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CHAPTER
12
TEMPERATURE AND HEAT
CONCEPTUAL QUESTIONS
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5
.
REASONING AND SOLUTION
A rod is hung from an aluminum frame such that
there is a small gap between the rod and the floor.
The rod and the frame are heated
uniformly; both the frame and the rod will expand. The linear expansion of the
vertical portion of the frame and the linear expansion of the rod can be determined
from Equation 12.2:
∆
L
=
α
L
0
∆
T
.
a. If the rod is made of aluminum, the fractional increase in length
∆
L
/
L
0
is the
same for the vertical portion of the frame and the rod. Since the rod is initially
shorter than the vertical portion of the frame, the rod will never be as long as the
vertical portion of the frame. Therefore, the rod will never touch the floor.
b. If the rod is made of lead, the heated rod could touch the floor. The coefficient of
linear expansion of lead is greater than that of aluminum. Therefore, the fractional
change in the length of the rod will be greater than the fractional change in the length
of the vertical portion of the frame. If the temperature is raised high enough, the
length of the rod could expand enough to fill the gap and touch the floor.
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11
. REASONING AND SOLUTION
According to Archimedes' principle, any fluid
applies a buoyant force to an object that is partially or completely immersed in it; the
magnitude of the buoyant force equals the weight of the fluid that the object
displaces. Therefore, the magnitude of the buoyant force exerted on an object
immersed in water is given by
F
B
=
ρ
water
Vg
, where
water
is the density of water,
and
V
is the volume displaced by the immersed object.
As shown in Figure 12.20, the density of cold water (above 4 °C) is greater than
the density of warm water (above 4 °C). Therefore, cold water provides a greater
buoyant force than warm water.
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15
. REASONING AND SOLUTION
Two identical mugs contain hot coffee from the
same pot.
One mug is full, while the other is only onequarter full. According to
Equation 12.4, the amount of heat that must be removed from either cup to bring it to
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 Spring '09
 DARICI
 Heat

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