Questions and Example Problems from Chaptdr 18
QuestionI
Threediffererrtmaterialsof identicalmassesareplaced,in tum, in a specialfrcczerthat can
extractenergyfrom a material at a certainconstantrate.During the cooling process,each
material beginsin the liquid stateandendsin the solid state;the figure below showsgraphsof
the'temperatueT versustime t for the threematerials.(a) For material 1, is the specificheatfor
the liquid stategreaterthan or lessthan that for the solid state?Rank the materialsaccordingto
(b) their freezing-pointtemperatures,(c) their specificheatsin the liquid state,(d) their specifrc
heatsin the solid state,and (e) their heatsof fusioir, all greatestfirst.
Q = c,",oT
dVlt = c.r".,dT/dt:
.ca.r*b^t
t**r*,
(o) @-tul l&^'1
(l)
l^e
(b) L53
(b)
lr_a!3
(.)
.\"r
(c)
(b)
a\)
J ) |
1.3'e.
+--Question 2
A sampleA of liquid water anda sampleB of ice, of identical
masses,areplacedin a thermally isolated(insulated)container
andallowedto cometo thermal equilibrium. Graphsb through
f areadditionalsketchesof T versust, of which oneor more
areimpossibleto produce.(a) Which is impossibleandwhy?
(b) In the possibleones,is the equilibrium temperatureabove,
below, or at the fieezing point of water?(c) As the possible
situationsreachequitibrium, doesthe liquid partly freeze,fully
freeze,or undergono freezing?Doesthe ice pafily melt, fully
melt. or undergono melting?
(a)
_ I 3f*otr*.f
-2_+
JrTna*-+ry:2,*,c
iD'"?- D\ ^ )/"-*4,^,r-."t
'
7'
l=*
Iflf
'---
7'
1.._
t/
II
I-?-
I
I
\a)
(tt
'!
t
|\
I f'
Y
J
1'
I
II
re
l.t)
I
l
ru,fr"-lq"r
' _no,^
(/)
t1)
d". no)tq*A
4l
^,\2 +xttA
r".er,,,,,1
q\s'Ib
("),_mtr#&'"* E"yH#A*P
21WW8".*
'e- /rt) /r-e /i..d*Z
Question3
The figure showstwo closedcycleson p'V diagramsfor a
gas.The threepartsof cycle 1 areof the samelength and
shapeasthoseof cycle2. For eachcycle,shouldthe cycle
be traversedclockwiseor counterclockwiseif (a) the net
work W doneby the gasis to be positive and (b) the net
energytransferredby the gasasheatQ is to be positive?
(")
b{&
__:=--
(b)
)r4tt
,Jo<^'ota"
)ia
A F= &-W
r$ax
,
/\ro -1.c, .rr llla
-A,)uv"ri Al-'O
Q= \4/
Problem 1
At what temperatureis the Fahrenheitscalereadiagequalto (a) twice that ofthe Celsiusand (b)
half that of the Celsius?
T, = q/ga" * 3{
(")
---+ '/rT.
7, = AT.
T, = l&o"c Ao furt
-f
n
2 1 n'tr'
F
-13
)-=-
-i
J
lo
-t1
|
6r,J
-"
2^a
J4
? " EI -
Problem2
An aluminum-alloyrod hasa lengthof 10.000cm at 20.000oCanda lengthof 10.015cm at the
boiling point of water.(a) Wtral is the length of tle rod at the freezingpoint of water?(b) What
if the lengthof therod is 10.009cm?
is the temperature
L = lO,ooocn
/JL=/-arT
6f-
TD.oooC'
AL:
o,olscn
d =
----o
-<=&
LbT
O,olScm
( to .ooo" - ) ( rc'o"" c)
t-..
AT= 3!
L-1
=
( o . o o g c m)
( ro.
".o.-)(
t a2"rc./.-)
= 4?.1C"
l_---_1
I - - l - - - ort \' Q
r or. '"' I
l, I
I
Problem3
At 20'C, a rod is exactly 20.05cm long on a steelruler. Both the rod andthe ruler areplacedin
an ovenat 270"C, wherethe rod now measures20,11cm on the sameruler. What is the
coefficientof thermalexoansionfor the materialof which the rod is made?
*+ drJ*,t = r- |y'b/c||
+,,^- b*L'& 19-x,
/tfie ^,har,v?o)i'x Jrjt"ZM
)
Ar*A Jff" ]o.
\lc".r .t6h^h
*L M"
AZ = L-)./)-r
-p"tfu"""^t -tA" O ".* nv..,a*{
"^-A\
)a
A L = ( )o.llc*) ( t)- to 7c")(ar""c-J-o"c)
-) fr\, a fu^l ,), 'g
)*, )-\h
"n
- ]o.o!.^)
()o-llcr1
AL
L bT
"4
= o. oSBc,r.,
M'r/'a :J i4
+ 6.oSga61 :
O ' ll5 crr\ :
LL
-lo"^=
Y.,oZsl
(ro,os",n)Cr5oc")
,-
O,ll5cn)
L-.--_-"--
Problem 4
What massof steamat 100.0oCmust be mixed with 150.0g of ice at its melting point, in a
thermallyisolatedcontainer,to produceliquid waterat 50.0oC?
