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PHYSICS SSS1 FIRST TERM LESSON PLAN SCHEME OF WORK

INTRODUCTION TO PHYSICS

CONTENT

1. Definition of Physics

2. The Importance of Physics

3. Aspects/Careers in Physics

4. Branches of Physics

Definition of Physics

The word ‘’PHYSICS’’ originates from the Greek word, ‘’PHYSIS’’, which means nature and natural characteristics.

Physics as a body of scientific knowledge, deals with the study of events in the universe, both remote and immediate universe.

In actual sense, physics deals with the behaviour of matter as well as the interaction of matter and natural forces.

Physics is the study of matter in relation to energy.

The Importance of Physics

Physics is important for the following reasons:

1. Physics is constantly striving to make sense of the universe. This is seen in the development of theories and new theories used for better understanding of the universe.

2. When we study physics, we acquire the knowledge and skills to understand how and why natural things happen the way they do, and to make reliable predictions about their future occurrences. (e.g mirage, eclipse, earthquake, thunder,…)

3. The knowledge of physics gives us a better understanding of our immediate and natural environment.

4. The study of physics has enhanced the communication and the transportation world, thus, making the world a ‘’global village’’.

5. Human health has been improved from the study of physics through the invention of modern medical equipment.

EVALUATION

1. What Greek word is physics derived from?

2. Define physics.

3. State five importance of physics.

Aspects/Careers in Physics

Physics has several applications on health, technology & engineering, agriculture and applied sciences. As a results, below are some of the aspects/careers related to physics.

A: In Health

We have:

1. Human medicine and surgery

2. Nursing & midwives

3. Radiotherapy

4. Pharmacology

5. Physiology

6. Anaesthesia

7. Veterinary etc.

B: In Engineering

We have:

1. Electrical engineering

2. Electronic engineering

3. Mechanical engineering

4. Aeronautic engineering

5. Petroleum engineering etc.

C: In Agriculture

We have:

1. Agricultural engineering

2. Agricultural production engineering

3. Horticulture etc.

D: In Basic/Applied Sciences

We have:

1. Geophysics

2. Applied physics

3. Biophysics

4. Medical physics

5. Space physics

6. Astronomical physics

7. Engineering physics, etc.

EVALUATION

Mention any four (4) careers related to physics in:

1. Health

2. Basic science

3. Engineering.

 

Branches of Physics

The following are the branches of physics.

1. Mechanics

2. Heat

3. Electricity

4. Optics

5. Sound

6. Magnetism

7. Atomic physics

8. Nuclear physics

NOTE: No. 7 & 8 above had been combined and addressed with the current name, ‘’NUCLEAR PHYSICS’’, since the energy comes from the nucleus of the atom. The OLD NAME is ATOMIC PHYSICS.

EVALUATION

1. Develop a mnemonic for branches of physics.

2. Mention the branches of physics.

3. What is the recent name for atomic physics?

4. What do you understand by the term, ‘Physics’?

5. How has physics made the world, ‘a global village’?

6. State five importance of physics.

7. Mention five careers each related to physics in the following areas. i. Engineering ii. Health iii. Applied sciences

8. Mention the branches of physics.

FUNDAMENTAL AND DERIVED QUANTITIES AND UNITS

CONTENT

Fundamental Quantities

1. The Concept of Fundamental Quantities

2. Other Fundamental Quantities

Derived Quantities

1. The Concept of Derived Quantities

2. Dimensions and Units of Derived Quantities

Fundamental Quantities

The Concept of Fundamental Quantities

Fundamental quantities are physical quantities whose dimensions and units are not usually derived from other physical quantities. Basically, there are three fundamental quantities in mechanics. They include:

(i) Mass

(ii) Length and

(iii) Time

(i) Mass: This is a fundamental quantity with dimension ‘M’, usually written in capital letter. The S.I. unit of mass is kilogramme (kg). Mass can also be measured in gramme (g), tonne (t), etc.

(ii) Length: This is another fundamental quantity with dimension ‘L’, written in capital letter. The S.I. unit of length is metre (m). Length can also be measured in kilometre (km), centimetre (cm), inches (inch), feet (ft), etc.

(iii) Time: Time is a fundamental quantity with dimension ‘T’, also written in capital letter. The S.I. unit of time is second (s). Time can also be measured in minutes and hours.

