Grade 10 2nd term Free Lesson. College Physics Enotes SS1. Concept of Energy, Law of conservation of Energy, Social Development.

ENERGY

CONTENT

1. The Concept of Energy
2. Types of Energy
3. The Law of Conservation of Energy
4. Sources of Energy
5. Classification of the Sources of Energy
6. Uses of Energy
7. Energy and Social Environment
8. The Impact of Energy Usage on the Environment
9. Energy Crises
10. Oil Spillage

WEEK 1

The Concept of Energy

Energy is the ability or capacity to do work. Its unit is Joules.

Types of Energy

Energy exists in various forms some of which are;

1. Mechanical energy
2. Chemical energy
3. Solar energy
4. Heat energy
5. Sound energy
6. Electrical energy
7. Nuclear energy

Mechanical Energy

Kinetic energy and potential energy constitutes mechanical energy. Kinetic energy is the energy a body possesses as a result of its motion. Potential energy on the other hand, is the energy possessed by a body because of its position. A body can also possess potential energy as a result of its nature. For example, an elastic material when stretched stores up energy (potential energy) which is given as ½ k e² where k is what we call the elastic constant and e is extension in metres. Another form of potential energy is chemical potential energy which is energy stored up in a substance because of its chemical composition. Examples are; energy in the food we eat, electrolytes in cells or batteries.

Mathematically, Kinetic energy K.E=12(mv2).

M is mass in kilogram, v is velocity in m/s.

Examples of bodies that possess kinetic energy are

1. A rolling ball
2. An object falling under gravity
3. wind or air in motion
4. An athlete running a race
5. A bullet movement
6. A plane flying.

If a body  is raised to a height  h, its potential energy is given as

P.E = mgh. Where m is mass in kilogram, h is height in metres and g is acceleration due to gravity.

EVALUATION

1. Differentiate between potential energy and kinetic energy
2. What is the formula for calculating kinetic energy and potential energy

The Law of Conservation of Energy

Energy as we have treated earlier exists in various forms. Although energy can be converted from one form to the other, the total energy remains conserved.

This is the law of conservation of energy. It states that energy can neither be created nor destroyed but can be converted from one form to the other. This law can be illustrated by mechanical systems as shown in the figures below.

Energy Changes in a Simple Pendulum 

For fig 1

1. As the pendulum bob approaches A, the velocityreduces until it becomes zero at point A where it momentarily comes to rest; thereby making the KE zero.
2. Also at A, the bob attains its maximum height above the ground; thereby making the PE to be maximum.
3. as the bob returns towards B, the velocity increases and the height decreases such that at B, velocity is maximum (since K.E=12(mv2), KE is also maximum).
4. At B, height is zero, PE is equal to zero.
5. At the middle point either between A and B or B and C, energy is conserved. Hence, PE =KE

In fig. 2, as the body moves from the horizontal ground C to A, its velocity reduces and at point A, at height h, where the body is stationary, the velocity v is zero. Consequently its kinetic energy is zero but the potential energy is maximum. As the body drops to the ground, its velocity increases and the vertical height h reduces to zero. Therefore, potential energy just before it touches the ground  is zero and the body has maximum kinetic energy.  At point B, the body possesses both Kinetic energy and potential energy. From the two illustrations we see that although the energy changes from kinetic to potential energy and vice versa, the total energy of the system is conserved or remains unchanged.

Another example where it is applied is for a falling body.

Example 1

A ball of mass 8kg falls from rest from a height of 100m. Neglecting air resistance, calculate its kinetic energy after falling a distance of 30m. (take g as 10m/s²).

Solution

Initial velocity at height 100m, u = 0

Distance moved, s = 30m

a = 10ms^-2
Velocity after falling 30m, v = ?

v2=u2+2asv2=02+2×10×30v=6–√00v=24.5m/sK.E=12mv2=12×8×600K.E=2400J

Alternative solution:

K.E = potential energy loss

KE. = mgΔh   

K.E=8×10×30=2400J

Example 2

A body of mass 100kg is released from a height of 200m. With what energy does the body strike the ground? (g = 10 m/s²)

Solution

Gravitational potential energy is given as P.E=mgh=100×10×200=200,000

Example 3

A stone of mass 50.0kg is moving with a velocity of 20 m/s. Calculate the kinetic energy

Solution

mass = 50.0kg,  velocity = 20 m/s

K.E=12mv2=12×50.0×20.0=500J

EVALUATION

1. List eight forms of energy you know.
2. State the law of conservation of energy and apply it to any mechanical system
3. State the principle of conservation of energy. Using this principle explain how energy is conserved for  (i) objects falling under gravity (ii) swinging of a simple pendulum bob.
4. A ball of mass 1kg is dropped from a height of 5m and bounces to a height of  10m. Calculate (i) its kinetic energy just before impact. (ii) its initial  bouncing velocity and kinetic energy.

Sources of Energy

The following are the sources of energy:

1. Energy from the sun (solar energy)
2. Wood (fire wood)
3. Coal
4. Electricity
5. Fossil fuels
6. Chemicals as in cells and batteries.

