ProblemSolving
You shouldknow the relationshipsbetweenthe massof a molecule,the massof a mole of
andthetotalmassofa collectionof molecules'Ifa gascontainsN molecules,eachof
molecules,
massm, the totalmassis Nm. SincethereareNa moleculesin a mole,the gascontainsNA{e
:
ihe molarmassM is themassof NAmolecules:M Nam.If the gascontainsn moles,its
mo1es.
total massis nM- Note that this is exactlythe sameasNm'
:
Many problemsrequireyou to usethe ideal gaslaw PV nRT to computeone of the quaatities
that appearin it. You shouldalsoknow how to computechangesin one ofthe quantitiesfor
variousprocesses.
Heat(Q) is definedasenergythat flows from a higher temperatueobjectto a lower temperatue
or releasedasheatby a
in units ofjoules.TheenergyQ absorbed
oUleciira is measured
=
heat
.olrtuo". is relatedto the changein temperatmeAT by Q mcAT,wherec is the specific
capacity.
you shouldknow how to calculatethe final temperatureof two or more objects,initially at
affi"."rrt ,"*p"ratures, whenthey havebeenin contactlong enoughto achievethermal _
asheat
iJ* the conditionthat the energyreleasedasheatby oneobject is_absorbed
;qriil;;
specific
by the other.If the final temperatureis knovr;, this condition canbe usedto calculatethe
heator massof oneof the objects.
Therearethreemechanismsby which energyflows asheatfrom oneplaceto another:
conduction,andradiation.You shouldbe abieto differentiatebetweenthesethree
"o.u""tiorr,
andyou shouldknow the equationsdescribingthe conductionof heatthrougha
,rr."t *ir-,
materialandthe radiantheatemittedby an object'
12
QuestionsandExampleProblemsfrom Chapters11 and
Questiont
ts
Tirroidenticalmugscontainhot coffeefrom the samepot. Onemug is fuil, while the other
Explain'
onlv one-quarternr[. Sitting on the kitchentable,which mug stayswarmerlonger?
4
9w
-'D----'-
-4'r-
11
-
5 n* *"P, Ad^;k
9"n b-^ Q= llca-I Do
\-4e
AUt^J-TP=ah= eaArt
4
J
ho lt'"'" t.yY'*
bJ'tJltu\atvYk
.".n
d-A^a nrtp Nr\214''
W *t e i,-e
Qrr"itioo2 "!-su 44fv
iour headfeelscolderunderanaji-conditioniigventwhenyourhairis wetthanwlen it is dry'
whv?
,tiltr
r-aJ.^"-L!A
6r""-+
&v^\\
!e^
P^4 ^! An -I^a^t i
A4ar4
Question3
right'
drandmasaysthat it is quickerto bakea potatoifyou put a nail into it' ln fact, sheis
of heattransfer.
in termsofone ofthe threeprocesses
Justi! herbakingtechni-que
@)
)'^ila
Jfu r\"o.tr^-"at",d" Ald N'*"v"
d6bu VAfu
Question4
Assumingthat air behavesiike an ideal gas,explail what happensto the pressurein a tightly
sealedhousdwhenthe electric furnaceturns on for a while.
n a/,^AV o"" ltdh cA'uob^J) fr'\
?V=nA-t
)O'o
Wv fu'*y"*4"
V/r=*'co",,trt
Problem I
A weightlifter works out at the gym eachday.Part of her routine is to lie on her backandlift a
40 kg barbell straightup fiom chestheightto firlLarm extension,a distanceof 0.50m. (a) How
muchwork doesthe weightlifter do to 1ift the barbell onetime? (b) If the weightlifter does20
repetitionsa day,what total energydoessheexpendon lifting, assuminga typical efficiency
foi energyuseby the body. (c) How many400 Calorie donutscan sheeata day to supplythat
energy?
(^)
\M=Fdcr.O
(t"v)
(b)
: (*g)
d, ca:D"
= gq
1n,"s/,w)P"*/^*>
n a.
-{-
dD
z-
oFl
( q.?o",/s+)
( o,son') -----F-,
/
7
,
frc^i)4
E*t
.t'
/ddJ!
