Set Book Guides and Free Revision Materials

SET BOOKS-2023 to 2026

FORM FOURS 2023

✅”Blossoms of The Savannah”(The Compulsory novel)

✅ “A Doll’s House,” (The Compulsory play)

✅”A Silent Song and other short Stories,” (Anthology of short stories)

✅ “Inheritance.” (The Optional play)

✅”Artist of the Floating World (The Optional novel)

FORM THREES-2023

✅ “The Samaritan” (The Compulsory Play)

✅Fathers of Nations (Compulsory novel)

✅”A Silent song and other short stories” (Anthology of short stories)

✅ “A Parliament of Owls” (The Optional play)

✅”Artist of the Floating World.” (The Optional novel)

FORM TWOS-2023

✅ “The Samaritan” (The Compulsory Play)

✅Fathers of Nations (Compulsory novel)

✅”A Silent song and other short stories” (Anthology of short stories)

✅ “A Parliament of Owls” (The Optional play)

✅”Artist of the Floating World.” (The Optional novel)

LATEST SET BOOKS ANALYSIS, GUIDES AND REVISION MATERIALS

A DOLL’S EXCERPTS S1 Q (3).pdf
A_Dolls_notes[1].docx
BLOSSOMS ESSAYS S1 Q (3).pdf
SILENT SONGS GUIDE SPLE S1-2 (2).pdf
CHOZI LA HERI KCSE QNS (3).pdf
FUNCTIONAL WRITING S1 (2).pdf
KCSE INHERITANCE ESSAYS (3).pdf
THE SAMARITAN GUIDE SP S2 (2).pdf
KCSE CLOZE-TEST REVISION S1 (3).pdf
ISIMU JAMII REVISION S1 (3).pdf
KCSE GRAMMAR REV S1 (3).pdf
THE SAMARITAN KCSE ESSAYS S1 (3).pdf
THE SAMARITAN KCSE ESSAYS S2 (2).pdf
A DOLL’S HOUSE GUIDE SP (3).pdf
A SILENT SONGS KCSE QNS-1 (2).pdf
A SILENT SONGS KCSE S2.pdf
AN ARTIST OF FLOATING WORLD GUIDE SP-1 (3).pdf
ARTIST OF FLOATING WORLD ESSAYS S1.pdf
BEMBEA YA MAISHA REVISION S3 (3).pdf
BEMBEA YA MAISHA S2 Q (3).pdf
CHOZI LA HERI GUIDE SP (3).pdf
FATHERS OF NATIONS ESSAYS S1 (3).pdf
FATHERS OF NATIONS ESSAYS S2 (3).pdf
FATHERS OF NATIONS EXCERPTS S1 (3).pdf
FATHERS OF NATIONS GUIDE SAMPLE-1 (2).pdf
KCSE BEMBEA YA MAISHA QNS-1 (2).pdf
KCSE ENGLISH PASSAGES S1 (3).pdf
KCSE ENGLISH PP1 REVISION S1 (3).pdf
KCSE ENGLISH PP1 REVISION S2 (3).pdf
KCSE ENGLISH PP2 REVISION S1 (3).pdf
KCSE ENGLISH PP2 REVISION S2 (3).pdf
KCSE ENGLISH PP3 REVISION S1 (3).pdf
KCSE ORAL NARRATIVE S1 (2).pdf
KCSE POETRY REVISION S1 (3).pdf
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MAPAMBAZUKO YA MACHWEO QNS-1 (3).pdf
MWONGOZO WA BEMBEA YA MAISHA SAMPLE-1 (3).pdf
MWONGOZO WA MAPAMBAZUKO SAMPLE-1 (3).pdf
NGUU ZA JADI GUIDE SAMPLE-1 (3).pdf
ORAL LITERATURE S1 (3).pdf
PARLIAMENT OF OWLS GUIDE SP-1 (3).pdf

CHAPTER SIX

WAVES II                          

Properties of waves

Waves exhibit various properties which can be conveniently demonstrated using the ripple tank. It consists of a transparent tray filled with water and a white screen as the bottom. On top we have a source of light. A small electric motor (vibrator) is connected to cause the disturbance which produces waves.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The wave fronts represent wave patterns as they move along.