C'_\=
qrjo-r/fr.f
-.tfut"-irg
)
Q,,1"^ +.Qi^o =O
-uootah)
L9= 332* 1o3:/f1
Zv = ).r5{e,lo3s/y*
-- TqeL- + tqs c-,ATs
t te; /4 -t tqa \aTi
lJ,ot^" - loo.o"c
J A1 = -$o.6c"
-- - Eb-DK
'
It- So'o"c?
-- So.oc"
fr',,,-\ =6-cI AT-"a
= So'oi'
{ns = ( o-rsolti) (r.ttto/p,.r<)(9".of
|rl, (/u -c-oT,) : t.....9T;* ni k
lTl: =
IOcC- AT. * n; L+
(Lu-c-aT")
!!o -t s"Yil(zz z, ro'-t/ yz)
(1esr"* to's/b) - (q nos/rx.L)(- sr.ok)
f0r=
O.633F1
- 339
=6
Problem 5
Calculatethe minimum amountof enerry, in joules, requiredto completelymelt 130.0g of silver
initially at 15.0"C.
--) JJ, ^.,rlJl'-d
-7; = /5.o"c aTtK
f\
u(
= la35)<
T.
'JL :
\lv
'T:
*L /rfuta ;a
^ -'r-
-
\_-lr) /J r
lA35 K
t
t't 4-+
T
{
AD"Ae )Qrrr,+o&
-,v)"r4
-S/rr.*
\
.t'*,,'4" .Fl^-* 4"-,
)-L'A)o'..fuw.d
L+- l05'\oayK
fq:
Q = (:au-t/vx.u)(o.r:oKx)(rr:sK-tasx) +
O'l?oKg
(ro5" rcta/v')
( o. ruoKT)
t-
I| Q - 4-A't"loqf,- I
Problem 6
Two 50.0 g ice cubesare droppedinto 200.0 g of waterin a thermally insulatedcontainer.If the
water is initiaJlyat 25.0"C, andthe ice comesdirectly from afteezer at-15.0'C, what is the final
temperatureat thermalequilibrium?
t0.,;q= O.teofg
--'4
f,
= 6"g'OooFg
nq
"r&
\
a,q*rl.tvry Tg<CfC
nb i^2 "wclb, rr-*qri4
:::-
dW'tp.r^.e,H) 7+ > o'g
7a'-,a=r.s.o'c
T;, ^i" = 't 5.D'c-
,Arclf
7) ="
C,-.q = l9orfr2'r
\t=
-l5.o"C -+ O"C :
^.rrJE cAa",gr .b-*4
"6,^" +'z.y\
Iq ;,." Clir
^'fi", = (o a'oFgx ).e:os/ra.v)( l s.o c)
\x- 3 3 3 0 5
g_ = 1a1os71rg.K
Lr= 333t1ot57,o
""O^
b.mryt"g
"rerr;rJ
Q = m*,,4 Cu*, aT.,h
dt uldbr -|4ae).s.o"q -r o"C i.
4r"i
= (o.:oovg;(alco5l€-r)(-es.oc)
a=* 1 . .l D * l o qc
,ru-f ^*r;
l\7r..dtrac i Q = m.ut, L4- = CD"tooFg)
</vs).= 3. 33,. toq=.
1aa31163
,$ = D'C
!
Ot-
+g"#^*
+ Q^--x. =O -=> m,^1C; aTn -r n Lg ,CI*,,*,,e,_& AT;_rc =o
-aEcflio.ro)(>u) (s
[\=
tn=
l = u .0.05!!?
u > a P q : b 3 = 53s
3ZZ^1otsr/p*
Problem 7
from 40 Pato 10 Pa.
A sampleof gasexpandsfrom I .0 m3to 4.0 m3while its pressuredecreases
How much work is doneby the gasif its pressurechangeswith volume via eachof the three
patlr shownin the p-V diagramin the figure below?
W = ( tJV
q
gdl s o
k\
cr,vr,,},-rt {44d4^r,o --r
WL
ve^.{l,rd nntt't'ttr.o
n-\^
s.,
-- ,o,^.r.q-t,^ Jrt ^-^r'\ rt
W= P AV
) W'D
-10
0
9
A:
1.0 2.0 3.0 4.0
Volume(m3)
V/"= llof
,ar.na-u^Atr z1r;,v\r<-* ,|tlxz-Ir^ou
Ja{l ...,x/^r,{ = (loP.)(t.o"l)
:
alAo--.-,p = -lov*so
C :
= (qoPq)(a." -w^) -o
W=prV+O
)
}
= lot
W= Spdv= f
t(-,orr.r9dV-?ST
\ryr= O + p av '= o=+(lop^)(4.o,,'31.o".)=E
Problem 8
Gaswithin a chamberpassesthroughthe cycle shownin the figure below. Determinethe enerry
transfenedby the systemasheat duringprocessCA if the energyaddedasheat Qasduring
processAB is 20.0 J, no energyis transferredas heatduringprocessBC, and the net work done
duringthe cycleis 15.0J.
a
Qo*= + Ao.o5
N
ti \\
oi
\.'