The below table summarized the dimensions and units of the basic fundamental quantities.

	S/N	Quantity	Dimension	S.I. Unit
	1	Mass	M	Kilogramme (kg)
	2	Length	L	Metre (m)
	3	Time	T	Second (s)

EVALUATION

1. List the three basic fundamental quantities.

2. What are their dimensions and SI units?

 

Other Fundamental Quantities

	S/N	Quantity	S.I. Unit
	1	Temperature	Kelvin (K)
	2	Current	Ampere (A)
	3	Amount of substance	Mole (mol)
	4	Luminous intensity	Candela (cd)

NB: The educator should carry out activities on simple measurement of current and temperature with the students.

ACTIVITY: PRACTICAL

1. Measuring the temperature of boiled water in a specific interval of time say, 2mins as it cools down.

2. Measuring the current value in a simple electric circuit.

EVALUATION

1. Mention the three other fundamental quantities and their SI units.

2. How many fundamental quantities are there altogether?

3. Enumerate all the fundamental quantities with their SI units.

4. Write down the dimension of the three basic fundamental quantities.

5. Why are the above quantities called fundamental quantities?

Derived Quantities

The Concept of Derived Quantities

Derived quantities are physical quantities whose dimensions and units are usually derived from the fundamental quantities. E.g, force,speed, etc.

Other physical quantities apart from the fundamental quantities are derived quantities. This is because their dimensions and units are usually derived from the fundamental ones.

Derived quantities include:

1. Work

2. Energy

3. Momentum

4. Impulse

5. Volume

6. Area

7. Pressure

8. Power

9. Density

10. Moment

11. Torque, etc.

 EVALUATION

1. What are derived quantities?

2. Mention five examples of derived quantities.

Dimensions and Units of Derived Quantities

1. Derive the dimensions and the S.I. units of (i) speed (ii) acceleration (iii) Force.

SOLUTION

(i) Speed =distancetime=lengthtime=LT=LT−1

∴ The dimension for speed is LT−1

The S.I. unit of length is ‘m’ and that of time is ‘s’

∴ The S.I. unit of speed is msorms−1

NB: Speed and velocity have the same dimension and S.I.unit.

Also, velocity =displacementtime

(ii) Acceleration =velocitytime=LT−1T=LT2=LT−2

∴ The S.I. unit of acceleration = =ms−1s=ms2=ms−2orms2

(iii) Force =mass×acceleration=m×LT2=MLT2=MLT−2

∴ The unit of force is kgms2

But the S.I. unit of force is Newton (N). This is the unit used in all calculations

2. Show that the dimension of pressure is ML−1T−2. Hence, derive the S.I. unit.

SOLUTION

Now, pressure =forcearea

∴ pressure =MLT−2L2=MT−2L=ML−1T−2

The S.I. unit of force is Newton, N; while that of area is metresquare, m2

Hence, the S.I. unit of pressure =Nm2orNm−2

3. Derive the dimension for work. What is the S.I. unit of work?

SOLUTION

Work =force×distance

∴ work =MLT−2×L=ML2T−2

Unit of work =Nm

But the S.I. unit of work is Joule (J). This is the unit used in all calculations.

In summary, the table below shows the dimensions and S.I. units of some derived quantities.

	S/N	Quantity	Dimension	S.I. Unit
	1	Work & Energy	ML2T−2	Joule (J)
	2	Momentum & Impulse	MLT−1	Newton-Second (Ns)
	3	Volume	L3	metre cube (m3)
	4	Area	L2	Metre square (m2)
	5	Pressure	ML−1T−2	Newton per metre square or Pascal metre cube (Nm2)
	6	Power	ML2T−3	Watt (W)
	7	Density	ML−3	Kilogramme per metre cube (kgm3)
	8	Moment	ML2T−2	Newton-metre (Nm)

EVALUATION

1. Derive the dimensions and the units of the following quantities:

(i) Volume   (ii) Power  (iii) Density.

2. Differentiate between fundamental and derived quantities.

3. List ten examples of derived quantities and explain why they are called derived quantities.

4. Write down the SI unit of (i) acceleration (ii) force (iii) momentum (iv) density

DIMENSIONS AND MEASUREMENT OF PHYSICAL QUANTITIES

CONTENT

1. Measurement of Length/Distance

2. Measurement of Mass/Weight

3. Measurement of Volume

4. Measurement of Area

5. Measurement of Time

6. Units of Measurement in Industries

Measurement of Length/Distance

Length is measured using the following instruments.

