# heat is extracted or added to a system ?

Urban and Civil

Nov 29, 2013 (4 years and 5 months ago)

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1

HEAT

EXPANSION & CONTRACTION

What changes in
dimensions occur when
heat is extracted or

2

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

3

DEMO: Heating of Iron wire?

Show expansion of wire as the result of heating.

Day 2:

DEMO: Heating of Iron wire?

Show expansion of wire as the result of heating.

Possible demos you might have seen:

(don’t try these at home, watch on
)

1.Heat/cool bimetallic strip
-

curls up!

2.ball/ring
-

ring expands
-
hole gets bigger

3.drop hot skillet into cold water
-

warps!

4. Hot wire foam cutter
-

wire gets thicker

5. Thin film coatings
-

dr.v

lab pictures

6. Shrink tubing
-

heat activates chemical reaction

vs

cold copper

Tempered glass:
breaks into pieces since faces hold in middle:

top & bottom under compression, middle is under tension.

Cracks on surfaces: called crazing, surface cools faster
than inside, different in contraction causes stress cracks

Outer surface cools faster, and if same material,

inside holds back contraction so outside under tension

9

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

10

Holes get bigger

11

T
1

<
T
2

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.

12

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

13

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

lower metal expands more than
upper metal when heated

Q

14

Most solids and liquids expand when heated. Why?

Internal Energy
U

is
associated with the
amplitude of the
oscillation of the atoms

Average distance between atoms

Inter
-
atomic forces

“springs”

15

Collisions of thermally oscillating atoms make them
shift further apart

PE

Separation of 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

Attractive force

Repulsive force

average distance between atoms

E
1

E
2

E
3

16

Ceramics

(deep PE troughs) low expansion coefficients

~10
-
6

K
-
1

Polymers

high expansion coefficients

~ 10
-
4

K
-
1

Metals

~ 10
-
5

K
-
1

o
L L T

  
LINEAR THERMAL EXPANSION

coefficient of linear expansion

17

L
o

L

A

A
o

V
o

V

L

o
L L T

  
o
2
A A T

  
o o
3
V V T V T
 
    
Linear

Area

Volume

* Simple model: assume

and

are independent of temperature,

T

< 100
o
C

* Wood expands differently in different directions

18

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

19

0.9998
1
1.0002
1.0004
1.0006
1.0008
1.001
1.0012
1.0014
1.0016
1.0018
1.002
0
4
8
12
16
20
temperature T (°C)
998
998.2
998.4
998.6
998.8
999
999.2
999.4
999.6
999.8
1000
1000.2
volume
density
density

(g/mL)
volume V (L)
WATER 1 kg sample

kg.m
-
3

m
V

20

BUOYANCY
-

FLOATING AND SINKING

Why do ice cubes float on water?

21

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.

22

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.

23

Solution

Identify / Setup

2L
o

h

= ? m

L

L

T

= 32
°
C

= 2.5

10
-
5

K
-
1

L
o

= 3.77/2 m = 1.885 m

h

= ? m

L

= ? m

Linear expansion

L

=
L
o

+

L

=
L
o

+

L
o

T

L

L
o

h

24

Execute

From Pythagoras’ theorem

L
2

=
L
o
2

+
h
2

h
2

=
L
2

L
o
2

= (
L
o

+

L
o

T
)
2

L
o
2

= 2

L
o
2

T

+

2

L
o
2

T
2

h

= (2

T
)
½

L
o

neglecting very small terms

h

= {(2)(2.5

10
-
5
)(32)}
½

(1.885) m

h

= 0.075 m

Evaluate

25

Problem B.2

gas to get the most for your money?

2 pm

2 am

26

-

more dense

2 pm

2 am

o o
3
V V T V T
 
    
27

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

θ

28

Problem B.4

A surveyor uses a steel measuring tape that is exactly
50.000 m at a temperature of 20
o
C.

(a) What is the length
on a hot summer day when the temperature is 35
o
C
? (b)
On the hot day the surveyor measures a distance off the
tape as 35.794 m. What is the actual distance?

steel

= 1.2

10
-
5

K
-
1

29

Solution

I

L
0

= 50 .000 m

T

= 15
o
C

= 1.2

10
-
5

K
-
1

L

=
L
0
(1 +

T
) = 50.009 m

Part (b) is “tricky”

The actual distance is larger than the distance read off the tape by a factor

L / L
0

true distance = (35.794) (50.0009) / (50.000) m = 35.800 m

expansion by a factor 2

Possible lab: how would you find the
linear expansion coefficient of a spring?

Given: ice, hair dryer, spring, mass, temperature meter

Drawing is by Courtesy of the University of Minnesota.

www.ph.utexas.edu/~phy
-
demo/demo
-
txt/1r10
-
10.htm
l

lab: how would you find the linear expansion
coefficient of a wire pendulum?

Given: ice, hair dryer, wire, mass, temperature meter, stop watch

Drawing is by Courtesy of the University of Minnesota.

www.ph.utexas.edu/~phy
-
demo/demo
-
txt/1r10
-
10.htm
l

Lab pictures