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Unformatted text preview: Problem #1: Part 1:
Traveiing waves move along five strings as shown below. All five strings have the same
finear mass density M, but are not necessarily at the same tension. fen“ﬂ”? e. Rank the five strings according to their tension, from highest to lowest (7 ' 5 4t? __________ 4 Part 2: Two cylinders, A and B, each initially contain 4 cubic meters of (diatomic) nitrogen gas
at identicai pressures and temperatures. Cylinder A then expands isothermaily to a final volume.attiredb‘ic;_._rtjetersr, while cylinder I
B expands adiabatically to the same final volume of 8'.cu't§§te}'mete s‘i';':._: _ __ In each square of the followrng table, write ” l; " If the quaint
expansion, ” ” if it decreases, and "  ” it it stays the sameii Cylinder A
(isothermal) Temperature of
the gas H— Entropy of the gas Mass of a single
gas molecule Mean free ath Of ‘
as molecules 4? awv _
w Average see I = v _ ‘ 0e ules
i" j
‘I' ? Extra credit: next to each quantity that you marked as increasing or decreasing above,
indicate the factor by which it changed. (1e, write "x 4” if the quantity became four times
bigger, or “x 1/3“ if it became three times smaller.) Problem #2: True/False Mark each statement as true or false. 7
if a statement is false, then correct it, by adding, deleting, or changing a few words, so that it becomes true.
M" ‘9 7 1) An irreversible process always causes the total gy of the universe to
dé‘CI‘ease, while a reversible process does not change the universe‘s Mam inn/mac  09%? m gall“ 922406 2) High frequency sound waves travel 3 er )hﬁ lowfrequency sound waves in
the same medium. 3) At the same temperature, the molecules of a diatomic ideal gas have a higher
avera  nergy than the molecules of a monatomic gas. (more aggro? mf I 4) Two otherwise identical guitar strings are at different tensions. If waves travel .
nine times faster on string A than on string B, then the tension in string A must be t etimess er.
2g w 'W W” J?) 5) The fundamental difference between the past and future directions in time, is
that eyKQy increases as we move toward the future.  6) if an ideal gas contracts isobarically, then the entropy of the gas ingeés. i _ decider>305
(Le/(mug, Lwéat‘i‘ (aw; (Dz/FD ' Problem #3: Sanity Check As always on sanity check problems, do not try to solve this problem directly
(unless you want to try for extra credit at the end.) Instead, think about the
physical situation, examine the five equations given as possible answers, and try
to reason out why at least four of the equations give impossible or physically
absurd answers. The Situation:  An airfilled cube of sidelength L floats on the surface of a lake. The water in the
lake has density pw, while the airfilled cube can be considered to have zero
density in comparison. (Thus, it floats on the surface of the water with none of its
volume submerged.) A diver then ties a string to the cube; on the other end of the string is a metal
sphere of density p and radius R. The sphere's weight pulls the cube downward
until they come to a new equilibrium, with the bottom of the sphere a distance 2:
below the water's surface. ' The possible answers: iil Z; gﬁéﬂ—ﬁ ’ a) What units should the answer have? Min/5 Which equation(s), if any, does this eliminate? Eli} 69M} 0m¥d§Mm9EmQ795> b) If the density of the sphere were equal to the density of water, what would be
the value of z? Which equation(s), it any, does this eliminate? Briefly justify
your answer. W Wat/kl; h€h+ﬁtl£9 g0
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i9 TF9» Z a c) If you were to replace the sphere with a larger sphere of the same density,
would .2 increase, decrease, or remain the same? Which equation(s), if any,
does this eliminate? Briefly justify your answer. 0155miminﬁ 'l’laat‘ 7fcl/ 0' [0593f waif?
