Thermal%20Expansion

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HEAT EXPANSION CONTRACTION
What changes in dimensions occur when heat is
extracted or added to a system ?
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HEAT EXPANSION CONTRACTION 17.4 p576
18.2 p617 Linear, Area, Volume Thermal
expansion of water Thermal Stress
(no) Molecular properties of matter
References University Physics 12th ed Young
Freedman
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How does a change in temperature affect the
dimensions of a system? Give examples where you
have to consider the changes in the dimensions of
a system when heat is added or extracted
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A iron disc with a hole in it is heated. Will
the diameter of the hole (a) increase, (b)
decrease or (c) not change?
Q
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Holes get bigger
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T1 lt T2
Q
As metal expands, the distance between any two
points increases. A hole expands just as if its
made of the same material as the hole.
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A nut is very tight on a screw. Which of the
following is most likely to free it? (a)
Cooling it (b) Heating it (c) Either (d)
Neither
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Bimetallic strips Two strips of different metals
welded together at one temperature become more or
less curved at other temperatures because the
metals have different values for their
coefficient of linear expansion ?. They are
often used as thermometers and thermostats
Q
lower metal expands more than upper metal when
heated
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Most solids and liquids expand when heated. Why?
Average distance between atoms
Inter-atomic forces ? springs
Internal Energy U is associated with the
amplitude of the oscillation of the atoms
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Collisions of thermally oscillating atoms make
them shift further apart
Repulsive force
PE
Attractive force
Solid heated ?? increased vibration of atoms ?
increase max displacement either side of
equilibrium position ? vibration is asymmetric ?
mean distance increases with increasing
temperature
E3
E2
E1
Separation of atoms
THERMAL EXPANSION
average distance between atoms
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LINEAR THERMAL EXPANSION
Ceramics (deep PE troughs) low expansion
coefficients ? 10-6 K-1 Polymers high
expansion coefficients ? 10-4
K-1 Metals ? 10-5 K-1
? coefficient of linear expansion
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Linear Area
Volume
Ao
Lo
Vo
DL
L
A
V
Simple model assume ? and ? are independent of
temperature, ?T lt 100 oC Wood expands
differently in different directions
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Volume expansion solid cube Vo Lo3 V L3
(Lo ? Lo ?T)3 Lo3(1 ? ?T)3 V Lo3 (1 3
? ?T 3 ?2 ?T2 ?3 ?T3) V Lo3 (1 3 ? ?T)
(ignoring higher order terms) V - Vo ?V 3
? Lo3?T ? Vo ?T
? ?
?V0

• coefficient of linear expansion
• ? coefficient of volume expansion

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• Water has an anomalous coefficient of volume
  expansion, ? is negative between 0 C and 4 C.
• Liquid water is one of the few substances with a
  negative coefficient of volume expansion at some
  temperatures (glass bottles filled with water
  explode in a freezer) it does not behave like
  other liquids
• T gt 4 C water expands as temperature
  increases
• 0 lt T lt 4 C water expands as temperature
  drops
• from 4 C to 0 C
• T 3.98 C water has its maximum density

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? kg.m-3
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BUOYANCY - FLOATING AND SINKING
Why do ice cubes float on water?
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Lakes freeze from top down rather from bottom
up Water on surface cools towards 0 C due to
surrounding environment. Water as it cools and
becomes more dense, it sinks carrying oxygen with
it (it is most dense at about 4 C). Warmer water
moves up from below. This mixing continues until
the temperature reaches 4 C. Water then freezes
first at the surface and the ice remains on the
surface since ice is less dense than water (0.917
g/mL). The water at the bottom remains at 4 C
until almost the whole body of water is frozen.
Without this peculiar but wonderful property of
water, life on this planet may not have been
possible because the body of water would have
frozen from bottom up destroying all animal and
plant life.
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Problem B.1 As a result of a temperature rise of
32 C a bar with a crack at its centre buckles
upward. If the fixed distance between the ends of
the bar is 3.77 m and the coefficient of linear
expansion of the bar is 2.5x10-5 K-1, find the
rise at the centre.
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Solution Identify / Setup

• ?T 32 C
• 2.5?10-5 K-1
• Lo 3.77/2 m 1.885 m
• h ? m
• L ? m
• Linear expansion
• L Lo ?L Lo ? Lo ?T

2Lo
L
L
h ? m
L
h
Lo
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From Pythagoras theorem L2 Lo2 h2 h2 L2
Lo2 (Lo ? Lo ?T)2 Lo2 2 ?
Lo2?T ?2 Lo2 ?T2 h (2 ? ?T)½ Lo
neglecting very small terms h
(2)(2.5?10-5)(32)½ (1.885) m h 0.075 m
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Problem B.2 When should you buy your gas?
2 am
2 pm
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When should you buy your gas?
2 am
2 pm
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Problem B.3 A square is cut out of a copper
sheet. Two straight scratches on the surface of
the square intersect forming an angle ?  . The
square is heated uniformly. As a result, the
angle between the scratches A increases B
decreases C stays the same D depends on angle
being acute or obtuse
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Problem B.4 A surveyor uses a steel measuring
tape that is exactly 50.000 m at a temperature of
20 oC. (a) What is the length on a hot summer day
when the temperature is 35 oC? (b) On the hot day
the surveyor measures a distance off the tape as
35.794 m. What is the actual distance? Y F
Examples 17.2 /3.
?steel 1.2?10-5 K-1
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Solution L0 50 .000 m ?T 15 oC ?
1.2?10-5 K-1 L L0(1 ? ?T) 50.009 m
Part (b) is tricky
expansion by a factor 2
The actual distance is larger than the distance
read off the tape by a factor L / L0 true
distance (35.794) (50.0009) / (50.000) m
35.800 m