You shouldknow how to calculatethe fina1temperatureof two or moreobjects,idtially at
differenttemperatures,whenthey havebeenin contactlong enoughto achievethermal
equilibrium.Usethe conditionthat the energyreleasedasheatby oneobjectis absorbedas heat
by the other.Ifthe final temperatureis known, this conditioncan beusedto calculatethe specific
heator massofone oft}e objects.
Therearetlree mechanismsby which energyflows ashealfrom oneplaceto anotler:
convection,conduction,andradiation.You shouldbe ableto differentiatebetweenthesethree
mechanismsandyou shouldknow the equationsdescribingthe conductionofheat through a
materialandthe radiantheatemittedby an object.
You shouldknow the reiationshipsbetweenthe massof a molecule,the massof a mole of
molecules,andthe total massof a collection of molecules.Ifa gascontainsN moiecules,eachof
nuss m, the total massis Nm. SincethereareNe moleculesin a mole, the gascontainsN.AIa
moles.ThemolarmassM is themassof NA molecules:M : Nam. If the gascontainsn moles,its
total massis nM. Note that this is exactly the sameasNm.
Many problemsrequireyou to usethe ideal gaslaw PV = nRT to computeone of the quantities
that appearin it. You shouldalsoknow how to computechangesin oneofthe quantitiesfor
variousprocesses.For a changein volume (andtemperature)at constantpressure,PAV = nRAT
andfor a changein pressure(andtemperature)at constantvolume,VAP : nRAT. ln eachcase,
the amountof gaswas assumedto remainconstant.
Questions and Example Problems from Chapters 12, 13, and 14
QuestionI
Two identicalmugscontainhot coffeefrom the samepot. Onemug is fuIl, while the other is
only one-quarterfuIl. Sitting on the kitchen table,which mug stayswarmerlonger?Explain.
5x
-W-w^ia,C
ffi
]-^y",
u\je^/n\e^t
. %A% )Ev
^^4^]^h
fu '*n<
4 -r"ro.)CP=eoni 4) 9r4 &,^^ Q =rocaTfu -tu"p,t'rttl
guestion2 <lto",*5"-U"a +-, *
q.^, yra..yY-u,
.\.j ryy.,rt
.bte
ventwheriyour hair is wet thanwhen it is dry.
Your headfeelscolder rinderaniir-6onaitionia!
Whv?
fun
B-r'cc,Jt"r"
o1A aD
Question3
Grandmasaysthat it is quickerto bakea potatoif you put a nail into it. ln fact, sheis right.
Justif her bakingtechniquein termsof one of the threeprocessesof heattransfer.
,c,o,\t\utr]b,t > fr" rwrr"^A
,^ a"^*-ArJ
,v'"q 19, / \a/oi, 4 fiv
Question4
Assumingthat air.behaveslike an ideal gas,explainwhat happensto the pressurein a tightly
sealedhousewhenthe electricfumaceturns on for a while.
|V= nAl-
Plr=!#'M
-)
fiv
4 n 1V o.ente ,^,fu,^*)-P-1
p-wa'u',n@
-=-=:
"^/f "4/\9or4L4
aafrv h'ryttofua"
\\
Problem I
On the moon,the surfacetemperaturerangesfrorn 375 K during the day to 1.00 x 102K at night.
What arethe temperatureson the (a) Celsiusand @) Fahrenheitscales?
-Ia^r=3?5K
-L*P
-r" * 3a"F
T. = Tx-A'13,J5 T* - ( l't"Ffc)
= 1o5g
r------:---:/ ^\
(^)
Jr* = 3?5- a"ts"ts= {lZ.e-El
-T^rrr^)
= f oo - I"t Z = fCiE
-l"t%=
(t"t'F/"c)(roa'c)+3a.F =
(t)
i@_
problem2 T^rll1 - (t.z.F/".)(-rr: "c)+ 3t"F =l-afq"f
/
A temperature
of absolutezerooccwsat -273.15oC.Whatis this temperature
on theFahrenheit
scale?
'L
T"= -a?3.1s
---1rF -- 2\
\-,
'T= =
(t"t Y/r")t",
T
= (t.sF/rq(ttt.ts
7
=.- '1s1.6'l"F
3e'F
oc)+34'F
Problem3
Whenyou take a bath,how manykilograrnsof hot water (49.0 oC)mustyou mix with cold water
(13.0'C) sothatthetemperature
of thebathis 36.0'C? The total massof the water(hotplus
cold) is 191kg. Ignore anyheatflow betweenthe waterand its extemalsurroundings.