Classification of the Sources of Energy

Sources of energy can be classified into:

1. Renewable sources of energy: These sources are not usually depleted as a result of usage. e.g, solar energy, tidal waves, wind, waterfalls and dams.
2. Non renewable sources of energy: These sources are usually reduced as they are being used. E.g, fossil fuels-coal, oil, natural gas and wood.

Uses of Energy

1. Solar energy is a universal source of light to planet earth. The plants also use it to manufacture their own food through photosynthesis.
2. Fire wood gives heat for cooking our food.
3. Energy from coal is used to boil water, then, produce steam used in steam engines.
4. Energy from waterfalls is used in hydro-electric power stations like kanji dam to produce electricity.
5. Natural gas, petroleum, diesel oil, etc are all derived from fossil fuels.
6. Chemical energy from cells and batteries are used to power our electronics and phones.

EVALUATION

1. State five source of energy discussed.
2. What fuel can we derive from fossil fuels?
3. State three uses of energy.

Energy and Social Environment

The availability of electricity and petrol is very essential to every society. In fact, all lives on earth depend on the availability of energy. This is because all our electrical gadgets at home and in offices, big machines and engines in the factories and manufacturing industries, our day to day activities, all depend on the availability of energy.

In advanced countries like the USA, Japan, Canada, Russia, etc, the availability of electricity is everywhere. This has enhanced the economy of the countries and thus having a better Gross Domestic Products (GDP). The reverse is the case in the under-developing world like Nigeria, Liberia, Togo, etc where the availability of electricity is nothing to write home about. This has therefore jeopardized the economy, thus, giving rise to low GDP.

Energy is indeed needed in every society for the production of food, efficient transport system, good health programmes, good educational system, etc.

The need for energy availability in every society can never be over emphasized. In short, energy is a major factor to societal development.

The Impact of Energy Usage on the Environment

The impact of energy usage on the environment could be friendly or unfriendly.

The friendly impact is the display of light to give beauty to cities, at night and other significances; while the unfriendly impact include the hazardous radiations from nuclear reactors, gases from industries, etc which could be detrimental to human health.

Global Warming

Global warming is the rise in the average temperature of Earth’s atmosphere and oceans.Since the early 20th century, Earth’s mean surface temperature has increased by about 0.8 °C (1.4 °F), with about two-thirds of the increase occurring since 1980.

Warming of the climate system is unequivocal, and scientists are more than 90% certain that it is primarily caused by increasing concentrations of greenhouse gases( like carbon (iv) oxide, methane, etc) produced by human activities such as the burning of fossil fuels and deforestation.

The Greenhouse Effect

The greenhouse effect is the process by which absorption and emission of infrared radiation by gases in the atmosphere warm a planet‘s lower atmosphere and surface. It was proposed by Joseph Fourier in 1824, discovered in 1860 by John Tyndall,was first investigated quantitatively by Svante Arrhenius in 1896,and was developed in the 1930s through 1960s by Guy Stewart Callendar.

Human activity since the Industrial Revolution has increased the amount of greenhouse gases in the atmosphere, leading to increased radiation from CO₂, methane, tropospheric ozone, CFCs and nitrous oxide. According to work published in 2007, the concentrations of CO₂ and methane have increased by 36% and 148% respectively since 1750.

EVALUATION

1. What is green house effect?
2. The concept of green house effect was developed by who?
3. Mention any four countries of the world that has high GDP
4. Why do you think that the mentioned countries above have high GDP?

Energy Crises

Meaning of Energy Crisis

An energy crisis is any great bottleneck (or price rise) in the supply of energy resources to an economy. It often refers to one of the energy sources used at a certain time and place, particularly those that supply national electricity grids or serve as fuel for vehicles.

There has been an enormous increase in the global demand for energy in recent years as a result of industrial development and population growth. Since the early 2000s the demand for energy, especially from liquid fuels, and limits on the rate of fuel production has created such a bottleneck leading to the current energy crisis.

Causes of Energy Crises

1. Market failure is possible when monopoly manipulation of markets occurs.
2. Large fluctuations and manipulations in future derivatives can have a substantial impact on price.
3. Pipeline failures and other accidents may cause minor interruptions to energy supplies

Oil Spillage

Meaning of Oil Spillage

Oil spillage is the release of a liquid petroleum hydrocarbon into the environment, especially marine areas, due to human activity, and is a form of pollution. The term is usually applied to marine oil spills, where oil is released into the ocean or coastal waters, but spills may also occur on land. Oil spills may be due to releases of crude oil from tankers, offshore platforms, drilling rigs and wells, as well as spills of refined petroleum products (such as gasoline, diesel) and their by-products, heavier fuels used by large ships such as bunker fuel, or the spill of any oily refuse or waste oil.

Spilled oil penetrates into the structure of the plumage of birds and the fur of mammals, reducing its insulating ability, and making them more vulnerable to temperature fluctuations and much less buoyant in the water. Cleanup and recovery from an oil spill is difficult and depends upon many factors, including the type of oil spilled, the temperature of the water (affecting evaporation and biodegradation), and the types of shorelines and beaches involved.Spills may take weeks, months or even years to clean up.

