20.110_Exam_1_KEYFall2008

20.110_Exam_1_KEYFall2008 - Page 2 of 12 /\ Name: l 155‘...

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Unformatted text preview: Page 2 of 12 /\ Name: l 155‘ 1.) (5 points each, 25 points total) Short answer a) You have an ideal gas in a piston. The pressure on the piston is doubled, decreasing the voiume of the gas at a fixed‘temperature. What is change in energy, U? W, AU 7—— AUCTj 2:; 0 b) Work is done on a linear protein by stretching it using an AFM tip. Two force (F) vs. extension (I) curves are measured, one where the extension was done reversibly, and the other was irreversibly. Which one is which? State your reason why. F wsfrdamm. we lie am rfcfuife rel/Us; H6 §7VOC€SS€S marrow M/orlfi c) A hot block (T = 400K) and a cold block (T=300K) are brought together at time to. The blocks are encased in a box with impermeable, rigid, adiabatic walls and exchange energy through contact with each other. The heat capacity of the hot block is 4 MM and that of the cold block is SkJ/K. The blocks come to equilibrium. What is the value of T14? 53gb“ (Lo-l +6063 {3 [go loci-Pd Page 3 01°12 /’ ' 7 Name: It 1156 Z _._.___..... d) A simple model of dimerization involves 2 particles on a 1—D iattice with V sites. When adjacent, the particles experience an attractive energy ~s. This piot shows the Helmholtz free energy (F/A) of dim s -- and monomers plotted, for a pair of conditions, low and high concentration. Solid lines correspond to one condition and dashed lines to another. On the diagram, label which lines are correspond to monomer and dimer, and indicate which set of lines is for the higher concentration. Sahel - tweak Comgntrqtieo (JO'Hed " low Lance’nt'rahon F/A :Helmholtz free energy (e You have a friend in Denver who - also loves thermo. You decide to do identical experiments -- a reversibie isothermal PV expansion of an ideal gas —- and compare resutts. Atmospheric pressure varies as PL?) 2 P (0)e'mgz"“. Cambridge is at z x 10 m and Denver is a z : 1600m. You each expand the gas from a pressure of 2 aim to a pressure equal to that of the local atmosphere. You then compare values for AU of the expansion _ do you expect your friend will reporter a greater value (presume that you each conduct the experiment perfectly)? Expiain the expected results in 10 words or fewer. Dew fills -> U onlkj m£uncli0n at AUTO tor lbafl — Page 4 of12 .é:\ Name: «ff/f w 2 (15 points) You are cooking with friends and have been given a recipe for roasting garlic that requires heating to 160°C for 30 rnin. You accidentally heat the oven instead to 200°C. You place the garlic in the oven. After the garlic has been in for a bit, you realize your mistake and turn the heat back down to 160°C. You can presume that the garlic heated up to 200°C before you realized your mistake, and that it cooled back to 160°C by the end of the roasting time. (a) Calculate the enthalpy change for the garlic from the time it was placed in the oven until the end of the roasting process. The initial temperature of the garlic was 20°C before being placed in the oven. You may presume the garlic weighs 100 gm and has a heat/:aéaclty 0f CPL: il‘J/gm'K’ i Hi ml“ l WY Lawn (Marl—24W E,- = 4* i”! .__ H +53% (M, .t , _( ‘ / Jr :— a" WM? ._ m" ' _ 1 ._..._ “(’09 (ZUU 4: 2U o) : Wt + W Crook- > ‘ e rare; 1 1““ (b) Calculate the entropy change for the garlic forthe time it were placed in the oven until the end of the roasting process. __ Ale: aim I. r m merrier 0" t T e ‘ ' §rg SRSJIV‘xk'gmg .__I lL’ A§.H5_ :: rm ~<(C:>C-": {c Zebc, (Emmet C tle ((od We?wa Page 5 ofll Name: 3! (7;); 3 (15 points) Liquid A and Liquid B are mixed together to form a solution. If A and B show no preferential interactions (ideal solution) calculate the entropy change when a 50/50 mixture is diluted by addition of B to give 25% A in the final mixture. Please work the problem in the following steps: (a) Define an initial 2D lattice containing the mixture and a separate initial 2D lattice containing pure B such that when they are combined, the mixture is 25% A, Sketch these 3 lattices. Use notation NA = number of A molecules, etc. gig; .wf 2, “A = fr r} {fifmffim . I II 2 i 5’7“. fik‘, __ I.) . ‘ ' C“ l a ' Xi- ' i ‘02:" i 3 {Wu—mm- \l_ i W} {K H .. -. -111- i M w m- h ‘ i i “a = “Witt . a We net mim_ “T’WJI f' I. (A A 5w «m a. -. :' jtfl g E :‘ WW 5"“ i O z a. _ , E‘k .» i “)0 Q? --I“\ : 5"“); 5' L7 “MA” We“ x._/K_J¥J VIE/s 53/: (b) Calculate the entropy change for the mixing process. Your final answer should be a number times the Boltzmann constant R, but show your intermediate work. 35‘ ’ 2 -. a? i 'fl" 7 ‘N "z W 51“ Y" 55"; 5"”? fluirfi'CMkJF \l- k E ’ u , a . i . i v .r '\ ' ‘ my :, ;. Aim/i - '- _I ._ -,r-.i;;r’\_31“1¢ \M; .e t" - ‘- .' =— ‘ 77‘ j: 5* ‘. , 5f * r ‘ : _, ‘l 1) . ~ «0 i \é' 5*— - 73 . 