-f
.)br
t ' , l _ = 4tQt . , 2r -
l:
= :;:?
Q
= anc AT
-8"-" @t\a!)wu'*r'a^
ox t'twfr't
)
/\r\
= rirKg
ra.taa,
Yffffi
rr*r!€-'ffr\a\'ut*** :
= *ffit"H
i/\
f0-€{ L AT*'A
Eq* C ATr*t
fl).q"*C"-ri AI"*
-
ilrqC.,,,t,
ifl"q= lll\-rt)t6
A*T..d
6a4 (+f"o'C-3b,o"c) = ( l9 | [g - m-,,*) (aa.o'g-13.o"c)
= i 1lK3 - ili,,1
l0-0"t ( ''."t^)/
\ ,'3,oc"
,
= l\lYg
/,5"7rfr'^a.
'--
0,5? rq.e*= l9l[g -rQ5"1
IT),ut= i),?.Kg
Problem4
oc
Find tib'massof waterthatvaporizeswhen2.10kg of mercuryat205 is addedto 0.110kg of
oC.
waterat 80.0
rofi" fiat
)
arr^a,
""*
M,+A^fu* '8 Murl+frw
C""'N = 4lsuS/yqc"
C.'*""""1= l3ls/prc'
a$ f,9\, '$;@, N",f,a.Qil
al
) i\D< ,!l$\n-4p b! &"e'
^i loo"o"c
Qlrot"n@^il,"d
=
!*r*
Q*t
f}"",--z a^,** AT'^% --- I!*.r"C;
f0""r^""%= A"loKg
m
A
o
-Tt ,to*o
-= / q ^ c " l( -r"
-- /{)5C"
=
AT; + nLv
fflr.np-. C.r^',t- AT;4"t,-
Lv
rr^o..\
lc.vJ-e )
$ = ( t, tovil ( B q qrq r ) ( tosc"\ - ( o. rorl\Q$bVrr,")Apc
,AT,-& . ( loo'c-|o.o"c)
problems = a.c"oc"
---*- jA.br'lo,:/Ys
lnO.=?.'-tAtKal
of an object,the temperatureof
Ideally, when a thermometeris usedtoGas-lF]FGfrpfEffire
the objectitself shouldnot change.However,ifa significantamountof heatflows ftom the
objectto the *rermometer,the temperaturewill change.A thermometerhasa massof 31.0 g, a
of 12.0oc. It is immersedin 119g
specificheatcapaoityof c = 815J(kg c"), anda temperature
oC.What wasthe
o}water, andthe final temperatureof the water andthermometeris 41.5
temDeratureof the waterbeforeinsertionof the thermometer?
ffirrr^n^$,
*id
4/\Dr\ rz\tAt"
---
4d s...Atg:
PQ=3to3= 3l.orlO-?Vb
t., = lt.o'6
T"
'tll.6"L
I
Xru*.-&
AT=
aq.sc"
@
Q,'**
\X q \tf J4,6
c= Srss/1yxc")
-f
n
..
^L)5t9^'. A
rr |
trOl,tfu\
,r*"*
ATr.u =
flo^
t;=
'-'l=
t+
Cx,-. A-l --.
/J | *.y = (:r.o*to,ursxgr:
%*..\(a.r.sc')
(o"trtK4)(qfibyvsc")
7
1t"5"c
i
A T-*.
lr rur.b L i$.& AJ lu,r/l
l0*,a C
"**,,
I.i= lllC= (o.trgfi)
Qt$bs/pq,c)
-
L-1"-o,=LEX"
-I;,"*
--
lJ?
tr.u
- -T,.- L|i.E"L
xon
l,,
fYl= l}o'otrg
2
--=:
Problem o,./
a (0.[t!,5toct< of ice hasa temperature
of-10.0 oC.Theblockof ice thenabsorbs8.11x 107J
of hdtlVhat is the final phase(liquid or gas)and temperature?
=
C"-l
C,w
4lgt,5/vx"c" Lr=ZZ"S^lo+{/b
= 7.oot1o3 J/vg<"
/u= Aa'r"r)o5d/fs
'8 q64^-or'i )-<e e -lD"ooc b ,t,te
)
'h'c)(r'"o.)= -.-_.--n2 d = f\')4A T - (1oo"o/g)(l.oo* to3</yA.L".