- ?1r6s,4"4
--.--+-!:
o,15
/ 5,aao5/,
\.. (c) /s,r"tu7to+(H)(ffi,5= O,oogzt M/X"
Problem 2
a 1500kgcarftom restto 15m/s.How muchenergyis
A 10%effrcientengineaccelerates
transferredto the engineby buming gasoline?
? = lD70- O"Io
ry..l_- 7 SooK3
V;= Onfs
-)
e
= @q*i;'
--s
upd w"A^^ toPog
E"r_^a
,.-Q
.-D
AK+AUr*AU,+ .
^K= )(+- l(i
7"n
r/S=tE^fs
'/u
1ttu" trc)[(
g=
W-r^"gr;
VJ"^^*;
Eb'*"4
t- ywil.
'
(4'- vr)
r5 . n,"r'- o1 = l.?"In5--r-
\w
I.?, t655
d.lo
= /.'l*
)obd-
Problem3
In qn averagehuman,basiclife processesrequireenerryto be suppliedat a steadyrate of 100W.
What daily energyin take,in Calories,is requiredto maintain thesebasicprocesses?
P = E/c -+ E*?.x
E = (1oow)(ro,+oo9
$,b'l"to'<-( xc"'
\
./
lros.-z
\
'i
Problem4
An ideal gasis at 20"c.If we doublethe averagekinetic energyof the gasatoms,what is the
new temperaturein oC?
&-w ]'=Z
,V
K-eu-', *X V^a S^two, fuTa^u'tq
's
(+ rna, T *"-* !.r< 't^ Ka'*^)
= 3(rt:K) = sraK
57 b\( -+
,
'-a^
'7
| /- o.\
/ = 5tJ\_
r-
nn Mv earult^ ,ea-pt
Problem 5
How manyatomsofhydrogen arein 100 g ofhydrogenperoxide(H202)?
Mn=Ju ?
Il.=rr,u J
M,..--X(1u)"l(rLq)=3.t
"l'u"
\
q
I L^"<nu[ ilro. )waarn*ua '6 3iQ
I
L*flzqg)= X.g1*,c g Haoe
(roos1(
a ;^*" Mp aapAfr bt":-'4 #.O", frv^,i S.Lry4_g#
.rr -l)
Nr+
'- -<1
I
t-D
--
xt \ t - - -2
I
o
/ffL.f<
-l
6.o1*(O''r,uo
l
Problem6
Total lung capacityof a typical adult is approximately5.0 L- Approximalely 20% of the air is
oxygen. At sealevel and at an averagebody temperatureof 37"C, how manymoles of oxygen
do the lungscontainat the endof an inhalation?
V = F"oL = S.o| lD-r*3
pv= nA)-
p = Jalrn= I.o)3^losF<
,^ \/
( t - oI ? ^ 1 o 'P . \ ( s . o - r d t r )
Y\ = _y:-:' = -.-----------
I
-.1-=3?"c = 3to l(
BT
\-,-=?
ls.zts/.-)(arn
\
//
g;
\
t11o\' ,- /
n = O"Xq-11 l --:) A67"al Wi )a
O"OHo,t"l
Problem 7
oC
a volumeof 2.81m3.(a)How
of 1.72x 105Paoccupies
Aa idealgasat 15.5 andapressure
manymolesof gasarepresent?(b) If the voiume is raisedto 4. I 6 m' andthe temperatureraised
of the gas?
to 28.2oC,whatwill be thepressure
7 = lE"E'c=)zz.bsY
,
a)
'!
oV
,AT
pV " n AT ----)
--
q-
P.l,'/?rlo-fq
V = a.a\ $3
't_.:rl*
,-^..,-\n
\ /L*"f1
(| L'?1*
losP")
n:
L\
\)=
Eol^Yr.,+
)
I t .z tt1",*,r;( rrr"r"sK
n=3
V= 4l I {or,)3
--t
P=Y
-- ( aola*a)Lv"ll r*,,'e-K)(aol f)
4"tb*,3
7-= a8.ec. 30lK
Problen 8
tank holds 0.500mi of air al a temperatureof 285 K anda pressureof 850 kPa.
A compressed-air
What volumewould tlle air occupyif it werereleasedinto the atmosphere,wherethe pressureis
is 303K.