Causes of Oil Spillage

1. When oil tankers have equipment faults.
2. From nature and human activities on land.
3. Water Sports.
4. Drilling works carried out in sea.

EVALUATION

1. What are the causes of energy crises?
2. Define oil spill.
3. State two causes of oil spillage.
4. Define the concept of energy.
5. Why do you think that energy is one of the vital factors to societal existence?
6. Discuss the impact of energy use on environment.
7. Discuss the concept of global warming and the green house effect.
8. Enumerate the factors to be considered in cleaning up the water bodies as a result of oil spillage.

WORK AND POWER

CONTENT

1. Work Done in a Force Field
2. Power
3. Interchangeability of Work and Energy
4. Calculations on Work and Power

Work Done in a Force Field

Definition of Work Done

Work done in Physics is simply defined as the product of force and distance moved in the direction of the force. If work done is w, distance covered is s and force is f, then mathematically,

Work done =force×distanceW=f×s

The S.I unit of work done is Joules ( J ). Since unit of force ‘F’ is Newton (N), unit of distance ‘s’ is metre, the unit of work done is also Newton-Metre (Nm). Other units are kilojoules and megajoules. Note: If no distance is covered, work done is zero. Work done is a scalar quantity.

Every object on the earth’s surface is under the influence of the force of gravity. This force pulls the object towards its centre. The earth’s gravitational field is an example of force field. If a body is to be lifted vertically upwards, work has to be done against this force of gravity. The work done is given as

Work done =force×distance=m×g×h

Where m = mass of the body in kilogram, g = acceleration due to gravity and h is height in metres. If on the other hand, the body falls freely from a vertical height h to the ground, the work done is also mgh.

Work is said to be done whenever a force moves a body over a distance in the direction of the force. i.e.

work = force (F) × distance(d) moved in the direction of the force (f × d).

Mathematically,

Work done W(d)=F×d

The unit of work is joules with the symbol J.s

Work =F×dcosθ

Component of F along the direction of motion.

WD=Fx×dcosθ=FxFFx=Fcosθ

∴ WD=Fcosθ×d

Power

Definition of Power

Power can be defined in a number of ways:

1. Power is the time rate at which work is done.
2. Power is energy expended with time.
3. Power is work done in a given time interval. Its S.I unit is watt. Larger units are horse power (hp), kilowatt (kw) and megawatt (mw).

Mathematically,  Power \((P) = {\text{work done(w) or energy expended} \over \text{

A 40kg girl climbing a flight of  stairs expends energy at the rate of  50W. The time taken for her to reach a height of 20m is (t)}}\\ = \frac{w}{t}\\ =\frac{f \times s}{t} \\ = f  \times v\)

Where f is force and v is velocity (i.e ^s/ _t). that means power can also be defined as the product of force and velocity. The instrument for measuring power is watt-metre.

One horse power is equal to 746watts (1h.p = 746W).

Example

A machine is rated 2500watts. Calculate the power in horse power

Solution

1 horse power = 746watts

Therefore 2500watts=2500746=3.35 horse power

The Interchangeability of Work and Energy

Energy and work can be used interchangeably because they are almost the same thing. They have the same unit which is Joule. For example, if someone has energy, it means he can do some work and if someone can do some work, it means he has some energy. Thus work and energy cannot be separated.

EVALUATION

1. Define work, energy and power. State their S.I units.
2. Can energy and work be used interchangeably? Explain.

Calculations on Work and Power

Example 1.

A body of weight 300N climbs to the top of a hill of height 20m. What is the work done by the body against the force of gravity?

Solution

Force F = 300N, distance s = 20m

Work done =force×distance=f×s=300N×20m=600J

Example 2.

An object of mass 12kg is held at a height of 10m above the ground for 15 minutes. Calculate the work done within this period.

Solution

Since the body is not falling freely under gravity, acceleration due to gravity is zero. Hence work done is also zero.

Example 3.

A bag of rice of mass 50kg was pushed through a distance of 5m for 10seconds by a force of 500N. Calculate the work done.(g = 10ms^-2)

Solution

m = 50.0kg, F= 500 N,  s = 5m and t = 10 seconds.

Work done =force×distance=f×s=500N×5m=2500J

Example 4.

Calculate the power of a pump which lifts 1000kg of water through a vertical height of 2m in 10 seconds. ( g = 10ms^-2)

Solution

Mass (m) = 1000kg,  distance (s) = 2m,  time (t) = 10s

Power =work donetime taken=force×distancetime=m×g×sT=1000×10×210=2000W

Example 5.

An engine develops a power of 750W while moving a car at constant velocity of 3ms^-s.  Calculate the force exerted on the car by the engine.

Solution

Power = 750W,  velocity = 3m/s,   F = ?

Power =force×velocityForce=PowerVelocity=7503=250N

Example 6.

A stone of mass 10kg falls from a height of 2.0m. Calculate the work done. (take g = 10ms²)

Solution

Mass (m) = 10kg,  height (h) = 2.0m

Work done =mgh

=10×10×2=200J

EVALUATION

1. Differentiate between work done and power.
2. What other unit is used in measuring work done?
3. A girl applied a force of 20N on an object for 5s. if the object remains stationary, calculate the work done
4. A boy lifted up a bag of yam of weight 5N through a height of 2m in 10s. Calculate his power.

