Thermal Expansion

Thermal Energy

The Concept of Heat

Explain the concept of heat

Heat – Is the transfer of energy due to temperature differences.

Temperature – Is the degree of hotness or coldness of a body.

Or heat is a form of energy which raises the temperature of the substance.

SI Unit  of  Temperature  is  Kelvin (K).Conversion  of  centigrade into  fahrerinheit  given  by:f  =

9/5ºC + 32

Conversion  of  Fahrenheit into  centigrade given by  C  =  5/9/  (  F  –  32).  Thermometer used  for

measurement of  temperature.  Maximum thermometer is  the  one  which  is used  to  measure the

highest temperature obviously filled with mercury.

A Minimum thermometer is used to measure the lowest temperature and it is filled with alcohol.

Combined maximum and minimum thermometer (Six s thermometer) is used to measure highest

and lowest temperature at the same time.

SI Unit of Heat is Joule (J) mathematically heat energy given by:

H = MC (Q

– Q

)

2

1

M = Mass of substance

C = Specific heat capacity

Q

= Final Temperature

2

Q

= Initial Temperature

1

Source of Thermal Energy in Everyday Life

State the source of thermal energy in everyday life

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There  are  numerous  sources  of  ener gy  such  as  the  sun,  fuels,  nuclear  sources,  geothermal,

electricity  among  others.  The  most  important  source  of  thermal  energy  is  the  sun.  The  sun

generates its energy by a process  called thermonuclear fusion. Most sources of thermal energy

derive their energy from the sun. Thermal energy from the sun makes life on earth possible.

Difference between Heat and Temperature

Distinguish between heat and temperature

Heat

and

temperature

are  related  and  often  confused.  More  heat  usually  means  a  higher

temperature.

Heat

(symbol:

Q

) is energy. It is the total amount of energy (both kinetic and potential) possessed

by the molecules in a piece of matter. Heat is measured in Joules.

Temperature

(symbol:

T

) is not energy. It relates to the average (kinetic) energy of microscopic

motions of a single particle in  the  system per  degree of freedom.  It is  measured  inKelvin (K),

Celsius (C) or Fahrenheit (F).

When you heat a substance, either of two things can happen: the temperature of the substance

can rise or thestateof substance can change.

Heat  Temperature

Def inition

Heat  is  energy  that  is  transferred  from  one

Temperature is a measure of hotness or coldness expressed in

body to  another  as  the result  of a difference

terms  of  any  of  several  arbitrary  scales  like  Celsius  and

in temperature.

Fahrenheit.

Symbol

Q  T

Unit

Joules  Kelvin, Celsius or Fahrenheit

SI unit

Joule  Kelvin

Particles

Heat is a measure of how many atoms there

Temperature  is  related  to  how  fast  the  atoms  within  a

are  in  a  substance  multiplied  by  how  much

substance  are moving.  The  „temperature  of  an  object  is  like

energy each atom possesses.

the  water  level  – it  determines  the  direction  in  which  „heat

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will flow.

Ability  to

do work

Heat has the ability to do work.  Temperature can only be used to measure the degree of hea

Thermal Expansion of Solids

Expansion of Solids

Demonstrate expansion of solids

When a solid is heated one or more of the following may occur:

Its temperature may rise

Its state may change

It may Expand

Expansion of solids is the increase in dimensions of a solid when heated.

Contraction of solids is the decrease in dimensions of a solid when is cooled.

DEMONSTRATION OF EXPANSION OF SOLIDS

In order to demonstrate the expansion of solid we can use following method

1.

The ball and Ring Experiment

2.

The Bar and Gap Experiment

The ball and Ring Experiment

1

Case:

When the ball is not heated then it will pass through the ring very easily because it has

st

a small volume.

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2

Case:  When  the  ball  is  heated,  it  will  expand  and  increase  in  volume,  so  itwill  not  pass

nd

through the ring.

The Bar and Gap experiment

1

st

Case:

When the Bar not heated (Not raised with temperature) then the dimension will remain

constant.

2

Case:

When the Bar is heated (raised  with  temperature) then the dimension of  the  Bar will

nd

increase and eventually will not pass thought the Gap.

Expansion of Solids in terms of Kinetic Theory of Matter

Explain expansion of solids in terms of kinetic theory of matter

When a

solid

is  heated, its atoms vibrate faster  about  their fixed points. The relative increase  in

the size of solids when heated  is therefore small.  Metal railway tracks  have small gaps so that

when the sun heats them, the tracks expand into these gaps and don t buckle.