101kPaandthetemperature
V,,= o-5oo.3
?V=
T, -- ats K
li
3o3K
pa.=lorIfn
T
?,V,= ?'V,
T"
96oY?a
.]'....4
V^--?
-lo-
hBl- ----r PJ-= nB ----t
rtY a. = P, V,T1
(o"s"on')(a.il
V* = ( TsoKP^)
Ic\
( 1otKp")
(rzsK)
P"T,
qF+.
Problem 9
What minimum heat is neededto bring 100 g of water at 20oC to the boiling point and completely
boil it awayl
=) -fr:^,t, b^.p,b*Ja tv'*.*," 4".o"\)cfe b--,
-- 0"lDafq
M = /Doq
tt
t6o'c (6 -=;'zl
caT) t^aW''n
C= 4r1o/yx.r
?\,0"1r>5-s/yg
/v.
y):: -["-' ry
r-*
"L*"ntl
(Q- Vu')
Fo7'o'
,All-= SOCO= 6o l(
aT * l'nlL,
Q = M ch
+ lo,.ro-yr)(aa.t* to't/Fa)
U{ -- Co"loofr)({\%ntu,*\,(xoi<)
Problem 10
of-10.0 oC.Theblock ofice thenabsorbs8.i I x lOi J
A 100.0-kgblockof ice hasa temperatwe
of heat.What is the final phase(liquid or gas)andtemperature?
L+ = 33"s x [oqt/Yz
Cuq = 4rtc-/vr".
= )A-Gr lo"
1Vz
C;t, = 2.oDr1o'f/vs.c: /u
)
)-., to|^^'^ i,u €-ro,o'L-I^ J'te J o"c- rury''t'rta"'
=
(a,oo
6 = rqc AT = (roo"ors)
" top)(1o"oc") i4=
)
l- n*.q't t6o"oYz"6,L "*o"c fit
loa.oKg4 d"& g onc ^syrL'u'"
:
Q = M lc = (rlo"of))Lzu.s"lD'lT/Fz) 3;lEr}Q15
)
n W $^,
u,o*' dl- o"c b u-Jr' ..i 1oo,ot /'T
& = M . AT :
Y"e"6*
=
c'\, =
( rou.uk;(l ttt"a/n.c) (too"o
4 . t E Gx i o ? f ,
='- !.oo ^1ob=-- 7.35 xlol J - q, lXr.x l{
V .ll rl,rsa
3.'74xtoig -
=
Q = )'4Lu-= l'4 V,
*4t"/
-a-at2
f
W W )rfi b^r"'br7 u,"t wfi /fut"\
-- ?"'74 > lD"{ -= 1.65y2
':
)A.t"^tos5/fz
plv/, D I.f"5f1 ,6 fun^* 1ro"c a.d qt.: yz
"(,"-to.*
1bo'c-
'.-,
Problem 11
When you take a bath,how manykilogramsof hot water (49.0oC)must you mix with cold water
(13.0"C) scithatthetemperature
of thebathis 36.0oC?Thetotalmassof the water(hotplus
cold) is 191 kg. Ignoreany heatflow betweenthe water and its externalsurroundings.
7"a= 4?'0"9
&""r = ej."r. Q.-l =o
M,n* C,a* ATqd,t+ M-q C,.rib,ATo,.p1 =o
7*ra-
l3.o"c
4,".,'
36'D"c
* M*rt Aa pea =o
M,g'.*,AT-n**
=
( trrr2- M^*')(:t'e"c-l3'o'c)=6
Y w^ M.o"r*M,.1Yu L3'"'o"c-'iC'ob)+
= \9r Ks
--o
Mr* (-l3.oc") -r-(lqrfZ-Mr*) (A3.oc")
(tztvx-M1"l)()3,o6:1- Me*(ll.oc)
> (nrx-y4*)
= Mr*(*:)
19tfg-M** : o"s?M.,r,t----: letYx=l.s? Ml*
|._, -t
Yl+"t= Iaq&-l
IY---------------
\_-,/
Problem 12
Ideally, when a thermometeris usedto measurethe temperatureof an object,the temperatureof
the object itself shouldnot change.However,ifa significantamountof heatflows from the
object to the thermometer,the temperaturewili change.A themrometerhas a massof 31.0 g, a
specificheatcapacityof c: 815J(kg C"), anda temperature
of 12.0oC.It is immersedin 119g
of water, andthe frnal temperatureof the water andthermometeris 41.5 oC.What wasthe
temoeratureof the waterbeforeinsertionbf the thermometer?