WOVJCQPV‘H w CMEC/ pnr’f'wif MV‘J@VM#VI Tia, am; 2 5ch will, Er‘w‘una 9 culmle DION“? “Fl/“71+ 0‘9 2i. d) If the cube were replaced by one with a larger side length L (but sill zero
density), would z increase, decrease, or remain the same? Which equation(s), if
any, does this eliminate? Briefly justify your answer. I]? L Mug \afggr/ ]’Le (LAM Cat/1U 670‘s” 0! SLerDI/ 433mm 0M4 G16” W “KL gape, VOlmwe §MEMV§e4 0W;
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clean/ml on Lori all. e) Which etion(s), if any, might be the correct answer to this problem? Extra C redit: Derive the answer to this problem " or real ", from ﬁrst principles. (Try using logic
similar to the damn dam problem ﬁom your homework, with a few important details
changed.) Does your answer match the eqaation(s), ifany,,_that you selected in part (e)? Problem #4: A cylinder of radius Ft = '10 cm contains a movable piston as shown below. Initially,
the piston is a distance x1: 2 meters from the (closed) left end of the cylinder. The (airtight) section to the left of the piston contains a quantity n == 3 moles of helium
gas, at unknown temperature T1 and pressure P1. The section of the cylinder to the right of the piston is open to the outside, and will remain at pressure Patm
throughout the problem. ' A string is attached to the piston, passes over a pulley, and supports a weight of .
mass M: 60 kg. a) Calculate the initial pressure P1 of the helium gas. ‘ Page/“ball; JFajl’aM Pig'ka ' 4: 77—22 b) Calculate the initial temperature T1 of the helium gas. Heat is now gradually added to the cylinder, and the piston moves slowly to the
right until it is a distance X2 = 3 meters from the left end. This process takes place very slowly ("quasi—statically"), so that you can assume the piston's acceleration is
essentially zero at ali times. ‘ “gm”? [E
0) During this expansion, does the gas pressure P increase, decrease, or remain
the same? Briefly justify your answer. hemning ‘H‘mﬂ, 90ivaj w ‘Furcaé W‘o/ COWGI'JQVeCé \lv‘ Patl+ Oi WWW mgr stall 10:41am in may! “ll/“\ch News Ovif SOKW‘t—BOA ﬁw P! Lolclﬁg Tkm‘ﬁ/ ‘19 OWL {go‘OCtrt‘C Prof/€49, d) Calculate the final temperature T2 of the helium gas. «—.—~ ,. W; of HA V r 77rle I __
2 _
N k WAR V; ‘ EiVt [91% (52:9 Nokwm MOM; {feat/wee) l’x’ Ctrﬁ‘l’le éawe
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(014% QLgo’ til/Lyle RAUL? HUME” Eta$2; TJQQK?Q§ (OW/ q9¢sz 9) Calculate the work done by the gas on the piston during the expansion ‘hmé 76 01 Camsltﬁw‘l‘ ’ ﬁn‘ﬁéw/a Precesg $0 W 2“ 'PA r I
: (gllocvo POO (VaV.)
: (at 000 Pa) (0.094256. 062%?) f) Calculate the amount of heat 0 which was added to the gas.
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at) ' ' __—“ » 39l‘93 Problem #5: An inventor of mass m = 60 kg wants to rescue a cat who is trapped in a tree, at a
height h = 5 meters above the ground. She can‘t remember where she put her
ladder, so instead she builds a perfectly reversible engine which extracts heat
from a furnace at temperature Tr: 1127 Celsius. The engine turns a wheel which can be used to do work on the environment (and thus to lift the inventor up the
tree.) ' The engine also dumps a certain amount of heat into its coolant lines, which
contain water at temperature To = 77 Celsius. ‘ She fires the engine up for a test run. In a time tfest 20 seconds, the engine
extracts Of: 400 Joules of heat from the furnace. a) What was the change in the furnace's entropy during this twentysecond
interval? b) How much heat 00 was dumped into the coolant lines during this time?
(Remember: the engine is perfectly reversible.) aimCZ Me Pfage§5 TS ﬁve/9mg A SC Jr A :o c) How much work did the'engine do during this interval? Eyérﬁy QWSQVVOL‘Flrf/‘Vl '1
Call 3 W + Q0
W ‘3’ 0H "— QC} Satisfied with the engine's performance, the inventor now hooks the engine to a
pulley, and uses it to lift herself from the ground, moving upward at constant speed. d) How much time does it take the inventor to reach the stranded cat? w (Mei/«e; can clcr 2003" o(" Work ’in 2C9 Semi/[{9} “Pl/MS} 1+ (p69 :9; (or [EM/aha mang if: W (Free) _ a  ‘
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 Winter '08
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