Forces due toexpansion

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Normally  Expansion  and  contraction  is  accompanied  by  tremendous  forces;  The  presence  of

force indicates the expansion and contraction is Resisted.

Bar breaker

Consists a strong metal blocker with a pair of vertical jaws J and a strong metal Bar R.

The metal bar has a wing nut N at one end and an eye at the other end.

The bar is placed between the two pair of Jaws

A short cast iron C is inserted in the eye of the bar.

The bar is then heated it expands and the wing not screwed to tighten the bar R against

the jaws.

The bar is then allowed  to cool as it cools,  it contracts the short cast Iron rod C which

presses against the jaws of the bar breaker, Resists the contraction of the Metal bar R.

The resistance  to  the contraction  of the bar sets  up very  large forces which breaks  the

short cast Iron rod C in the eye of metal bar, Because the contracting bar is trying to pull itself

through the small gap in the frame.

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Expansivity of Different Solids

Identify expansivity of different solids

The coefficient of linear expansion or linear expansivity (x)

The amount by which the linear dimension of a given solid expands depends on:

The length of the solid

The temperature to which the solid is heated

The nature of solid

Coefficient of linear Expansivity (x) is the fractional increase in length of the solids per original

length per degree rise in temperature.

Mathematical formula

Thus

SI Unit of coefficient of linear expansivity (X) is per degree centigrade ºC

-1

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Example 1

A copper rod has a length of 40cm on a day when the temperature of the room is 22.3ºC. What

will  be  its  length  become  on  a  day  when  the  temperature  of  the  room  is  30ºC  ?  The  linear

expansivity of copper is 0. 000017/ºC

Solution

Table which shows the coefficient of Expansivity Constant.

Substance

Linear Expasivity (PerºC)

Aluminum (Al)

0.000026

Brass

0.000019

Copper

0.000017

Iron

0.000012

Steel

0.000012

Concrete

0.000011

Glass

0.0000085

Invar ( Alloy of Iron and Nickel)  0.000001

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The Application of Expansion of Solids in Daily Life

Explain the applications of expansion of solids in daily life

There is a large number of important practical applications of thermal expansion of solids; While

laying the railway tracks, a small gap is left between the successive lengths of the rails. This will

allow expansion during a hot day. The iron tyre is to be put on a wheel, the tyre is first heated

until its diameter becomes more than that of the wheel and is then slipped over the wheel.

Thermal Expansion of Liquids

The Apparent Expansion of Liquids

Explain the apparent expansion of liquids

Liquids expands when  heated  and  contracts  when cooled.  It  is  easier to  observe  expansion in

liquids  than  in  solids.  Different  liquids  expand  at  different  rates  in  response  to  the  same

temperature  change. Liquids expand much more  than  solids for  equal changes of  temperature.

Apparent expansion of liquids is always less than the true expansion of the liquid.

Demonstrate the Effects of Heat on Liquids

Demonstrate the effect of heat on liquids

Liquids unlike solids can be poured. If a liquid is poured  into a vessel, it takes the shape of the

vessel.  For  this  reason a liquid can't  have  linear  and aerial expansivity, thus liquids  have  only

volume  expansivity.  Liquids  molecules  have  kinetic  energy.  This  energy  increases  if  the

temperature  of the  liquid is  raised by  heating. Heating  causes the molecules of liquid  to move

faster.

Activity 1

Items Needed

Large heat safe glass bowl

Cooking Oil

Food Coloring

Two 2×4 blocks

Candle

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Match or Lighter

Instructions

1.

Begin by filling a large glass bowl with cooking oil.

2.

Next, add between 5-10 drops of food coloring into the oil. Helpful Tip: Place the drops

near the center of the bowl.

3.

Prop the bowl up off the table using two 2×4 blocks.

4.

Light  a  candle  and  carefully  place it  under  the  bowl.  The  flame  of  the  candle  should

touch the bottom of the glass bowl.

5.

Look  through the side of  the  glass bowl  and watch carefully to observe  what happens.

Helpful  Tip:  It  will  likely  take  5  minutes  before  you  see  anything  happen  to  the  liquid/food

coloring.

