations using a time step of 0.1 hr, but this time use the midpoint method. (4) (10 pts) Describe the differences between the Euler method and the midpoint method. Be sure to address what are the differences in the logic, the computationat requirements, and the accuracy. (A sketch might be helpful in describing the logic.) Y NW A. 41,, gm) M . +L{ Legit: Eta/CM: “two/ml; 5/0/41, [[6, 1%) mew“? (Wm/A W'dpmht:ewr‘rq/76Mc " " up 7’0 ":1", 1‘va eve/{wait af‘W pack/f (ﬂu w'a’pmhf). (/9? 2% w‘a’pm‘wf 37W fa Wrgw/wé’ {ram {ff} ya 71” a”; W loam; WH- +3 thfaﬁmi mid/401W 1': z‘w'a a! Mac/A do 6&sz wince £11 BM W'ﬂ’poi'nf I} W 17/ Wot/4, W Maura/1'2 194% My 6410‘ wrﬁf 1"— Cwnﬁﬁa +3 Acouer Moot“ T070? uya f6 W Mid/aﬁﬂf WW Tag/W oy/ﬂ So w’dpM‘WF 1'! mm arc/Wade) £5735“. [Al/Um, ' (5) (10 pts) Consider the differential equation d3y dy . dy dzy —+t ——=0W1th' 0=2,-—-———0=O,~———-—-—0=-—l of? Val: ﬂ ) dt( ) dtz ( ) Explain how you would solve for yﬂ). You should specify a numerical method we learned in class, and set up the equations in the form needed to use it. However, you do NOT need to actually calculate any numerical answers. NM 2 vat/gm: out 051:2}, = {:(Uui‘=£9 ® = iguana; a) 3:3: —61/;3:'=1f3(ﬁé,,21,a3 ...
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ChBE 2120 Summer 07 Exam_001 Solution - ChBE 2120 Professor...

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