PHYSICS_FORM-III_SIMPLIFIED NOTES OF THERMAL EXPANSION

 Introduction

Thermal energy or heat content of the body

Is the energy possessed by a body due to its temperature.

The heat content of an object is due to the random motion  of particles that make up the object.

The thermal energy of an object increase with an increase in temperature.

Heat is a form of energy transferred from one body to another due to a difference in temperature between the two bodies.

Temperature is degree of hotness or coldness of a body.

Or

Temperature is a measure of the average kinetic energy of the particles in matter.

When two objects having different temperatures are placed in contact, their temperature change until they reach a thermal equilibrium.

At thermal equilibrium the two objects will be at the same temperature. The thermal equilibrium is achieved by the flow of the thermal energy from the hotter object into the cooler object.

Heat is usually represented by letter ‘Q’.

 Heat changes the state of matter

If heat is transferred to an object from the surrounding, the temperature of the object rises until it reaches a point when the object’s intermolecular attraction forces are weakened. At this point, the object changes into its other state. If it was a solid, it changes into a liquid a process referred to as melting. If it was a liquid it changes into a gas a process referred to as vaporization. For some substances like iodine a solid directly changes into a gas a, process known as sublimation.

If heat is transferred from an object to its surrounding, the temperature of the object will decrease until a point when the intermolecular attraction force become very strong. At this point, the object changes state. If it was a gas it changes into a liquid, a process called condensation. If it was a liquid it changes into a solid, a process known as freezing. For some substances like iodine,it changes directly from gas to solid, a process known as deposition/reverse.

Differences between heat and temperature;

Heat	Temperature
The amount of thermal energy contained in an object	The intensity or degree of hotness or coldness of a body
SI unit is the joule (J)	SI unit is the kelvin (K)
It increases or lowers the kinetic energy of a substance	Is the kinetic energy of the molecules of a substance

Thermal expansion

Is the tendency of matter to change its size due change in its temperature.

Expansion result to

1. Bimetallic strip to bent
2.  The bridge or roof is fixed while other side is rest on rollers so that movement of bridge or roof allowed during expansion or contraction
3. Rail lines are laid in such a way that the gaps is left at the junction between two rail bars
4. A bottle contain cold liquid cracks if placed near strong fire
5. Thick walled glass tumblers break when hot substance are poured in it

EXPANSION OF METAL WHEN HEATED

Expansion is the increase in dimension of a solid when heated.

Contraction is the decrease in dimension when a solid cooled.

DEMONSTRATION

1. The ball and ring experiment

RESULT

A metal ball just slips through a metal ring before heating. This shows that diameter of the metal ball is slightly smaller than that of a metal ring. After heating the metal ball it does not slip through the metal ring. This shows that the diameter of the metal ball increases when heated (the diameter of the ball is slightly larger than that of the metal ring)

NOTE:

Due to kinetic theory of energy, all matter are made of small particles that are in state of random motion. Hence when a solid metal is heated tends to expand due to that random motion of  such particles.                   

DISADVANTAGES

1. When the solid is expanded/ contracted large forces are created to resist either expansion contraction respectively. That is why the railway lines are laid in such a way that a gap left at the junction of two rail bars.

Note: The slits through which the nuts pass are rectangular in shapes so that when the rail bar expands/ contracts the slight movement is free otherwise the rail bars are likely to cause accidents.

 
  2. In steel bridges and roofs of both sides are fixed, the bridge or roof would elongate and hence buckle during expansion and crack during contraction.

        

                                

NOTE; To avoid these situations, one side of the bridge or roof is fixed while the other side’s rests on rollers so that movement of bridges or roofs is allowed during expansion and contraction.

 
     3. Glass ware breaks easily by expansion e.g. Bottle contained cold liquids cracks if placed near to the strong heat.

Why substance expand?

When a substance is heated kinetic energy of particle is increase, its particle move around vigorously and tend to move away or separate further from each other thus why volume of substance increase. All state of matters (solid, liquid, gas) are expand when heated.

Sources of heat/thermal energy

There are several sources of thermal energy. These include

1. The sun

The most important source of thermal energy is the sun. The sun generates its energy by a process called thermonuclear fusion

Thermonuclear fusion is the process by which the sun generate energy

In fact, most sources of thermal energy on the earth derive their energy from the sun. Thermal energy from the sun makes life on earth possible.

2. Fuel

is any things that can be burn and produce heat.

Fossils are remains of plants and animals that died millions years ago.

Fossils fuel are fuel derived from remain of plants and animals that died millions years ago. Examples of fossils fuels oil, gas and coal

Fossil fuels are non-renewable sources of thermal energy. They also emit carbon dioxide to the atmosphere. Carbon dioxide contribute to global warming and climate change.