You can alternatively follow the experiment through the following vedio

Verification of Anomalous of Water

Verify the anomalous expansion of water

The instrument used to demonstrate anomalous expansion of water is called hope's apparatus. it

consists of a brass cylinder, jacket J with a mixture of ice and salt and two thermometers A and B

at regular intervals upward and at the bottom.The hope's experiment shows that water contracts

as it  cools down to 4  degree centigrade  and then expands as  it  cooled further below 4  degree

centigrade.

In  the  year  1805,  the  scientist  T.  C.  Hope  devised  a  simple  arrangement,  known  as  Hope s

apparatus, to demonstrate the anomalous behaviour of water.

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Hope s apparatus consists of a long cylindrical jar with two openings on the side, one near the

top  and  the  other  near  the  bottom  to  fit  thermometers  in  each  of  these  openings.  A  metallic

cylindrical air-tight trough  with an  outlet is also fitted onto the jar,  on its central portion. Two

thermometers are fitted air-tight in the two openings of the cylindrical jar. The thermometer near

the bottom of the jar is  T

, and the one near the top of the jar is T

. Now the cylindrical jar is

1

2

filled with water. The cylindrical trough at the central portion of the jar is filled with a freezing

mixture of ice and common salt.

The Application of Expansion of Liquids in Everyday Life

Explain the applications of expansion of liquids in everyday life

Water in lakes and ponds usually freezes in winter. Ice, being less dense floats on the water. This

insulates the water below against  heat loss to the cold air above. Water  at 4  degree centigrade

being most dense, remains at the bottom of the lake, while ice, being less dense than water floats

on the layers of water. This enables aquatic animals to survive in the water below the ice.

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Thermal Expansion of Gases

The Concept of Thermal Expansion of Gases

Explain the concept of thermal expansion of gases

Gases expand when heated just like solids and liquids. This is because the average kinetic energy

of the molecules in a gas is directly proportional to the absolute temperature of the gas. Heating

the gas increases the kinetic energy of its molecules, making them vibrate more vigorously and

occupy more space.

The Relationship between Volume and Temperature of Fixed Mass of Air at

Constant Pressure

Investigate the  relationship  between  volume  and  temperature  of fixed mass  of air  at  constant

pressure

Three  properties  are  important  when  studying  the  expansion  of  gases.  These  are;  pressure,

volume and temperature.  Charles  law  states  that the volume  of a  fixed mass of  gas  is directly

proportional  to  the  absolute  (Kelvin)  temperature  provided  the  pressure  remains  constant.

Mathematically V

T

= V

T

.

1

2

2

1

Example 2

the volume of gas at the start is recorded as 30 cm3with a temperature of 30°C. The cylinder is

heated further till the thermometer records 60°C. What is the volume of gas?

Solution:

We know,V/T = constant

therefore,

V

/T

=V

/T

1

1

2

2

V

=30 cm

3

1

T1 =30°C = 30+273 = 303K

(remember to convert from Celsius to Kelvin)

T2 =60°C = 60+273 = 333K

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V2 =?

V1/T1=V2/T2

V

=V

xT

/T

2

1

2

1

V

=30x333/303

2

= 32.97 cm

3

The  Relationship  between Pressure  and Volume of  a  Fixed  Mass of  Air  at

Constant Temperature

Investigate  the  relationship  between  pressure  and  volume  of  a  fixed  mass  of  air  at  constant

temperature

The relationship obtained when the temperature of a gas is held constant while the volume and

pressure ar e varied is known as Boyle s law. Mathematically, P1V1 = P2V2. Boyle's law states

that the volume of a fixed mass of gas is inversely proportional to its pressure if the temperature

is kept constant.

PressurexVolume = constant

pxV = constant

Example 3

The volume of gas at the start is 50 cm

3

with a pressure of 1.2 x 10

5

Pascals. The piston is pushed

slowly  into  the  syringe  until  the  pressure  on  the  gauge  reads  2.0  x  10

5

Pascals.  What  is  the

volume of gas?

Solution:

We know

p x V = constant

therefore,

p

xV

= p

xV

1

1

2

2

85

p

=1.2 x 10

5

Pascals

1

V

=50 cm

3

1

p

=2.0 x 10

Pascals

5

2

V

=?