NryUr/'u
L99tt
)
)
\
+
A
t-^
,b ,$tW I oo.ofg ,[ ^"" * D"^"h 1oo'ofx "6 ";E\ € Ouc
= Ooo.oYg)(Z3.5xlo4
i/q) = 34
& = r Lj
D"Ch w& e toooc,r+uA!A 6)=rncAT
.,b ?$.a.q wdb t
e : Iroo.ott*\(4tg\d/q.c) ( loo.oco)= 4. ts toxlo'tJ-
'txb'b'7J =.4a
Q-or{r\= 8ollx lo?:r- A"oo/lobr- 3.39x to?u- ?
rlobr
\ fiu apu*ih c wqfu,!
O=no/u --) f/-)=A/tu-- 3,?f
+;Tf
H,."r*f.,fJ**,,P#o#",##","m.r],,Ho
at oneendand 112'Cat the otherend.Bothrodsare0.750m in length,andthe leadrod is 2.60
cm in diameter.If the combinedrate of heatflow throughthe two rods is 33.2 J/s, *hultf_tttl4.u5 q /b"^
diameter of the copper rod?
lOooc't 9S,: Vg'rfut
n^lr--F:r
-vv'a'l
)kn
co?per
r'o^b\J
c
I l.oo",r
I
--)
L--*----
V
h cagprr
K^;.'
-7
Ln1?r, r '"
o
6.75om
Q
qt rt ,, 5 /
J
/5.n.("
5 >
*
Qt l^*e 23.tVs= (V.)*-" (%)^
7s.n.c"
B.tr7t
I-o"l = 0'Ol3onr
-I
_,v*=
ry
N'\'^1
vAl.-r
l\ coll'^, f1<o1y,
-
/J
I
Ku A.a*rA-I
L
33.tf/,
=
-ry
( Kq'r, t
L
i^
f*r*, * KluAn
/-^a
\
t -t.J /
Problem8
A person'sbgdyis coveredwith 1.6m2of wool clothing.Thethicknessof the wool is 2.0 x 10-'m'
oC,andthe skin temperatureis 36 oC.How
The temperatureat the outsidesurfaceof the wool is 11
to't do.bra it
muchheatper seconddoesthepersonlosedu" to@
ft= l'b"'a
( K+or-)t
/ = A'o*lo-3r.r
L
,Af = 36"C-l-t".
:
Q/.'t
/T
!5C"
K: o,olDft.c"
a/t
'<
a/. =( o,ouo6.,")(\, tn'_l!jj
-2
'\/r<r"\
- r
].o r lD-3c.r
= 7 'oo'to\ty'
Vt
'----.-.------.------------------------_-_
Problem 9
If thebodyloses
A person'sbodyis producingenergyintemallydueto metabolicprocesses.
drop'
If the drop is
generating,
will
processes
its
temperature
are
energy
that
metabolic
more
severe,it canbe life tlreatening. Supposea personis unclothedand energyis beinglost via
oCafld an emissivity of
radiationfrom a surfaceareaof 1.40m2,which hasa temperatureof34
0.700.Supposethat metaboiicprocessesareproducingenergyat a rateof 115J/s. What is the
temperatureof the coldestroom in which this personcould standandnot experiencea drop in
body temperature?
A = i.qun'*
9,:o
, rnr.f,
-i- = 3l"C = lo? K
-T- 'j
I = o.?oo
Q/*= \tss/s
I
"'r- Il
6A(T'?
-T
-
lD
"r4
t-
'1
.
-r- 'l \
D*
_!gu-
e6A
?"a/uo*
-I [...--,
L
-T -?
lo*'.
L
l"= ag?K
(o.roo)(s.c?xr;"ff(i.rom')
")
-T
l
D
= lil 2".
v
I.L"
l
I
C6H J
( r ts t/s)
r
l'= l(:otr)l-
?*-i
-'--
1,/'1
Problen 10
Supposethe.skin temperatue of a nakedpersonis 34 oC when the personis standinginside a
room whoseternperature
is 25 oC.The skin areaof the individualis 1.5 m2.(a) Assumingthe
emissivity is 0.80, find the net loss of radiant power from the body. (b) Determine the number of
food Calories of enerry (1 food Calorie = 4186 J) that is lost in one hour due to the net rate
obtained in part (a). Metabolic conversion offood into energy replaces this loss.
