1PHYS1001Physics 1 REGULARModule 2 Thermal Physics

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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5

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.

8

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

lower metal expands more than upper metal when heated

Q

10Most 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”

11Collisions 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

E1

E2

E3

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Ceramics (deep PE troughs) low expansion coefficients

~10-6 K-1

Polymers high expansion coefficients

~ 10-4 K-1

Metals

~ 10-5 K-1

oL L T LINEAR THERMAL EXPANSION

coefficient of linear expansion

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Lo

L

A

Ao Vo

V

L

oL L T o2A A T

o o3V V T V T

Linear Area Volume

* Simple model: assume and are independent of temperature, T < 100 oC* Wood expands differently in different directions

14Volume 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 Lo3T = Vo T

coefficient of linear expansion coefficient of volume expansion

V0

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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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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

17BUOYANCY - FLOATING AND SINKING

Why do ice cubes float on water?

18Lakes 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.

20Solution

Identify / Setup

2Lo

h = ? mL L

T = 32 °C = 2.510-5 K-1

Lo = 3.77/2 m = 1.885 m h = ? m L = ? m

Linear expansion

L = Lo + L = Lo + Lo T

L

Lo

h

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Execute

From Pythagoras’ theorem

L2 = Lo2 + h2

h2 = L2 – Lo2

= (Lo + Lo T)2 – Lo2

= 2 Lo2T + 2 Lo

2 T2

h = (2 T)½ Lo neglecting very small terms

h = {(2)(2.510-5)(32)}½ (1.885) m

h = 0.075 m Evaluate

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Problem B.2

When should you buy your petrol?

2 pm2 am

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When should you buy your petrol?

2 pm 2 am

o o3V V T V 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 increasesB decreasesC stays the sameD 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 = 1.210-5 K-1

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Solution I S E E

L0 = 50 .000 m T = 15 oC = 1.210-5 K-1

L = L0(1 + T) = 50.009 m

Part (b) is “tricky”

The actual distance is larger than the distance read off the tape by a factorL / L0

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

expansion by a factor 2