Name:
Student
Number:Recit 01Physics 73
TWHFALumantas
17
August
2016
Section:
Recit
Teacher:
^#;
fo'
3a,
Instructions. Answer
the
following
problems completely.
Write
your
complete
and
tractable
solutions
on
the
space
provided
and
box your
final
answers.
You
may
discuss
with
your
classmates.
You
are
also
allowed
to
ask
your recit
instmctor. However, you
are
not
allowed
to
open
any
notes,
books, orelectronic
devices.
Problem
1.
Thermal Expansion[5pts]
You are
making
pesto
for you
pasta and have
a
cylindrical
measuring
cup
of
1O.O
cm high
made
of
ordinary
glass
[p
:2.7
x
1Os(Co)1]
ttrat
is
filted
with
olive oil
[c
:2.27
x
1g+16'o;r]to
a
treiitrt
of
3.Ofrelow
the
top of
the
cup.
Initially, the
cup and
oil
are
at22.OoC.You
get
a
phone call and
forget
aboutthe
olive oil which you
leave on
the hot
stove. Thecup and
the
oil
heat
up slowly
and have
a
common
temperature.
At
what
temperature
will
theolive oil start
to spill
out
of
the
cup?
olofTabe+[etcmpena{rere...Pl'o $reoliueoilo}q'thospit}
Vo1
,
p
t
bo
*Be
,,Xl'X,it
ood
uolurnq
cxyaosioo
oDQ+f^uc$l
vat
r
da
be
tie
,f,r',ItrJ
onol
(.tn'or

'0
'ltrc
ot(,oe
oit
sta/k
t
slitt
trhtvt
V rp
(Ir)

Vorirrroil
(T.)
,%r
*
prV.s
a'[ =
Vo.
+
f Vo,
61
of
1*
orf
tt
u
oh'.e
oi
I
8o,
Vo1
f
P,
Url
AI
=
Vo,
+
td,bVo.
Ai
AT=
Vr1
U0,,
(te
Vo.

P,
Sr)
Problem
2.
Temperature
Scales
(A) you
put
a
bottle
of
soft
drink
in
a
refrigerator
and
leave
it until
its temperature
has
dropped
iO.Of.
What is
its temperature change
in
(a)
C
[2pts]
and
(b) F ? [3pts]
(o)
lo' o
0'
=b
Tz
=
vcrvr
rTr
=&B)
{Tr
.XItorhr
p,t
)
or
a[,=
s4T,l32
oV,
=
u/rucr)
se
Lb
)
oc,

[
'F, 
b')
5
o
9rU
/s
=[
9t
/5
o
F=
(lo)
Gn.Uor'
p,
Va
1
L
=
G3''1
C
Porit

O1
Recit
01Physics 73
TWHFALumantas
17
August
2AL6@)
Another
temperature
scale
having
an
absolute zero is the Rankine temperature
scale.
The
freezing
point
and
boiling point
of
water
correspond
to
491.67 R aod
671.67\
respectively.
Give
&e
conversion
from
Fahrenheil to Rankine
(i.e., F to
R).
[5pts]
7rce;i1
y
oiot
4
gt.
07
l?
gaoF
[ iliy
yt.
Jiy. Ld
orthlry
f+
I
lnrjf
6T.
al
\
o
2t2
F
t60
tg0
farki e
{crnntq
f
So,
Problem
3.
Melting
Ice [Spts]
Suppose
you
have some
ice
kept
at
0 C.
You
want to bring 450
[mL]
of
lukewarm Iiquid
waterfrom
27 C
to
OoC
at
atmospheric
pressure.
How
many grams
of
ice should
you put
in the
water?
(c
:
419O1/kg'K,Lf =
3.34x10s
J/kg, Lv=2.256xL061/kg)
Q;,, .t
Qwow
,
O
rnice
Lt
1
lttwCw
AT =
O
rhr.e
: 
Iwcw
Df
=

4Eo^L
(ts/^L)Awo
tr)(
ttb)
Lr
i.n
xros
11*
o(
Problem
4.
Calorimetry
[spts]
A 30g
silver
teaspoon at
room temperature
(20 C) is placed
into
200
g
of
hot
tea (100 C).
No
heat
escapes
the
spoontea system. You may
assume
that the
specific heat
of
tea
is
the
same
as
that
of
water.
The specific heat
of
silver is 0.0564
cal/9.R.
What
is
the
equilibrium
temperature
of
the
system?
[10pts]
cc=
Q.ostclca'L
(1tt}'tl)(+Z) =
235'97?b
Tf. \
tc^t
/\tvg
I
Q
silver
*
0rro
i
O
msqATs
+
mscaAls
=o
fnsct(1 
zot)
+
r*cu('rt