HEAT ENERGY: THERMAL EXPANSIVITY

CONTENT

1. The Concept of Heat and Temperature
2. The Differences between Heat and Temperature
3. The Kinetic Theory of Matter
4. The Effects of Heat on Substances (Expansion, Vaporization)
5. Using Kinetic Theory to Explain the Temperature of a Body
6. Linear Expansion, Coefficient of Linear Expansivity
7. Expansion in Liquids
8. Applications of Expansion

The Concept of Heat and Temperature

Heat is a form of energy that moves from one point to the other due to temperature difference. When you dip one end of an iron rod into fire and hold the other end with your hand, this other end soon becomes hot because energy has flowed from the point dipped into the fire to this other end. This energy flow is what is known as heat. Temperature is a measure of how cold or hot a body is.

The Differences between Heat and Temperature

	S/N	Heat	Temperature
	1	It is a form of energy	It is not a form of energy
	2	It is measured in joules	It is measured in Kelvin
	3	It is a form of energy transferred from body at a higher temperature to one at a lower temperature	It is a measure of the average kinetic energy of the constituent particle of the a substance
	4	It is a derived quantity	It is a fundamental quantity
	5	Other unit for measuring heat: calorie (Cal), kcal, …	Other units include: 0F, 0C
	6	It can be determined using a calorimeter	It can be measued using a thermometer

The Kinetic Theory of Matter

The kinetic theory of matter states that:

1. Matter is made up of atoms and molecules.
2. The molecules are in a state of constant random motion.
3. They possess kinetic energy because of their motion.
4. The kinetic energy of the molecules is directly proportional to the temperature of the body.

EVALUATION

1. Define temperature and state its unit.
2. State three assumptions of the kinetic theory of matter.

 The Effects of Heat on Substances (Expansion, Vaporization)

When heat is applied to a substance, it can lead to the following changes

1. Chemical changes.
2. Temperature changes.
3. Expansion/Contraction
4. Change of state (melting, vaporization, sublimation).
5. Change in pressure in gases at constant volume.
6. Thermionic emission.

Thermal Expansion

Most solid substances expand when heated. The rate of expansion varies from one solid to another. Expansion is more pronounced in gases followed by liquids and least in solids. A substance whether solid, liquid or gaseous consists of molecules. When the substance is heated, the molecules gain kinetic energy and move faster and hence the molecules take up more space in the substance. This leads to expansion.

Ball and Ring Experiment

Experiment to demonstrate expansion of a solid.

Apparatus: Bunsen burner, ball and ring apparatus

Solid Expansion

Procedure: Allow the metal ball to pass through the ring. Heat the metal ball for some time in the Bunsen burner and make it pass through the same ring. The metal ball will no longer pass through the same ring it passed through earlier as a result of expansion. When allowed to cool down for some time and allowed to pass through the ring once more, it will pass through because it has contracted and regained its original size.

Using Kinetic Theory to Explain the Temperature of a Body

According to the kinetic theory of matter, the average kinetic energy of the molecules is directly proportional to the temperature. This means that as the kinetic energy of the molecules increases, the temperature also increases. When a body is subjected to heat, the velocities of the molecules increases and hence they gain more kinetic energy this of course will lead to increase in the temperature of the body. On the other hand, if we reduce or lower the heat, the velocities of the molecules will decrease leading to a decrease in the kinetic energy of the molecules. Hence the temperature falls or reduces.

EVALUATION

1. Give three differences between heat and temperature
2. Explain the phenomenon of expansion using the kinetic theory of matter
3. Give four effects of heat on a substance

Linear Expansion, Coefficient of Linear Expansively

Types of Expansion

1. Linear expansion
2. Area or Superficial Expansion
3. Volume or cubic Expansion

1. Linear Expansion

Linear expansion is expansion in length of a body. Different solids expand at different rates, this is because they have different coefficient of linear expansivity.

Coefficient of Linear Expansivity (α)

It is defined as increase in length per unit length per degree rise in temperature. The unit is per Kelvin or 1/K or K^–1

α=Increase in lengthoriginal length×temperature rise=L2–L1L1(θ2–θ1)

L₂ – L₁ = Increase in length or expansion

θ₂ – θ₁ = Temperature rise or increase in temperature

θ₂ is final temperature

θ₁ is initial temperature

L₂ is new length

L₁ is original length

Question 1.

What is meant by the statement, the linear expansivity of copper is 0.000017/k?

Solution:

It means that the increase in length per unit length per degree rise in temperature of copper is 0.000017m.

Question 2.

A brass is 2 meters long at a certain temperature. What is its length for a temperature rise of 100k, if expansivity of brass is  1.8 x 10^-5/k

α =Increase in lengthoriginal length×temperature rise=L2–L1L1(θ2–θ1)

L2–L1=αL1(θ2–θ1)L2=L1{α(θ2–θ1)+1}L2=2{1.8×10−5(100)+1}L2=2{0.0018+1}L2=0.0036+2=2.0036m

Question 3.