\_xBc -
\./
/
Q*" =
-\-,/
4*,
=
-Lr"a*+
( Q > O .a.^n"',,.-e
M oll4 a'Lb'Ld" )
J
2.UJ
(
-LI-W
AT
Q*"* Qe.'ci"*)
/l L = l
o ttJ,Arc.e^&
6)r'-.sLe,4-,bE=O
Q4e * Oa""
Qg6 -W
\n/ - (:)*p, - Qe.
"A=
/ 5'o5 - eo.o5-o5
-
E
"==--
^\ -r-
- W
Problem9
The figure below showsa closedcycle for a gas.From c to b, 40 J is transferredfrom the gasas
heat.From b to 4 130J is transferredfrom the gasas heat,andthe magnitudeof the work done
by the gasis 80 J. From a to c, 400 J is transferredto the gasrisheat.What is the work doneby
the gasfrom a to c? (Eint: You needto supplythe plus andminus signsfor the given data.)
j
o /v-yj;-
&^
= -L/o5
Q:-=::::=:.u
\n/o6 = as-
eu:-:L:gr
Wuo = :39:
-.===-:--
Oo" = 4ool
W^"=?
Q,'a<e*t'''--z
AE= Q-W = o
'==-:-
l.'+.-^- ov <o)
(
e"4:"
(O"" * Q"u i Qu" ) _ (W^"'W.u' Wu) =o
Wo^ = Qo"* O"r"* Quq-W"r Wuu
'=
4oor r (-ror) + (-'ta"r) -('=)Woo
--
3 lo f,-
...-a
f :os)
,w,.cu|ot.t)pt.t4 W >o rrri;,* AV>o
Probleml0
A cylindrical copperrod of length 1.2m andcross-sectionalarea4.8 cm' is insulatedto prevent
heatlosstlrough its surface.The endsaremaintainedat a temperaturedifferenceof100 C' by
havingone end in a water-ice rnixture andthe other in boiling water and steam.(a) Find the rate
at which energyis conductedalong the rod. @) Find the rateat which ice melts at the cold end.
l.J,r.,
4" trc'i)"'
ei,8"\tiama
loooL-o"clooco = looK
zlot
Ws
(b) Q=roL+L
l
= D'/L+
=
t%r
/1,;z3z' t035/fz
p = (rrotwA.X)(4.r"
ro'!^'>)(looK)
i"an
P = lcW
d%t'
*
L+*
P=(d'%*)L'
9JZ = 4-tt-t?
\
-Yt/'
-E
Problem11
(a) What is the rate of energyloss in wattsper squaremeterthrougha glasswindow 3.0 mm
thick ifthe outsidetemperatureis -20'F andthe insidetemperatureis +72"F? (b) A storm
windowhavingthe samethicknessof glassis installedparallelto thefirst window.with an air
gapof 7.5 cm betweenthe two windows. What now is the rateof energyloss if conductionis the
only important energyJossmechanism?
?*-s." XA (rH--l-)/L
= 3,O mq,- J,O* lo -rv\
L
^^art
/J.'l'-\-o''
l.:
/n-
-
)\ do- "
-
/7t ^
"2oF)
.r
tl
(")
A
fn
Yd I
\
- \ |/
1,u w/m.l(
?,
I cp^t
=
-.-<.
4'.,"*r i4.
-T.)
qSFo'
L
._T*u
- -1,
lx-3'7 '----> 7.^'1. =
----K
rT
1^!@
'
Kt**
a,_\
Y,-s/ t/"l =
5l"lC"
J-..--_
5"D* lO - fr)
rI
( b)
(\
" )<
D i. t \_
+ LA
K.o
P"gJL
= \tvt/ra
l-r
t1
LProblem12
Ifyou wereto walk briefly in spacewithout a spacesuitwhile far from the Sun (asan astronaut
doesin the movie 2001),you would feel the cold of space-while you radiatedenergy,you
would absorbalmostnonefrom your environment.(a) At what ratewould you lose energy?
(b) How muchenergywouldyou losein 30 s?Assumethatyouremissivityis 0.90,andestimate
otherdataneededin the calculations.
?rd = P"* - ?.-n*= ae A (tn- r;: )
?p; - L€ AT"
t
O. 5t"?^lf $n
Nt
t = o"9o
A "" An,*
-f
x 3o"K (zroK,J^ro,..l)
-f.nu
.
') (e'"r;{
wA'rJ(a.
(s't'^I"
(o.ro)
ldt
?o"S^
P*"r-
(r)
t' lDqW
P= E/t -----)E = Pt
JF.
E = (?"lo'v)(:os)
':'
*
5 ,-l'*;"
2'.,\D'd