13‘ g l i v- ! , 5 -- ‘x‘ v: _ e. j :1 <7 " ‘ '- ‘ V ( WWI—1 j , it} \ _‘ -’ F“ .19, /-:. . ,- 1)” /f::‘,\ fair-l if: .2: Effie shy? m?” .V ‘t C K {r Lia E! a m // Emmi E Page 6 of 11 Name: 0 x (0) Would your answer in part B change if you double the size of all your lattices (and double the number of molecules accordingly), and if so, by how much? if you reason that it changes, your answer should contain a specific numerical value for how the entropy changes (e.g., “bigger” or “smaller” are not acceptable answers). pmgg :1: w. encased-gs {AC/Wang WINCH. 9"? f' U M l' H" "m, L . ' a. In: if a n F7: JAI’ 3‘ Jar x, ~ - xiii-:33“; 5m; at 5751ng a)? 4- . "'" 1- .' . . .. ,I....__ _..M...-,._.~.-,fi, , f Page 7 of 12 Name: 4) (20 points) PV expansion in Boston vs. Denver You and your thermo-ioving friend in Denver decide to further investigate the expansion and contraction of ideal gases. You again decide to do identical experiments on a reversible isothermal PV expansion of an ideal gas and compare results. This time, you prepare two vessels that each contain 0.5 L of an ideal gas under a pressure of 2 atm and ship one vessel to Denver. Pressure varies with altitude P(z) = P (me'MgZ’m’ Where M = 28.94 >~<1O‘3 kg/mol, the molar mass of air, 9 2 9.8 m/se, and P(D) is the pressure at sea level, which is 1 atm. The attitude of Boston is at z = 10 m, while Denver is atz: 1600 m. Assume that the temperature in both cities is the same when you do the experiment, T 2 298K, and that you both do the experiment isothermally. a) Calcuiate the work per mole of gas, WBOSm when the gas is aliowed to expand reversibly to a final volume until it reaches the same atmospheric pressure, pBoston for a reversible isothermal expansion. ,8 2 law M -.- . gs/K Nisanw =2 “fin-“T In WW.) RM?— flfl. r :- 172% V1 WW :- lZT “(Pa/fl.) V‘i : (9,3,4 3k-'MUI‘1)(’2?8K) in (05") lime Pg; k3 Moi” 7‘ b) Caicuiate the work per mole of gas, Wgemr, tor your friend’s identieai experiment in Denver. Is it more or less than what you did? #(zgflmemwxjczajéfy P217 E glaring W'EK)’; I WWW: (LT M 391/?) .2; 0,5324%... : (8.2/4 '3‘ K"Moi”)(2qgg)(fm Page 8 of 12 Name: c) If you both were to compress it reversibiy from atmospheric pressure to 2 atm, completing a cycle, who does more work? WDW : fl<wwmfizq,) M W305?“ 2:. -" C N.“ 2 HL 051W1q\) Q0 \/\) Qjcée, 2 W'BoSTon + WW ‘7': J V “142 2—, d) If you go around in a cycle, what is the AUBOSmn and AUDenUer? '8 OfloN Page 9 of .12 5. (25 points) A system comprising N = 9 molecules has an energy of U = 4 x 10’21 J as shown in the figure. individual molecules can exist in either a ground state or an excited state where e :2x10’21J. Heat is added to the system such that the final energy U = 8 x 10‘21 J. Initial State (example configuration) 8 2 0 G96 Bfi' CO Laq Final State (example configuration) 2 0 (a) What is the change in entropy associated with this process? The value of Boltzmann’s constant k: 1.4 x 10'23 JIK. {1} Fmtg) AS : Slihal “- initial AS 2; Klnwh‘re‘ m" ‘“ Wt‘nfl'ifil I. k I“ Page 10 of 12 Name: (b) What is the finai temperature T2, relative to the initial temperature, T1, if the value of the heat capacity mC:V = 3 x 10‘23 J/K? (b poi“:th (“U M :: va M ‘ (339 ~ T} A3“ £94 Qi- M3 r f ‘ W P h 1 FT‘ {581M}; kin _ NJ ~ TL- "F- lt |*’,}_§’NO 3 _ " 3 we“) 1 “ TL: Y 3' t“ T 3%: Hon. (0) What arethetemperatures T1 and T2? (apwws) OHW‘ équrf‘f’em Shanta, @mb‘mhqg (I) QCID toe at (C) W79“ “amt, l”; T\ '=— tag]: T7,: $0114 10 Page 11 of 12 Name: (d) This model is a very simple model for how energy distributes between different levels in a population when the temperature is raised (U is increased) and we have used it to describe modest increases above basal energy levels. Consider now how the model behaves as T9 =0 (is, as U increases to its maximum value). Does the value of AS predicted by the model correspond to what you would expect from the macroscopic models we have used? Why or why not? Do you think it would correspond better if an additional energy ievel were added? [ Intact, real systems have a very large number of accessible energy states] (33’ entails fl lb Hits WF‘CVQSCOFit moJel , S 8% got/1% (£0qu 6% Ulst (see w luv u: were? y; \N ~§:OV‘ Lt: llfialOU-uj). J1 {ac/i” ck MIL/may S: 0 bféCLL/Lge, a” W MOlecr/Lleg aye, at W imagine? emerm level. Mmogwpimlllj, go 3 Show“ Life? i‘rthPasr‘hj 01$ 61/ inCreages} H’il‘g (jOég “all came 1% Wrong More, {R0331 level; Wot/rial Mp iWS as erfl Wmmflamanig COMM SailSift‘ 0i {ha/i3; g/Q’ZC , 11 ...
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