A metal of length 15.01m is heated until its temperature rises to 60⁰C. If its new length is 15.05m, calculate its linear expansivity.

Solution:

L₁ = 15.01m, L₂ = 15.05, θ₂ – θ₁ = 60^o, L₂ – L₁ = 0.04

α=Increase in lengthoriginal length×temperature rise=L2–L1L1(θ2–θ1)α=15.05–15.0115.01×60o=0.04900.6=0.000044=4.4×10−5/k

EVALUATION

1. What is meant by the statement that the linear expansivity of copper is 0.000017/k.
2. Steel bars each of length 3m at 29⁰c are to be used for constructing a rail line. If the linear expansivity of steel is  1.0 x 10^-5/k. Calculate the safety gap that must be kept between successive bars, if the highest temperature expected is 40⁰c.

Experiment to Determine the Linear Expansivity of a Metal Block

Aim: Experiment to determine the linear expansivity of a metal block

Apparatus: Thermometer, Micrometer screw gauge, steam jacket, metal rod, meter rule

Method:

(i) Measure the length of the metal rod (L₁).

(ii) Insert the metal rod in the steam jacket and take the initial temperature of the metal rod with thermometer (θ₁).

(iii) Screw the micro-meter to touch the end of the rod and take the reading of micro-meter (x_i).

(iv) Unscrew micro meter to make room for expansion of metal rod.

(v) Introduce steam into the steam jacket for several minutes then the metal rod will expand.

(vi) Screw the micrometer screw guage to touch the end of the metal rod again and take the reading again (x₂).

(vii) Record the final temperature (θ₂).

Calculation:

α=x2–x1x1(θ2–θ1)

Conclusion: Since all parameters are known, α can be calculated.

2. Area or Superficial Expansivity (β)

It is defined as the increase in area per unit area per degree rise in temperature

β=Increase in Areaoriginal area×temperature rise=A2–A1A1(θ2–θ1)

A₂ – _A1 = Increase in area or expansion

θ₂ – θ₁ = Temperature rise or increase in temperature

θ₂ is final temperature

θ₁ is initial temperature

A₂ is new area

A₁ is original area

Relationship between Linear Expansivity and Area Expansivity: β = 2α

Question 1: A metal cube of cross sectional area 3.45m² at 0⁰C is heated at a temperature rise of  70K, when the final length of the cube is 3m. Find the:

(i) coefficient of superficial expansivity.

(ii) coefficient of linear expansivity.

Solution

(i) β=Increase in Areaoriginal area×temperature rise=A2–A1A1(θ2–θ1)A2=L2=3×3=9m2θ2–θ1=70kA1=3.45m2β=9–3.453.45×70=5.55241.5=0.023/k=2.3×10−2/k

(ii) β=2αα=β2α=2.3×10−22=1.15×10−2K−1

EVALUATION

1. The linear expansivity of a metal is 0.000019 per k. What will the area of 400mm² be if its temperature is raised by 10⁰C.

3. Cubic Expansivity

Experiment to Determine the Apparent Cubic Expansivity

Cubic or Volume Expansivity (γ)

It is defined as the increase in volume per unit volume per degree rise in temperature

γ=Increase in Volumeoriginal volume×temperature rise=V2–V1V1(θ2–θ1)

V₂ – V₁ = Increase in volume or expansion

θ₂ – θ₁ = Temperature rise or increase in temperature

θ₂ is final temperature

θ₁ is initial temperature

V₂ is final volume

V₁ is original volume

Relationship between Linear Expansivity and Cubic Expansivity: γ = 3α

Question 2: The increase in the volume of 10cm³ of mercury when the temperature rises by 100⁰C is 0.182cm³. What is cubic expansivity of mercury.

γ=Increase in Volumeoriginal volume×temperature rise=V2–V1V1(θ2–θ1)

V₂ – V₁ = Increase in volume = 0.182cm²

θ₂ – θ₁ = Temperature rise = 100^oC

V₁ = original volume = 10cm²

γ=0.18210×100=0.1821000=0.00082/k=1.82×10−4K−1

Expansion in Liquids

Expansion in liquid is complicated by the expansion of the container because while the liquid expands, the container equally expands. So it is important to differentiate between real and apparent cubic expansivity.

Real or Absolute Cubic Expansivity (γ_r):

It is defined as the increase in volume per unit volume per degree rise in temperature.

Apparent Cubic Expansivity (γ_a):

It is defined as the increase in volume per unit volume per degree rise in temperature when the liquid is heated in an expansible vessel.

Question 3.

A cube with side 100cm at 0⁰C is heated to 100⁰C. If the side becomes 101cm long find,

(a) The linear expansivity

(b) The cubic expansivity

Solution

(a) L₁ = 100cm = 1m, L₂ = 101cm = 1.01m, θ₂ = 100^o, θ₁ = 0^o

γ=increase in volumeoriginal volume×temperature rise=V2–V1V1(θ2–θ1)γ=1.01–11×100=0.01100=0.0001/k=1.0×10−4/k

(b) γ=3αγ=3×1.0×10−4=3.0×10−4/k

Determination of the Apparent Cubic Expansivity of a Liquid

Apparent Cubic Expansion of a Liquid

Apparatus: Thermometer, Density bottle, Retort stand, Water, Source of heat, Beaker, Beam balance, Liquid, Stirrer.