I =21)"(. = 3O'll\
-t
|
-
To=As"C=2,18K
A=l"5tqa
€ = D'to
P^"t= 6't,g w
?=vr --t E
(b)
F
=
)"4t1,
= Pt = (6"t,sv/)(36oo<)
-/^
rn5 -1- /
\
LC^t
E = 5f
\
qtsbs /
col"","s
Problem11
The artificial sweetenerNutraSweetis a chemicaicalledaspartame(Cr+HrsNzOs).
What is (a) its
molecularmass(in atomicmassunits) and (b) the mass(in kg) of an aspartamemolecule?
frlc.lA,orl q
(q)
i{'tn= I.oo?91Ll
=
lOtp= i4.oo(o?u
ltl rnc + ig nj + ). rnr.r* 5 D,
1ti(lA,orlu)+ lt (1"o6?ctu) + I(tl,coto1u)
2.9't.3o? q
J,9,i.3o?q(
DV\\onYq WeJb
ftfuan4=
+ s (/5.qqqrq)
N)"= )5.qqCqq
(r)
**fn"^l*
".
I, bbo5 * lo-)?[a \
----a;/
L ] . 8 t " 7x
1"r{\a/aF,?.,'t?& = a,91,3 o'l Z/**
^t\r,u/ F{ m,OQpz.,Ao-= rCnc.aaFef m^'&
* n'Xot"tu/n*
-=
Problem12
Manufacturetsof headacheremediesroutinely claim that their own brandsaremorepotentthat
the competingbrands.The bestway of makingthe comparisonis to comparethe numberof
(csHqNoz), asthe
moleculesin the standarddosage.Tylenol uses325 mg of acetaminophen
Find thenumberof
dose,while Advil uses2.00x 102mg of ibuprofen(c13H13o2).
standard
(b)
(a)
Advil.
pain
and
of
Tylenol
doses
reliever in the standmd
moleculesof
f
f 0 c = l A . o tl ' . a
|fl*-- l.oo?4'19
'\---/
(n'oa'tu)t
1 , n o )- n C r f [ 1 N o n = 6 ( D . o l l v ) t 9 ( t , o o 1 n 1 r 7 n
----> Drv'-r :
y(15.4414u)
lEl"t b u
fl * : /t.oo{cJq
1 1 l o =i 5 , 1 q i L l u
ld)^au^frt't \'=
|5.r"-0t ( G,oaa"
O,oof,
_
-----.-_--:)
I\
/ta'i/L
(t)
/\dr,,lJ
t " e1 * lo^l at-eoo"taC, t'f1lto,
C,ztt,so).= lj(ra,ortu)rlf-(t,o<-?elu)-r X(15"1t1,/q)=aorr.3q
s. b1:,fu
;t:i"fl'Ns'3iT/]6
.,s/l$'p,;;"p("?
, ;;",,?"?""ri
["ir'.T# ",r5.5'cand
"i*
raised
manymolesof gasar" pt"reni?(b) If thevolumeis raisedto 4.16mr andthetemperature
,7;S
=J $,9rr ld-f
of thegas?
to z8.2'C,wiralwitt bethepressure
T=)5.5'C=],3?.b5K a)
g = 1,71rlot pq
r.r
1.{l
,i/
e u , .c,3
y = a
PV=nAf
---) \=ry
\ - a"t
" " r.t)'
n = ( l,?2.,.lo5P")/ 1
n=?
- - - - a',
l'("!tu'!'4
=
i;--_lll
lO
l m.
ft"tts4o"r)(mz.usl-)
b) ?= nAT-@
y = rl. lt ro3
= 3ot K
T= Xx.5"C
4 . t bm r
l-r
f = I"|)x lD5 fa
Problem 14
of285 K anda pressureof 850kPa.
tankholds0.500m3of air at a temperature
A compressed-air
What volumewould the air occupyif it werereleasedhto the atmosphere,wheretJrepressureis
is 303K.
101kPaandthetemperature
--)
n
BT
Y=
P
ru
V = O,Eoo
T,= \$sK
l,= tSoYPa
UL
T'
va.
-7^= 7o3K
f)
Drt
tlL:}
-___-_i Vn =
-4'
l6
Vn = (S5"KP")(o.E"o"t
.,(.\
fa= lDl Ffn
=
nB
a---+-I
( rorKP")(a.:sr)
IV"= 4"4lrz I
=.PV
= aeP5'|o1t
T
7,V,T^
P^T,
)