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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
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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-
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my :, ;. Aim/i - '- _I ._ -,r-.i;;r’\_31“1¢ \M; .e t" - ‘- .' =— ‘ 77‘ j: 5* ‘. , 5f
* r ‘ : _, ‘l 1) . ~ «0
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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\)
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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
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(0) What arethetemperatures T1 and T2? (apwws) OHW‘ équrf‘f’em Shanta, @mb‘mhqg (I) QCID toe at (C) W79“ “amt, l”;
T\ '=— tag]:
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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
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