(a) Metre Rule: A metre rule is a measuring device calibrated in centimetres (cm) with a range of 0 – 100cm. In using the metre rule, the eye must be fixed vertically on the calibration to avoid parallax errors.The smallest reading that can be obtained on a metre rule is 0.1cm (0.01cm).

(b) Callipers: These are used in conjunction with metre rule for measuring diameter of tubes, thickness of sheet, etc. The callipers are of two types –

(i) The external calliper and

(ii) The internal calliper.

The external calliper is used to measure the external diameters of solid objects; while the internal calliper is used to measure the internal diameters of solid objects.

(c) Vernier calliper

The vernier calliper can be used for measuring smalllinear length and diameters of objects within the  range of 0-12cm at least. It is calibrated in centimetres (cm). It has a reading accuracy of 0.1mm (0.01cm)

(d) The micrometer screw gauge: It is used to measure the thickness of a round objects  E.g, the diameter of a wire.  The micrometer screw guage gives a more accurate reading than the vernier calliper. It is calibrated in millimetre (mm). It has a reading accuracy of 0.01mm (0.001cm)

Other instruments for measuring length include: measuring tape, ruler, etc. The S.I. unit of length is metre (m).

EVALUATION

1. Mention any three instrument used in measuring length.

2. Which of the above instrument could give the highest degree of accuracy?

Measurement of Mass/Weight

Mass is defined as the quantity of matter a body contains; while Weight is the amount of gravitational force acting on a body or the force with which a body is attracted towards the centre of the earth. The weight of a substance varies from place to place due to variation in acceleration due to gravity,‘g’ over places but mass remains constant from place to place.

Mass and weight of objects are measured using instrument such as spring balance, beam balance, chemical balance, scale balance, etc.

However, the differences between mass and weight are shown below.

	S/N	MASS	WEIGHT
	1	Mass is a scalar quantity.	Weight is a vector quantity.
	2	Mass is the amount of stuff or quantity of matter contained in a body.	Weight is the amount of gravitational force acting on a body.
	3	Mass is measured using a beam balance, chemical balance	Weight is measured using spring balance.
	4	The S.I. unit of mass is kilogramme (kg)	The S.I. unit of weight is Newton (N).

EVALUATION

1. State three instruments used in measuring mass and weight.

2. Differentiate between mass and weight in four ways.

3. Why is weight a vector quantity?

Measurement of Volume

Volume of liquid objects is measured using instruments such as cylinder, burette, pipette, eureka can, etc. For regular solid objects, their volume could be determined using their mathematical formula.

	S/N	Solid Object	Formula for Volume
	1	Cube	l×l×l
	2	Cuboid	l×b×h
	3	Cylinder	πr2h
	4	Cone	13πr2h
	5	Sphere	43πr2

The S.I. unit of volume is metre cube m3

Measurement of Area

The area of a solid object could be determined using mathematical formulae after determining the two dimensions of the object.

	S/N	Solid Object	Formula for Area
	1	Triangle	12bh
	2	Rectangle	lb
	3	Square	l2
	4	Parallelogram	bh
	5	Trapezium	12(a+b)h

The S.I. unit of volume is metre square m2

WORKED EXAMPLES

1. Find the volume of a cylinder of diameter 12cm and height 15cm.

SOLUTION

d =12cm

∴ r =12cm2=6cm

h =15cm,π=227

Now, v =πr2h

∴ v =227×62×15

∴ v =22×36×157=118807

∴ v =1697.14cm3

2. What is the area of a triangular card board of base 6cm and height 4cm?

SOLUTION

b =6cm and h =4cm

Now, A =12bh

∴ A =6×42=242

∴ A =12cm2

EVALUATION

1. Calculate the volume of a rectangular prism of dimension 7cm by 3.5cm by 1.5cm.

2. A cube has an edge of 0.8cm. Find its volume.

Measurement of Time

The Concept of Time

You must have heard the following statements made about time:

1. “Time and tide waits for no man”

2. “Time is business”

3. “There is time for everything: time to sow and time to reap, time to laugh and time to cry, time to go to bed and time to wake up” and so on

Time is very important in our daily activities. Many people have failed in one area or the other because of mismanagement of time. In Physics time is very important. Wrong timing can lead to wrong observations, results and wrong conclusions.