O^e-eor"""*+ $*+=o
r$ = 3l*lo-3lzg
\_ -
D t>
-lr"r".l
7 , ' ' l ? - o \-
7+ = 4t"s
t4
? t 4= o . r t 1K ?
--r -o
'L
\---'
'7, =
4r
't
r ( " ' /c",.
\*
(
AT= aQ.5Co
{| G'
M:l,- r---M"^
Al;* + M *,noc".,.a
Nr^.*,
= - M"',,^C:rsn''A1;-.
11
|1*-* c*.b,
( o" i rc t g ) (r1t uc t/ yg.r:)
A-T"-b, = - /. so c" : -l-f -Ti
Problem 13
If the^bodyloses
processesa p".-""'r1nOV is producingenergyintemallydueto.metabolic
drop is
metabolicprocesiesar" generating,its temperaturewill drop-If the
[j;;;"rcy,1r",
is being lostvia
a ge59n is unclothedandenergy
t" tfe threatening.Suppo"se
;;;;;#;
oC
of 34 andan emissivityof
radiationfrom a surfaceareuoi t.+O^t,which hasa temperature
^0.;ffi.
a rtte of 115 J/s Wtrat is the
S;;;"t" that metabolicp.o""t'"' areproducingenTgy a!
standandnot experiencea drop in
temperatureof the coldestroo* in *trict this person-ould
bodytemPerature?
ff
= l.4D.,r\
y
<-
+-
/ ct"t
-T -_
3.1rC =3o.lK
-- b
"'loo
<
--.-1-
A
?";/"e N
.t
,o
l
,+_=ls%-?^*
-t-. =
- j41'/',
Tt a4 =Tl- ],B- ,-n
)-Tn
,-.
aof\ eoA
-T, =
--r- 2
= a a A (T'--T"')
A"-Lt
.i\
[
(sss/s)
(to?K),-
--1
t.to"')J
)(
1o.f.o)(s.a?,,Id?#
T = trlK -t- |_--_--_----1
= lt" 3"c
I
l-i-"
2--=
t0'3m'
of thewoolis 2.0xoC'
Thethickness
with 1.6m2of woolclothingis covered
lTlf#,:i*,
How
is
36
G o*t ia.-*#L" oitt " *oot is 1I'oC,andtheskintemperature
A;;;#
"t
;;th ffi p"t seconddoesthepersonlosedueto conduction?
n = (/. /^
r e ^^r
trl
/_1
7_ - !.o,1o3^
LT-36"c-lloc
-
A
V
-^G
J'
)1= b,otod/
'/s't\'C"
tt/
,t
(
0,2 = )!&Af
/tL
(fq)f
(o"o,to
%".,-\
--__4
[t "o* I o-"r"')
":l
7
:J!
,
/^
\-r
Problem 15
Supposethe skintemperatueof a nakedpersonis 34 oCwhenthepersonis standinginsidea
room whosercmperatureis 25 oC.The skin areaof the individual is 1.5mu.(a) Assumingthe
emissivity is 0.80,find the net lossof radiantpower from the body. (b) Determinethe numberof
food Caloriesof eneryy(. food Calorie:4186 J) that is lost in onehour dueto the net rate
obtainedin part (a). Metabolic conversionoffood into energyreplacesthis loss.
T=g1'C..3o?K
= e'oA(r'-T')
(") ?'* =
%
7,' l"s'c = t?rg
fr - l"b.".
g. = D"9a
lDkh)(r.s,") ltzovy-1rts
?^,*= (a,i.1qs.6ri\
f* = 6"t"7w
(rt ? = E/t
\-'l'
E= Yt:
E
(cr"rw) (la"o,;
= A..11x lo'--
(
\
E
= 5T Cqlo,ng
J-c"t a
4rrt-J )