Method:

(i) Dry the density bottle and weigh it (M).

(ii) Fill the density bottle with the liquid that the apparent cubic expansivity is required and weigh it (M₁)

(iii) Immerse the density bottle into a beaker of water and suspend with a thread on the clamp of the retort stand.

(iv) Take the original temperature of the water in the beaker (θ₁).

(v) Heat the set up gently until the water boils.

(vi) Some liquid are expelled through the orifice of the bottle cover, the heating continues until no liquid is seen expelled again.

(vii) The final temperature of water is taken (θ₂)

(viii) The density bottle is removed and wiped dry and re-weighed (M₂).

Calculation

Mass of empty density bottle = M

Mass of density bottle + liquid = M₁

Original temperature of water = θ₁

Final temperature of liquid = θ₂

Mass of remaining liquid + density bottle = M₂

γα=Mass of liquid expelledMass of liquid remaining×temperature rise=M1–M2M2–M(θ2–θ1)

Conclusion

Since all the parameters are known, apparent cubic expansivity can be calculated.

EVALUATION

1. Differentiate between Real cubic expansivity and Apparent cubic expansivity.
2. A glass bottle full of mercury has mass 500g on being heated through 35⁰C, 2.43g of mercury was expelled. Calculate the mass of mercury remaining in the bottle ( cubicexpansivity of mercury is 1.8 x 10^-4/k and linear expansivity of glass is 8.0 x 10^-6/k)

Applications of Expansion

(A) Advantages of Expansion

1. The use of the bimetallic strip in:

(i) Fire alarm

(ii) Bi-metallic thermometer

(iii) Temperature regulator in electric pressing iron

2. Red hot rivet used in ship

3. Fitting of wheels in rims

4. Removal of tight glass stopper

A1. Bi-metallic Strip

It consists of two different metals joined together. They expand at different rates when heated e.g brass and iron.

(i)  Electric Fire Alarm

When a fire breaks out in a building, the resulting heat causes the bi-metallic strip to bend towards the contact, thus completing the circuit. This causes the bell to ring out a fire alarm.

(ii)  Bi-metallic Thermometer

It consists of a coiled bi-metallic strip which expands outwards when heated. As this happens, the pointer moves along the scale and the reading on the scale is taken as the temperature.

(iii) Electric Pressing Iron

It has a device known as Thermostat, it is made of bi-metallic strip and it is used to regulate the temperature of the pressing iron, gas cooker, refrigerator, etc.

Mode of Operation of Pressing Iron

When the current is switched on, current flows through the circuit and the bi-metallic strip is heated up.  It expands and the strip bends away from the contact point thereby switching off the flow of current. The pressing iron cools down,straighten-out  and contact is re-made and current begin to flows again and the processcontinues. This make-and-break device regulates the temperature of a pressing iron.

A2. Red-hot Rivet Used in Ships

Steel plates and girders which are used in ship building and other constructional works are usually riveted together.

A3. Fitting of Wheels in Rims

The large driving wheels of locomotive are fixed with steel tyre which are renewed from time to time as they wear out. In order to ensure a tight fitting, the tyre is made slightly smaller in diameter than the wheel. The tyre contracts on cooling thus ensuring tight fitting.

A4. Removal of Tight Glass Stopper

A tight glass stopper can be removed by standing the bottle in hot water. The glass bottle expands and the stopper becomes loose.

(B) Disadvantages of Expansion

1. Expansion of metal on steel bridges/galvanized iron sheets: Cracking sounds are heard when galvanized iron sheets used in the roof of buildings are being heated. This is due to the expansion of sheet when heated. Bridges  made of steel equally expand during hot weather.
2. Cracking of glass cup when hot water is poured into it: When hot water is poured into the glass tumbler, it often cracks due to uneven expansion of the interior walls and exterior walls of the glass cup.
3. Expansion of balance wheel of a wrist watch. This makes the watch to give wrong reading
4. Sagging of overhead wires: Telegraph wires when laid in hot weather are allowed to sag so that in cold weather they can contract without snapping.
5. Expansion of railway lines: Gaps are left between rails in railway lines to allow for free expansion and contraction of rails, without the gaps, there would be buckling of rails.

