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Exam 4
Physics
Points Awarded
44.00
Points Missed
6.00
Percentage
88.0%
.
.
.
1
An aluminum tank of volume 0 0300 m3 is filled to the top with mercury at 20 0
.
.
.
℃
The tank is placed inside a chamber with an interior temperature of 70 0 ℃
.

The coefficient of volume expansion for mercury is 1 82 x 10 4
/
℃ and the
.
 /
.
coefficient of linear expansion of aluminum is 23 0 x 10 6 ℃
After the tank and
,
its contents reach thermal equilibrium with the interior of the chamber how much
[
.

.
.]
mercury has spilled? Note 3 5 x 10 2 m2 is 0 0035 square meters
.
a
.

2 52 x 10 5 m3
.
b
.

2 00 x 10 4 m3
.
c
.

1 92 x 10 4 m3
.
d
.

6 60 x 10 5 m3
.
e
.

1 69 x 10 4 m3
Question Details:
An aluminum tank of volume 0.0300 meters cubed is filled to the top with mercury at 20 degrees C. THe tank is placed inside a chamber with
an interior temperature of 70.0 degrees C. The coefficient of volume expansion for mercury is 1.82 x 104/C; and the coefficient of linear
expansion of aluminum is 23.0 x 106/C. After the tank and its contents reach thermal equilibrium with the interior of the chamber, how much
mercury has spilled [Note 3.5 X 103 m2 is 0.0035 square meters]
Response Details:
change in volume of Hg = ΔV = Vγ(ΔT) = .03*.000182*50 = .000273 m^3
change in length of tank = ΔL = Lα(ΔT)
change in width of tank = ΔW = Wα(ΔT)
change in height of tank = ΔH = Hα(ΔT)
change in volume of tank = (L+ΔL)(W+ΔW)(H+ΔH)  LWH
˜ LWH + LWΔH + LHΔW + WHΔL  LWH (neglecting higher order terms like ΔLΔW, etc., since they are very small)
= LWΔH + LHΔW + WHΔL
= LWH (3αΔT)
= 3αVΔT = 3*.000023*.03*50 = .0001035 m^3
Hg spilled = .000273 m^3  .0001035 m^3 = .0001695 m^3
.
2
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.
A household humidifier continuously takes water in at 20 0 ℃ at a rate of 5 60 x

/
10 5 kg s
.
and heats it until it evaporates
.
/
,
If the cost of electricity is $0 14 kWh
[
:
=
.
what is the daily cost of operating the humidifier?
Notes one kWh
3 60 x 10^6
;
,
/ (
);
J and for water the specific heat capacity is 4186 J
kg ∙℃
the latent heats of
.
/
.
/
,
.
fusion and vaporization are 3 35 x 10^5 J kg and 2 26 x 10^6 J kg respectively
.
a
.
$0 65
.
b
.
$0 49
.
c
.
$0 31
.
d
.
$0 58
.
e
.
$0 70
TUTORVISTA
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Textbook page 370 example 10
=
Q cm∆T
A household humidifier continuously takes water in at 20.0 °C at a rate of 5.60 × 10–5 kg/s and heats it until it evaporates.
If the cost of electricity is $ 0.14/kWh, what is the daily cost of operating the humidifier? Notes: one kWh = 3.60 × 106 J;
and for water, the specific heat capacity is 4186 J/(kg • °C) the latent heats of fusion and vaporization are 3.35 × 105 J/kg
and 2.26 × 106 J/kg, respectively.
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This note was uploaded on 07/24/2010 for the course PHYSICS ph205 taught by Professor Brumm during the Spring '10 term at Grantham.
 Spring '10
 BRUMM
 Physics

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