Fossil fuels are in the following forms;

1. Solid fuels; coal, charcoal ,wood
2. Liquid fuels ;oil, gasoline, diesel
3.  Gaseous fuels; propane, methane ,butane

Nuclear energy

Nuclear energy is generated from nuclear reactions. In reactions, the nuclei of certain elements are split (nuclear fission) eg atoms of a material like uranium are split into smaller atoms. This splitting also cause a small amount of mass to be transforms into energy. Controlled nuclear fission can be carried out in a nuclear reactor. Combined nuclei (nuclear fusion) eg inside the sun, atoms of hydrogen are fused together to form a large atom, helium. In this process, a small amount of the mass of the hydrogen atoms is transformed into energy. The energy released can be determined by Albert Einstein’s famous formula, E=mc². (In the formula, E stands for energy in joules, m stands for mass in kilograms, and c stands for the speed of light in metres per second.)

Nuclear energy is becoming an important source of thermal energy. The disadvantage is that it produces hazardous radioactive by-products which have negative effects on the environment.

Geothermal energy

Geothermal is a form of thermal energy whose use is rapidly growing. Geothermal energy is derived from the internal heat energy of the earth. Geothermal energy reaches the earth’s surface in form of geysers, hot springs and fumaroles.

Geothermal energy is a renewable and a non-polluting source of the thermal energy.

Friction

Rub your hands together for 30 seconds, and then place your palms on cheeks. The heat you feel is the result of a mechanical force called friction. Often lubricants, such as oil, are used to decrease friction and the amount of heat created in machines.

Electricity

As electricity moves through a wire, it causes the particles randomly collide. In the processes of colliding, some of its kinetic energy is converted into heat energy. In order for electricity to be used as a source of heat, we must first produce the electricity. When a bulb is fixed in the circuit it offers some resistance to the flow of current which enhance conversion of electricity energy into heat energy.

Thermal expansion in solids

As the temperature of a solid increases, the atoms vibrate with large amplitudes and the average separation between them increases. As a result, the entire solid size increase as the temperature increases.

Amplitude- is the maximum distance where an object moves to and fro.

The expansion of solid substance is so small that its difficult to observe its changes.

Solids can be experience three different types of expansion. There are;

1. Linear expansion
2. Superficial expansion (Area expansion)
3. Cubical expansion (Volume expansion)

Linear expansion

Is a tendency of a solid increase its length due to change in temperature.

Consider the original length L_o of the solid substance placed at initial temperature θ₀ (at room temperature) when a solid substance is subjected under heat energy, the new length of the solid substance is L₁ at final temperature θ₁

     

Where ΔL represents the amount of increase in length after the expansion

Note: The amount of increase in length, ΔL depend on the following factors:

1. The amount of increase in length of the solid substance depends on the original length

i.e.   ΔL ∝ Lo.......... (i)

 2. The amount of increase in length depends on the temperature rise

                                      i.e.      ΔL    ∝    Δθ.......... (ii)

 3. The amount of increase in length depends very much on the nature of the substance 

                                  Using expressions (i) and (ii) above

          ΔL = ∝LoΔθ

Where ∝ = linear expansivity of the solid substance

                = coefficient of linear expansion

         

Material’s coefficient of thermal expansion is fractional increase in size of material per degree temperature  rise.

The linear expansivity / coefficient of linear expansion is the fractional increase in length per degree temperature rise

The SI unit of linear expansivity are K^-1

Note: Some linear expansivity solid metal substances are:

SOLID SUBSTANCE	LINEAR EXPANSIVITY K-1
Aluminum	0.000026
Brass	0.000019
Copper	0.000017
Iron	0.000012
Concrete	0.000011
Glass	0.0000085
Invar	0.000001

_{NB: The higher the linear expansivity of the substance the larger the amount of the expansion and the lower the linear expansivity the smaller the amount of expansion.}

_{EXAMPLE: 1}

1. _{Copper rod has a length of 40cm on a day when the temperature of the room is 22.3}⁰_{C. What will its length become on a day when the temperature of the room is 30ºC?}

_{Take the linear expansively of copper 0.000017 K^-1}

 Solution

L₀ = 40cm

θ_{0 =} 22.3^oC

θ₁ = 30ºC

L₁ =?

L₁ – 40 = 0.000017 X 308

L₁ = 0.000017 X 308 +40

L₁ = 0.005236+40

L₁ = 40.005236cm 

2. A block of concrete 5.0m expands to 5.00412m. When heated from 25ºC to 100ºC.

Find the linear expansivity of the concrete

 Solution

      

*linear expansivity is 0.00412/375 

=0.00011 K^-1

^{...TO BE COUNTINOUS...}