GENERAL EVALUATION

1. Explain four advantages of expansion in solids.
2. Explain three disadvantages of expansion in solids

WEEKEND ASSIGNMENT

1. Give three applications of expansion/contraction
2. What is a bimetallic strip? Give two applications of a bimetallic strip
3. Explain how a thermostat regulates the temperature of an electric iron
4. Mention three solids that undergoes sublimation

HEAT ENERGY: TRANSFER OF HEAT

CONTENT

Conduction of Heat

1. Meaning of Heat Conduction
2. Using Kinetic Molecular Theory to Explain Conduction in Solids
3. Conduction of Heat in Liquids
4. Experiment to Show that Water is a Poor Conductor of Heat
5. Applications of Conductors and Insulators

Convection of Heat

1. Meaning of Convection of Heat
2. Using Kinetic Molecular Theory to Explain Convection in Liquids
3. Applications of Convection

Radiation, Emission and Radiation by Different Surfaces

Conduction of Heat

Meaning of Heat Conduction

Conduction of heat is the process by which heat is passed along a material from molecule to molecule while the heated particles remaining in mean position. Most metals are good conductors but their thermal conductivities differ from one metal to another. Experiment performed to compare the conductivity of solid showed that copper is a better conductor than brass, followed by iron, lead…

Using Kinetic Molecular Theory to Explain Conduction in Solids

When the end A is heated, molecule A vibrates about its mean position with a greater kinetic energy and pushes the molecule B to do the same. Molecule B’s increase in kinetic energy is transferred to C and so on until this effect reaches Z. Soon the kinetic energy of molecule at Z is also increased. As the kinetic energies of the molecules increase, temperature increases and heat is then tranferred from the hot part to the cold part.

Conduction of Heat in Liquids

Liquids are poor conductors of heat except mercury and other molten metals. Experiment demonstrated below shows that water is a poor conductor of heat.

Experiment to Show that Water is a Poor Conductor of Heat

Aim: To show that water is a bad conductor of heat.

Apparatus: water, test tube, ice-block, Bunsen burner and wire guaze.

Method: i. Wrap the ice block with wire guaze to prevent the ice from floating in water, and drop in the water in the test tube.

ii. Heat the water near the top of the water with the Bunsen burner.

Observation: It is observed that while the water was boiling on top, the ice at the bottom did not melt

Conclusion: The ice did not melt because water is a poor conductor of heat and was not able to conduct the heat to the ice.

Applications of Conductors and Insulators

1. Cooking utensils: Bad conductors of heat are used as handles while the cooking pots are made ofmetals such as aluminium which are good conductors of heat.
2. Lagging: Insulators are often used as lagging materials in hot water pipes, stem boilers, hot water storage tanks and ovens to prevent them from getting colder.
3. Warmth: Woollen sweaters keep us warm during winter or cold weather to prevent conduction of heat from the body.
4. Double walls: Houses built with double walls with space in between them have air trapped in the spaces that act as insulators, thus, keeping the house warm.

EVALUATION

1. What is conduction?
2. Use the molecular theory to explain conduction.
3. Explain three applications of conductors and insulators.

Convection of Heat

Meaning of Convection of Heat

Convection is the process by which heat is transferred in a liquid or gas by the actual movement of the heated fluid from the hotter to the colder parts. Liquids and gases are poor conductors of heat but transfer heat by convection.

Using Kinetic Molecular Theory to Explain Convection in Liquids

When a liquid is heated at the bottom of its container, the molecules there expand and becomes lighter. They therefore move to the top and are then replace by denser colder molecules from the top. The new  dense molecules also get heated up and become lighter and hot then move to the upper part to be replaced by others. This action set up a convection flow of heat which continues until the water boils.

Applications of Convection

1. Land and sea breeze: This is convection current in nature. It happens in coastal area.

(a) Sea breeze: In a hot day the sun warms the air near the land quickly than the sea because the earth has a lower specific heat capacity than the sea. This warm air rises. Cooler air from the sea moves to replace the risen air. This cool breeze from the sea is known as sea breeze.

Land breeze: at night, the air above the sea is hotter. There is a conventional flow of hot air from the sea rises up.They are replaced by cool air from the land. The flow of cool air from the land to the sea is called the land breeze.

2. Ventilation: Air heated by respiration and fires rises towards the ventilators placed near the ceiling. This is replaced by fresh air from windows and other openings.

3. Cooling of motor car engine: Car engines require  cooling to prevent overheating. The heat generated by the engine is conducted by the metal to the water in the jacket. The water is cooled by the air circulating round the radiator as the vehicle moved and by the cool air from the fan

4. The Domestic hot water system: Water is heated in the boiler by conduction through the metal. Hot water rises by convection to the cylinder, cold water flows in to take its place.

EVALUATION

1. Describe an experiment to show Convection current in water.

Radiation, Emission and Radiation by Different Surfaces

Meaning of Radiation

Radiation is the process by which heat is transferred from a hotter to a cooler place without heating of the intervening medium. Radiation is a mode of heat transfer that does not require a material medium for its transfer. Radiation can be detected by a radiometer and a thermopile. A thermopile detects and measures radiant energy.

A black surface is a better radiator and absorber of heat than a polished/shining surface. This is why it is not advisable to wear a black cloth on a sunny day because one feels hot.

Polished surface, white surface and silvered surface are good reflectors of heat.

The Thermos Flask

This device is used to prevent loss of  heat energy from its content

The three modes of heat transfer are prevented in the thermos flask in the following ways:

1. The vacuum between the double walled glass prevents loss of heat by conduction and convection.
2. The silver colour of the inside of the double walls prevents heat loss by radiation
3. The cork support, or plastic prevents heat loss by conduction.
4. The cork stopper prevents heat loss by conduction, evaporation and convection.