 

Rectilinear propagation

This is the property of the waves travelling in straight lines and perpendicular to the wave front. The following diagrams represent rectilinear propagation of water waves.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Refraction

This is the change of direction of waves at a boundary when they move from one medium to another. This occurs when an obstacle is placed in the path of the waves. The change of direction occurs at the boundary between deep and shallow waters and only when the waves hit the boundary at an angle.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Diffraction of waves

This occurs when waves pass an edge of an obstacle or a narrow gap, they tend to bend around the corner and spread out beyond the obstacle or gap.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Interference of waves

This occurs when two waves merge and the result can be a much larger wave, smaller wave or no wave at all. When the waves are in phase they add up and reinforce each other. This is called a constructive interference and when out of phase they cancel each other out and this is known as destructive interference.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A ripple tank can be used to produce both constructive and destructive waves as shown below in the following diagram.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Interference in sound

Two loud speakers L₁ and L₂ are connected to the same signal generator so that sound waves from each of them are in phase. The two speakers are separated by a distance of the order of wavelengths i.e. 0.5 m apart for sound frequency of 1,000 Hz.

 

 

 

 

 

 

 

 

If you walk along line AB about 2m away from the speakers, the intensity of sound rises and falls alternately hence both destructive and constructive interference will be experienced.

 

Stationary waves

They are also known as standing waves and are formed when two equal progressive waves travelling in opposite direction are superposed on each other. When the two speakers are placed facing each other they produce standing waves. A rope tied at one end will still produce stationary waves.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHAPTER SEVEN

ELECTROSTATICS II

Electric fields

An electric field is the space around a charged body where another charged body would be acted on by a force. These fields are represented by lines of force. This line of force also called an electric flux line points in the direction of the force.

 

Electric field patterns

Just like in magnetic fields, the closeness of the electric field-lines of force is the measure of the field strength. Their direction is always from the north or positive to the south or negative.

 

 

 

 

 

	Electric field pattern for an isolated positive charge
			Electric field pattern for an isolated negative charge

 

 

 

 

 

 

 

 

 

 

	Electric field pattern for a dipole

 

 

 

 

 

Charge distribution on conductors’ surface

A proof plane is used to determine charge distribution on spherical or pear-shaped conductors. For an isolated sphere it is found that the effect is the same for all points on the surface meaning that the charge is evenly distributed on all points on the spherical surface. For appear-shaped conductor the charge is found to be denser in the regions of large curvature (small radius). The density of charge is greatest where curvature is greatest.

 

 

 

 

 

 

 

 

			Charge distribution for an isolated pear-shaped conductor
	Charge distribution for an isolated spherical conductor

 

 

 

 

Charges on or action at sharp points

A moving mass of air forms a body with sharp points. The loss of electrons by molecules (ionization) makes the molecules positively charged ions. These ions tend to move in different directions and collide producing more charged particles and this makes the air highly ionized. When two positively charged bodies are placed close to each other, the air around them may cause a spark discharge which is a rush of electrons across the ionized gap, producing heat, light and sound in the process which lasts for a short time. Ionization at sharp projections of isolated charged bodies may sometimes be sufficient to cause a discharge. This discharge produces a glow called corona discharge observed at night on masts of ships moving on oceans. The same glow is observed on the trailing edges of aircrafts. This glow in aircrafts and ships is called St. Elmo’s fire. Aircrafts are fitted with ‘pig tails’ on the wings to discharge easily.

 

The lightning arrestors

Lightning is a huge discharge where a large amount of charge rushes to meet the opposite charge. It can occur between clouds or the cloud and the earth. Lightning may not be prevented but protection from its destruction may be done through arrestors. An arrestor consists of a thick copper strip fixed to the outside wall of a building with sharp spikes.

 

 

 

 

 

 

 

 

 

 

 

Capacitors and capacitance

A capacitor is a device used for storing charge. It consists of two or more plates separated by either a vacuum or air. The insulating material is called ‘dielectric’. They are symbolized as shown below,

 

 

 

Capacitance C = Q / V where Q- charge and V – voltage.

The units for capacitance are coulombs per volt (Coul /volt) and are called farads.

1 Coul/ volt = 1 farad (F)

1 µF = 10^-6 F and 1pF = 10^-12

Types of capacitors are;

1. Paper capacitors
2. Electrolyte capacitors
3. Variable capacitors
4. Plastic capacitors
5. Ceramic capacitors
6. Mica capacitors

 

Factors affecting the capacitance of a parallel-plate capacitor

1. Distance between the plates: – reducing separation increases capacitance but the plates should not be very close to avoid ionization which may lead to discharge.
2. Area of plate: – reduction of the effective area leads to reduction in capacitance.
3. Dielectric material between plates: – different materials will produce different capacitance effects.

Charging and discharging a capacitor

 

 

 

 

 

 

 

 

 

When the switch S₁ is closed the capacitor charges through resistor R and discharges through the same resistor when switch S₂ is closed.

