PHYS1001Physics 1 REGULARModule 2 Thermal Physics

HEAT EXPANSION & CONTRACTIONWhat changes in dimensions occur when heat is extracted or added to a system ?

HEAT : EXPANSION & CONTRACTION

17.4 p576 18.2 p617

Linear, Area, Volume

Thermal expansion of water

Thermal Stress (no)

Molecular properties of matterReferences: University Physics 12th ed Young & Freedman

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

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

Holes get bigger

T1 < T2QAs metal expands, the distance between any two points increases. A hole expands just as if its made of the same material as the hole.

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

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 heatedQ

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 atomsInter-atomic forcessprings

Collisions of thermally oscillating atoms make them shift further apartPESeparation of atomsSolid heated increased vibration of atoms increase max displacement either side of equilibrium position vibration is asymmetric mean distance increases with increasing temperature THERMAL EXPANSIONAttractive forceRepulsive forceaverage distance between atomsE1E2E3

Ceramics (deep PE troughs) low expansion coefficients ~10-6 K-1

Polymers high expansion coefficients ~ 10-4 K-1

Metals ~ 10-5 K-1LINEAR THERMAL EXPANSION coefficient of linear expansion

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

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 Lo3T = Vo T coefficient of linear expansion coefficient of volume expansion V0

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 Cwater has its maximum density

kg.m-3

BUOYANCY - FLOATING AND SINKING Why do ice cubes float on water?

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.

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.

Solution

Identify / Setup

2Loh = ? mLLT = 32 C = 2.510-5 K-1Lo = 3.77/2 m = 1.885 m h = ? m L = ? m

Linear expansion

L = Lo + L = Lo + Lo T

LLoh

ExecuteFrom Pythagoras theorem

L2 = Lo2 + h2h2 = L2 Lo2 = (Lo + Lo T)2 Lo2 = 2 Lo2T + 2 Lo2 T2 h = (2 T) Lo neglecting very small terms h = {(2)(2.510-5)(32)} (1.885) m

h = 0.075 m Evaluate

Problem B.2

When should you buy your petrol?2 pm2 am

When should you buy your petrol?2 pm2 am

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

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

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 mexpansion by a factor 2