GENERAL EVALUATION

1. Mention the features of the Thermo flask and explain how heat losses are prevented.

ELECTROSTATICS

CONTENT

1. Definition of Electrostatics
2. Types of Charges
3. The Law of Electrostatics
4. Gold leaf Electroscope
5. Ways of Producing Charges
6. Charge Distribution in a Conductor
7. Lightning Conductors
8. Electrophorus

Definition of Electrostatics

Electrostatics is the study of charges at rest. It is electricity that does not move from one point to another in the substance in which it is produced.

Types of Charges

Positive charge

A body becomes positively charged if it losses electron. This can be obtained in the Laboratory if glass rod is rubbed with silk and there is a net transfer of surface electrons from glass to the silk. The glass becomes positively charged and the silk becomes negatively charged.

Negative charge

A body is negatively charged if it gains electron. This is obtained by rubbing ebonite rod with fur and there is a transfer of electrons from the atoms of fur to the ebonite rod. The fur becomes positively charged.

The positively charged protons deep in the nucleus are not free to be transferred. Hence bodies do not become electrically charged by transfer of protons. They become charged by transfer of electrons

The Law of Electrostatics

Like or similar charges repel each other; unlike or opposite charges attract each other.

Gold leaf Electroscope

An electroscope is an instrument used for the detection and testing of small electric charges. It consists of a flat brass disc or cap, a brass rod with a gold leaf. The metal case is made draught-proof and connected to the earth to prevent accumulation of charges due to external influence.

Uses of the Gold Leaf Electroscope

1. To detect charges: If a charged body is placed on the cap of a charged  electroscope an increase in divergence or collapse of the leaf shows the body is charged. If there is no change in the divergence, it means the body is not charged.
2. To determine the nature of charge on the body: If a charged body is placed on a charged electroscope, increase in divergence means the charge on the electroscope and the body are the same. If there is collapse of the leaf, it means they have opposite charge or the body is uncharged.
3. To determine the conducting properties of a body: If a good conductor is placed on the cap of an electroscope, the leaf collapses immediately. If it is a semi conductor, it collapses gradually and if an insulator, there is no alteration of the leaf

EVALUATION

1. What is electrostatics?
2. Explain three functions of a Gold leaf electroscope

Ways of Producing Charges

1. Electrostatic Induction:

Electrostatic induction is the act of charging a neutral body by placing a charged body near it without any contact between the two.

STEP 1: A negatively charged body is brought near the uncharged body, free electrons from the metal sphere are repelled by the excess electrons on the rod. They shift towards the right. They can not escape from the sphere because the stand and the surrounding air are insulated.

STEP 2: These excess charges called induced charges are released to the earth by touching the right part of the sphere with a wire and the other part of the wire to the earth.

STEP 3: The wire is disconnected.

STEP 4: The negatively charged rod is removed. A net positive charge is left on the rod.

2. Friction:

Charges can also be produced by friction. By rubbing as in ebonite and fur, glass rod and silk, charges are transferred from one by either of the two bodies involved. Equal and opposite charges are produced by friction.

Effects of Charging by Friction

1. Passengers stepping out of cars and buses complain of a slight electric shock as soon as their feet touch the ground.This is because friction between the air and the body of the fast moving car makes the body of the vehicle to be charged.
2. A chain is often left hanging from the rear of a petrol tanker to discharge the charges acquired on the body during movement as this may cause a spark when inflammable vapour is present.
3. Contact: This is done by bringing a charged body in contact with an uncharged body. Charges are transferred from the charged body to the uncharged body.

Charge Distribution in a Conductor

Charges are usually concentrated at places where the surface is sharply curved. The charge density is highest at the sharpest point of the conductor. Because of this high charge density, air molecule close to this point get ionized ( i.e broken down into positive and negative ions). Those with charge opposite to the conductor will be attracted to the conductor. Those with charge opposite to that of the conductor will be repelled. As these ions move, they collide with other molecules and knock off electron from them thereby ionizing those molecules. This process could continue leading to a geometrical increase in the number of ions around the conductor.

For a hollow conductor, charges reside only on its outside surface, no charges reside inside the conductor.

EVALUATION

1. What is electrostatic induction?
2. Explain the three methods of charging.

Lightning Conductors

Lightning conductors are used to prevent tall buildings from being damaged when being struck by lightning. They are made from a copper with a sharp point edge or spike at the top. It helps to conduct the charges generated harmlessly to the earth. When electrical charges in thunderclouds build up, attraction between unlike charges within a cloud increases steadily until a heavy spark  and sound is produced as the charges approach one another. This spark is observed as lightning and the sound is thunder. The heat generated can set a building or tree on fire.

The charge on the cloud induces electrical charges on the lightening conductor. This buildup at the sharp edge and cause ionization of air molecule around it. Some of the charge avalanche result from the  ionization of air around the lightening conductor travels toward the cloud and help to neutralize some of the charge on the cloud thereby reducing the possibility of a lightening.

Electrophorus

Electrophorus is used for storing and transferring electric charges. It consists of a metal disc fitted with an insulating handle and another flat disc made of insulating material such as ebonite

GENERAL EVALUATION

1. Explain the use of the following: (i) Lightning conductor (ii) Electrophorus