Transcript Thermal Expansion

PHYS1001
Physics 1 REGULAR
Module 2 Thermal Physics
HEAT
EXPANSION & CONTRACTION
What changes in
dimensions occur when
heat is extracted or
added to a system ?
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2
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
<
T2
Q
As metal expands, the distance between any two points
increases. A hole expands just as if it’s 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)
(b)
(c)
(d)
Cooling it
Heating it
Either
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
Most solids and liquids expand when heated. Why?
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Average distance between atoms
Inter-atomic forces

“springs”
Internal Energy U is
associated with the
amplitude of the
oscillation of the atoms
Collisions of thermally oscillating atoms make them
shift further apart
Repulsive force
PE
Attractive force
E3
E2
E1
Separation of atoms
average distance between atoms
Solid heated  increased
vibration of atoms  increase
max displacement either side
of equilibrium position 
vibration is asymmetric 
mean distance increases with
increasing temperature
THERMAL EXPANSION
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LINEAR THERMAL EXPANSION
L   Lo T
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
Linear
A
Lo
Area
o
Volume
V
o
L
L
L   Lo T
A
A  2 Ao T
V
V  3 Vo T   Vo T
* Simple model: assume  and  are independent of temperature, T < 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 > 4 °C
water expands as temperature increases
0 < T < 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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volume V (L)
density  (g/mL)
kg.m-3
WATER 1 kg sample
1.002
1000.2
1.0018
1000
1.0016
999.8
1.0014
999.6
1.0012
999.4
1.001
999.2
1.0008
999
1.0006
998.8
1.0004
998.6
1.0002
998.4
1
998.2
0.9998
998
0
4
8
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temperature T (°C)
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
m
V
volume
density
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
T = 32 °C
 = 2.510-5 K-1
Lo = 3.77/2 m = 1.885 m
h=?m
L=?m
Identify / Setup
2Lo
Linear expansion
L
L
L = Lo + L = Lo +  Lo T
h=?m
L
h
Lo
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Execute
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
Evaluate
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Problem B.2
When should you buy your petrol?
2 pm
2 am
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When should you buy your petrol?
2 am
2 pm
V  3 Vo T   Vo T
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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
B
C
D
increases
decreases
stays the same
depends on angle being acute or obtuse
θ
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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
ISEE
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