What then is time? Time may be considered as the interval between two successive events. It is a fundamental quantity. Its S.I unit is seconds.

Ways of Measuring Time

Time as mentioned earlier is very important. That is why early men developed various means of measuring time. They used the sun to tell time. Even today people still use the position of the sun to determine time. Other devices they developed and used are:

1. The water clock or hourglass

2. The sand clock

3. The primitive Sundials

Today, we have better time-measuring devices that measure time more accurately than the above mentioned devices. Some of them are:

1. The stop watch which is the standard instrument for measuring time in the laboratory

2. The wrist watch

3. The modern pendulum clock

4. The wall clock

It is worthy of note that:

1. 60 seconds makes one minute

2. 60 minutes makes one hour

3. 24 hours makes one day

4. 365 ¼days makes one year

5. 10 years makes a decade

6. 100 years makes a century/centenary

7. 1000 years makes a millennium

Calculations on Time

Example 1: How many seconds are there in 2 hours 15 minutes?

Since 60 seconds makes 1 minute and 60 minutes makes 1 hour, 1 hour will have 60 x 60 seconds. 2 hours will have 60 x 60 x 2 seconds = 7200 seconds.

15 minutes will have 60 x 15 seconds = 900 seconds

Therefore 2 hours 15 minutes will have (7200 + 900) seconds = 8100 seconds

Example 2: If it takes a pendulum bob 32 seconds to complete 20 oscillations, what is the period of oscillation of the bob?

Period ( T ) is time ( t )  taken for the bob to complete an oscillation.

i.e. T =timenumber of oscillations

=3220=1.6seconds

EVALUATION

1. What are the standard instruments for measuring time in the laboratory?

2. Mention 2 examples each of modern and olden days time-measuring devices you know.

 

Units of Measurement in Industries

Measurement of Length

Length was considered earlier as a fundamental quantity whose S.I unit is metre. We also learnt that other units of length are centimeter, millimitre,, and kilometer.

Units of Length

	Multiples of other units	Other units	Conversion to S.I unit
	_______	1 inch	=   2.54cm   =   0.0254m
	12 inches make	1 foot	=  0.3048m
	3 feet make	1 yard	=  0.9144m
	22 yards make	1 chain	=  20.12m
	10 chains make	1 furlong	=  201.2m
	8 furlongs make	1 mile	=  1.609 km

Class Activity

1. Mention the unit for measuring the following quantitiesby the following person

2. Classify these units under S.I units and other units.

	S/N	Persons	Physical quantity	Unit
	1	Bricklayers	Distance	___________
	2	Tailors	Length	___________
	3	Science teachers	Length	___________
	4	Petroleum engineers	Volume	___________
	5	Butcher	Mass of meat	___________
	6	Electrical engineers	Electrical energy	___________

Example 1

1. Convert 3550km to miles

2. The length of an iron rod is given as 66 inches. What is its length in metres?

Solution

1. 1 mile = 1.609km

Hence, 3550km = (3550 x 1.609) miles = 5,712 miles

2. 1 inch = 2.54cm

Therefore 66 inches = (66 x 2.54) cm = 167.64cm.

But 100cm = 1m,

Thus 167.64cm = =167.64100m = 1.6764m

Therefore the length of the iron rod in metres is 1.676.4m

EVALUATION

1. The height of a girl is 7.5 feet. Estimate her height in metres

2. Convert 30km to miles

Measurement of Volume

Volume is a measure of the space contained in an object. A barrel of oil is equivalent to 158.987 litres.

Example 2

The table below is a statistics of oil exportation to the United States for three years by NNPC

	Year	Price per barrel ( ₦ )	Volume exported (barrels)
	1993	140	1.05 million
	1994	135	1.5 million
	1995	162	0.9 million

(i) What volume of oil in litres was exported in 1994?

(ii) What is the highest amount gotten and in what year was it gotten?

Solution

(i) In 1994, 1.5 million barrels of oil was exported.