2

p1xV1= p2xV2

V

=p

xV

/p

2

1

1

2

V

=1.2x10

x50/2.0 x 10

5

5

2

V

= 30 cm

3

2

The Relationship between Pressure and Temperature of a Fixed Mass of Air

at Constant Volume

Investigate the relationship between pressure and temperature of a fixed mass of air at constant

volume

To  investigate  the  relationship between  the pressure  and  the temperature of  a  fixed mass,  the

volume of the gas is kept constant. The pressure  is then measured as the temperatur e is varied.

P1/T1 = P2/T2 ,this is called pressure law. The pressure law states  that the pressure of a fixed

mass of a gas is directly proportional to the absolute temperature if the volume is kept constant

Example 4

Pressure  of  gas  is  recorded  as  1.0  x  10

5

N/m

2

at  a  temperature  of  0

°

C.  The  cylinder  is  heated

further till the thermometer records 150

C. What is the pressure of the gas?

°

Solution:

We know,p/T = constant

therefore,

p

/T

= p

/T

1

1

2

2

p

=1.0 x 10

N/m

2

1

5

86

T

=0

°

C = 0+273 = 273K

(remember to convert from Celsius to Kelvin)

1

T

=150

°

C = 150+273 = 423K

2

p2 =?

p1/T1= p2/T2

p

=p

xT

/T

2

1

2

1

p

=1.0x10

x423/273

5

2

= 1.54 x 10

N/m

5

2

The General Gas Equation from the Gas Laws

Identify the general gas equation from the gas laws

The three gas laws give the following equations:

1.

pV =

constant

(when T is kept constant)

2.

V/T =

constant

(when p is kept constant)

3.

P/T=

constant

(when V is kept constant)

These 3 equations are combined to give the ideal gas equation:

Where,

p = the pressure of the gas

V = the volume the gas occupies

T = the gas temperature on the Kelvin scale

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From this equation we know that if a fix mass of gas has starting values of p1, V1 and T1, and

then some time later has value p2, V2 and T2, the equation can be written as:

Exercise 1

Sabah  pumps  up  her  front bicycle  tyre to  1.7  x  105Pa.  The  volume  of  air  in  the  tyre  at  this

pressure is 300 cm3. She takes her bike for a long ride during which the temperature of the air in

the tyre increases from  20°C to  30°C. Calculate  the new  front tyre pressure  assuming the tyre

had no leaks and so the volume remained constant?

Absolute Scale of Temperature

Explain absolute scale of temperature

Absolute  zero  is the lowest temperature  that can be attained theoretically.  It  is not possible  to

attain  this  temperature  because  all  gases  liquefy  before  attaining  it.  The  kelvin  scale  of

temperature is obtained by shifting the vertical axis to -273 degrees Celsius and renaming it 0 K.

On the scale 0 degrees Celsius becomes 273 K and 100 degrees Celsius corresponds with 373 K.

Convertion of Temperature in Degrees Centigrade (Celsius) to Kelvin

Convert temperature in degrees centigrade (celsius) to kelvin

The  Kelvin  temperature  scale  takes  its  name  after  Lord  Kelvin  who  developed  it  in  the  mid

1800s. It takes absolute  zero as  the starting  point  and temperature measurements are given the

symbol  K  (which  stands  for  "Kelvin").  Temperature  differences  on  the  Kelvin  scale  are  no

different to those on the Celsius (°C) scale. The two scales differ  in their starting points. Thus,

0°C is 273K.

Converting from Celsius to Kelvin

Temperature in °C + 273 = Temperature in K

Converting from Kelvin to Celsius

Temperature in K – 273 = Temperature in °C

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Example 5

The temperature of a gas is 65 degr ees Celsius. Change it to the kelvin scale.

Solution

T(K) = degrees Celsius + 273, T(K) = 65+273

therefore T(K) = 338 K.

Standard Temperature and Pressure (S.T.P)

Explain standard temperature and pressure (S.T.P)

The  standard  temperature  and  pressur e  (S.T.P)  is  a  set  of  conditions  for  experimental

measurements to enable comparisons to be made between sets of data. The standard temperature

is 0 degrees Celsius (273 K) while the standard pressure is 1 atmosphere (101300 Pa or 760 mm

of mercury).

Expansion of Gas in Daily Life

Apply expansion of gas in daily life

Land and sea breezes are the result of expansion of air caused by unequal heating and cooling of

adjacent  land  and  sea  surfaces.  The  piston  engine  and  firing  bullets  from  guns  work  under

principles of expansion of gases.

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