le (txl65) – Temperature – mohanty – (81440)
1
This printout should have 13 questions.
Multiplechoice questions may continue on
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beFore answering.
001
10.0 points
A scuba diver has her lungs flled to halF
capacity (5 L) when she is 14 m below the
surFace.
The acceleration oF gravity is 9
.
8 m
/
s
2
.
IF the diver holds her breath while quietly
rising to the surFace, what will be the volume
oF her lungs (in liters) at the surFace?
Correct answer: 11
.
86 L.
Explanation:
Given :
ρ
= 1000 kg
/
m
3
,
V
2
= 1
×
10
5
kg
/
m
3
,
V
1
= 5 L
,
and
h
= 14 m
.
We can take air as an ideal gas, so
P V
T
=
nR
can be used to describe this process. Thus we
have
P
1
V
1
T
1
=
P
2
V
2
T
2
,
where the subscripts 1 and 2 stand For the
initial and fnal states, respectively. Then the
fnal volume can be expressed as
V
2
=
P
1
V
1
P
2
=
ρ g h
+
P
2
P
2
V
1
=
ρ g h
P
2
V
1
+
V
1
=
(
1000 kg
/
m
3
)(
9
.
8m
/
s
2
)
(14 m)
100 kPa
(5 L)
+ (5 L)
=
11
.
86 L
,
iF the temperature is constant during the pro
cess as in this problem. The pressure under
the water is
P
1
=
P
2
+
ρ g h
= (1
×
10
5
kg
/
m
3
)
+ (1000 kg
/
m
3
) (9
.
8 m
/
s
2
) (14 m)
= 2
.
372
×
10
5
kg
/
m
3
,
where
P
2
is the pressure at the surFace;
i.e.
,
the atmospheric pressure.
002 (part 1 of 2) 10.0 points
A pendulum clock with a brass suspension
system is calibrated so that its period is 1 s at
9
◦
C.
IF the temperature increases to 36
◦
C, by
how much does the period change?
Correct answer: 0
.
000256467 s.
Explanation:
Given :
t
1
= 1 s
,
T
1
= 9
◦
C
,
T
2
= 36
◦
C
,
and
α
= 1
.
9
×
10
−
5
(
◦
C)
−
1
.
The length changes by
Δ
L
=
αL
1
Δ
T
Δ
L
L
1
=
α
Δ
T
The period oF a pendulum is
t
1
= 2
π
r
L
1
g
.
With the change in the length it becomes
t
2
= 2
π
r
L
1
+ Δ
L
g
= 2
π
r
L
1
g
p
1 +
Δ
L
L
1
P
=
t
1
√
1 +
α
Δ
T .
√
1 +
α
Δ
T
=
R
1 + [1
.
9
×
10
−
5
(
◦
C)
−
1
] (27
◦
C)
= 1
.
00026
,
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2
so the change in the period is
Δ
t
=
t
p
√
1 +
α
Δ
T

1
P
= (1 s) (1
.
00026

1)
=
0
.
000256467 s
.
003 (part 2 of 2) 10.0 points
How much time does the clock gain or lose in
one week?
Correct answer: 155
.
111 s.
Explanation:
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 Spring '11
 sdsd
 Absolute Zero, Correct Answer, Celsius

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