Since 1 barrel = 158.987 litres

1.05 million barrels = (1.5million x 158.987) litres = 238.4805million litres

(ii) In 1993, volume of oil exported = 1.05 million barrels.  Price per barrel = N140

Amount realized = 1.05million × 140 = N147,000000

In 1994, volume of oil exported = 1.5million, price per barrel = N135

Amount realized = 1.5million × N135 = N202.5 million

In 1995, volume of oil exported = 0.9 million barrels. Price per barrel = N162

Amount realized = 0.9 million × N162 = N145.8 million

Therefore, the highest amount of money gotten is N202.5 million and it was gotten in 1994

Measurement of Temperature

The S.I unit of temperature is Kelvin. Other units for temperature include degree Celsius and degree Fahrenheit. In the U.S.A, degree Fahrenheit is still in use. On the Celsius scale, the freezing point and the boiling point of water are measured as 0⁰C and 100⁰C respectively. But on the Fahrenhiet scale, the freezing point  and the boiling point of water are measured as 32⁰F and 212⁰F respectively.

The Celsius Scale is related to the Fahrenheit scale by the equation:

F is temperature in Fahrenheit scale, C is temperature in Celsius scale

F–329=C100orC5=F–329

Example: (a) Convert 77 degrees Fahrenheit to Celsius scale (b) Convert 105 degrees Celsius to degrees Fahrenheit

Solution

(a) Considering the equation:

C5=F–329C=5(F–32)9=5(77–32)9=5×459=25

(b) C5=F–329F=9C5+32=9×1055+32=9×21+32=189+32=221oF

EVALUATION

1. Discuss the significance of time to the study of science.

2. Highlight the various instrument for measuring time.

3. State four differences between mass and weight.

4. Draw the following measuring instruments: (i) Beam balance (ii) Spring balance

POSITION, DISTANCE AND DISPLACEMENT

CONTENT

1. The Concept of Position

2. The Concept of Distance and Measurement

3. The Concept of Displacement

4. Distinction between Distance and Displacement

The Concept of Position

The position of an object is its location in space. It is usually expressed in relation to a reference point. To locate an object in space, a co-ordinate system is needed. It is usually a mathematical construct with co-ordinates.

A coordinate system could be two-dimensional as in P(x,y) or three dimensional as in P(x,y,z).

The Concept of Distance and Measurement

Distance can be defined as a physical measurement of length between two points. It does not take into consideration the direction between the two points it measures; hence, it is a scalar quantity. This therefore means that distance has only magnitude but no direction. E.g, 10km.

Distance could be measured using instruments like measuring tape, ruler, venier calliper, micrometer screw gauge, etc.

The Concept of Displacement

Displacement is defined as the distance travelled or moved in a specific direction. It takes into consideration the direction between the different points it seeks to measure; hence, displacement is a vector quantity. Thus, it has both magnitude and direction. E.g, 10km due east. The ‘10km’ is the magnitude (or value), while ‘due east’ is the direction.

Both distance and displacement have the same S.I. unit, metre (m). They could also be expressed in kilometre (km), miles, etc.

Distinction between Distance and Displacement

We need to understand the concepts of distance and displacement.  Distance is the gap between two points with no regard to direction. On the other hand, displacement is distance covered in a particular direction. Therefore distance is a scalar quantity while displacement is a vector quantity. The only similarity between distance and displacement is that they have the same unit.  Let us consider a girl who walked and covered a distance of 20m between two points A and B as shown in fig 1 and fig 2 below

The two activities of the girl are not exactly the same. In both figs. 1 and 2, she covered a distance of 20m. If we are only interested in the distance covered, we can conclude that she did the same thing in fig. 1 and 2 i.e she covered the same distance (20m). If we are interested in both distance and direction, then her displacement in fig. 1 and 2 are not the same. In fig.1 she covered a distance of 20m due east while in fig.2, she covered a distance of 20m due west.   From these, we see that distance is a scalar quantity because it has magnitude only while displacement is a vector quantity because it has both magnitude and direction.

Summarily, the table below shows the difference between distance and displacement

	S/N	Distance	Displacement
	1	It is a scalar quantity	It is a vector quantity
	2	It is the length covered along the path of motion	It is the distance measured along a specified direction of motion.

EVALUATION

1. Define distance.

2. What is displacement?

3. State the SI unit of distance.

4. Differentiate between distance and displacement.

5. Why is 5km due east a displacement?

6. Enumerate the measuring devices for distance.

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

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 Expansivity

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

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 Expansivity

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

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