roo)'6
Te =
loe
tfiaCa)
+
ZO
lTtt
Cg
=
J
r€.'R
C*r
k
+ r'qcr)
fft
lT,
.
99.o
'c I
_'' ' ,tt
Paritol
too(o.d
Q r{.r)
t
eoitu.og%:Y2t:A
\
(o'otrt'*or2,.,,
q
l
R=
oFl
4se.coT
Recit
02
Physics
73 TWHFAx
Lumantas
24
August
2016
Name:
Student
Number:
Section:
Recit
Teacher:
Instructions. Answer the
following
problems
completely.
Write your
complete
and tractable solutions
on the
space
provided
and
box your
final
answers.
You
may
discuss
with
your
classmates.
You
are
also
allowed to
ask
your recit instructor.
You
are also
allowed
to
open
your
notes'
Problem
1. Heat
Conduction [9
Pts]
A
hollow cylinder
has
length
L,
inner radius,
a,
outer radius,
b,
and
the
temperature at
the inner
and
outer
surfaces
are
Tp
and
?6
where
Tru
)
Tc (The cylinder could
represent
an
insulated
hot
water
pipe. The
thermal conductivity of
the
material of which
the
cylinder
is made is
k.
(a)
Write
an
expression
of
the
heat
current,H,
in
terms
of
its
thermal conductivity,
k,latetal
surface
area,
A,and
temperature gradient
O'/Or(2
pts)
(b)
What is the
lateral
surface area
of
a cylinder?
Substitute
this
expression
in
your
answer
inpart (a).
(2pts)
(c)
Place
all
expressions
with
H,
r
and
dr
on the
left
side
of
the
equation
and
all
other
expressions,k,dT,
etc. on the
right
side
of
the
equation.
Put proper
limits
of
integration
for
thi
radius
r
and
the temperature
T
and
integrate.
Write
the
total
heat
current through the
wallsof
the
cylinder,
H,in
terms
of
k,
a,b,Ty
and'76?
(3pts)
(d)
Show that
the
equation
for
the total
heat
current
reduces
to
an
equation
for
the
linear
heat
flow
when the
cylinder
wall
is
very
thin'
(2pts)
Problem
2. A
Thermos
for
Liquid Helium [5 pts]
A
physicist
uses
a
cylindrical
metal can
of
0.250
m
high
and 0.900
m
in
diameter
to
store
liquid
heiium
at
4.22
K.
The
boiling point of
helium is
at
4.22
K
at
latm
and
its
latent
heat
of
vaporization
is2.09
x
104
I
/1rn.Co*pletely
surrounding the metal
can are
walls maintained
at
the temperature
of
liquid
nitrogen,TT
3K,with
vacuum between the
can and
the
surrounding walls.
How
much
helium
is
lost per hour?
The
emissivity of
the
metal can
is
0.200.
The
only
heat
transfer
between
the
metal
canand
the surrounding
walls
is
by
radiation?
H
n
r
a
he
r(l*
T,o
)
z
fi:
errh
l2trrz
=
\\n,r
=
Ae.d(lqt.t)
=
A
frJh
1.
Ln1L
'=
o.
o83zl
b
obs
th )
(s
.
G'tx;
s)to''1
(r.*t

't7'3
,)
a 
o'
(Y31'l
W
N
o
'
03?11 T/#
ngalirG
ri1
'ry(rnJ
$^{
\^16$
',,
#^0
lnt'f
c,''(d
+'
}te
+' }al
*U
11;;
\*ai
,crn
bc
olrotk),
rog
tg(.',
cavcoa6
i{
il'
V r1on'r<
rnlv
= o'wT
f/S
(Ecoo't)
*..,,@
Ll2
Recit 02
Physics
73 TWHFAx
Lumantas
24
August 2016Problem
3.
Ideal
Gas [6
ptslHelium
(M
:
4.00
g/mol)
gas
with
a volume
of
2.50
L,
under
a
pressure
of
0.180 atm
and
at
a
temperature
of
39.0oC is warmed
until
both
pressure and
volume
are
doubled.(a)
What
is
the
final
temperature? (4pts)
(b) How
many grams
of
helium
are there?
(3pts)
(q) ho'n
PU
=
nRT d> I
=
,60
=o
crvrFrn\
'\
./
?tU,
=
P* i
?z=2?,
i
uz,
?u,
T,
1x
?r{
=
ayw)
=P
Iz
'i
2
=
4
x
(usr
ar3
r5
K)
L5)
fl,
IrU,
TK

[o
ts6
rK)(a.q)vf
6;n;qv/(,
Ds?nG
V^4
)
Go\.F
i
fn.nM= 4'oo€ *
o'0l1tmo\
wo\
:
0.
D
l?L
rnole
Problem
4.
Counting [5 pts]Compute
the
number
of
molecules
in
1
mm3
of
nitrogen
in
standard temperature
and
pressure.
(Trtp
=
0.000 C,
Prtp
=
1
[atm]
=
101313
[Pa],
R
=
0.08206
fL'atm/mol'K]

8.3'L4
[]/mol.K],
1
[mL]
=
1
[cm3],
Na
=
6.022
x
1023)
Hint:
Compute
for
the
number
of
moles
first.
\@wAGo)'r'^ '/(
rc]'nr
/(
wo t'
)
h
=
Prl
FI
.l{
=
Os: fl)''s)k
jr=
tL49
(,
d(rxra6t*) ., =
4 4oxto8*,1
fo,oteol
LLb
\(
nu.ls
k)
f
;[*
')\
)
r1
Nn
=
Q
o6
x\p
Brol
)(t
.ozlxro
e'
9rk :)
Lo
I
tL
\)
z
7.
Gg
X
Io
r ,olec,,,l/l
Recit  02
212