 

Applications of capacitors

1. Variable capacitor: – used in tuning radios to enable it transmit in different frequencies.
2. Paper capacitors: – used in mains supply and high voltage installations.
3. Electrolytic capacitors: – used in transistor circuits where large capacitance values are required.

 

Other capacitors are used in reducing sparking as a car is ignited, smoothing rectified current and increasing efficiency in a. c. power transmission.

 

Example

A capacitor of two parallel plates separated by air has a capacitance of 15pF. A potential difference of 24 volts is applied across the plates,

1. Determine the charge on the capacitors.
2. When the space is filled with mica, the capacitance increases to 250pF. How much more charge can be put on the capacitor using a 24 V supply?

Solution

1. C= Q / V then Q = VC, hence Q = (1.5 × 10^-12) × 24 = 3.6 × 10^-10
2. Mica C = 250pF, Q = (250 × 10^-12) × 24 = 6 × 10^-9

Additional charge = (6 × 10^-9) – (3.6 × 10^-10) = 5.64 × 10^-9Coul.

 

Capacitor combination

1. Parallel combination – for capacitors in parallel the total capacitance is the sum of all the separate capacitances.

C_T = C₁ + C₂ + C₃ + ………..

 

1. Series combination – for capacitors in series, the reciprocal of the total capacitance is equal to the sum of the reciprocals of all the separate capacitances.

1/ C_T = 1 / C₁ + 1 / C₂ + 1 / C₃

For two capacitors in series then total capacitance becomes,

C_T = (C₁ C₂) / (C₁ + C₂)

 

Examples

1. Three capacitors of capacitance 1.5µF, 2µF and 3µF are connected to a potential difference of 12 V as shown.

 

 

 

 

 

 

 

            Find;

1. The combined capacitance
2. The charge on each capacitor
3. The voltage across the 2 µF capacitor

Solution

1. 1 /C_T = 1/ 1.5 + 1 / 3.0 + 1 /20 = 3/2 hence C_T = 0.67 µF
2. Total charge, Q = V C , (2/3 × 10^-6) × 12.0 V = 8 × 10^-6 = 8 µC.
3. The charge is the same for each capacitor because they’re in series hence = 8 µC.
4. V = Q / C, then V = 8 µC / 2 µF = 4 V.

1. Three capacitors of capacitance 3 µF, 4 µF and 5 µF are arranged as shown. Find the effective capacitance.

 

 

 

 

 

Solution

Since 4 µF and 5 µF are in parallel then, C_T = 9 µF, then the 9 µF is in series with 3 µF,

Hence C_T = 27/ 12 = 2.25 µF

1. Calculate the charges on the capacitors shown below.

 

 

 

 

 

 

 

 

 

Solution

The 2 µF and 4 µF are in parallel then combined capacitance = 6 µF

The 6 µF is in series with the 3 µF capacitor hence combined capacitance = 18 / 9 = 2 µF

Total charge Q = CV then Q = (2.0 × 10^-6) × 100 = 2.0 × 10^-4 C

The charge on the 3 µF capacitor is also equal to 2.0 × 10^-4 C

The p.d across the 3 µF capacitor => V = Q / C => (2.0 × 10^-4)/ 3.0 × 10^_6

= 2/3 × 10² = 66.7 V

The p.d across the 2 µF and 4 µF is equal to 100 V – 66.7 V = 33.3 V,

Hence Q₁ = CV = 2.0 × 10^-6 × 33.3 = 6.66 × 10^-5 C

Q₂ = CV = 4.0 × 10^-6 × 33.3 = 1.332 × 10^-4 C

N.B

Energy stored in a capacitor is calculated as;

Work done (W) = average charge × potential difference

                       W = ½ QV or ½ CV²

Example

A 2 µF capacitor is charged to a potential difference of 120 V. Find the energy stored in it.

Solution

W = ½ CV² = ½ × 2 × 10^-6 × 120² = 1.44 × 10^-2 J

 

 

 

 

 

 

 

CHAPTER EIGHT

HEATING EFFECT OF AN ELECTRIC CURRENT

When current flows, electrical energy is transformed into other forms of energy i.e. light, mechanical and chemical changes.

 

Factors affecting electrical heating

Energy dissipated by current or work done as current flows depends on,

1. Current
2. Resistance
3. Time

 

This formula summarizes these factors as, E = I² R t, E = I V t or E = V² t / R

Examples

1. An iron box has a resistance coil of 30 Ω and takes a current of 10 A. Calculate the heat in kJ developed in 1 minute.

Solution

E = I² R t = 10² × 30 × 60 = 18 × 10⁴ = 180 kJ

 

1. A heating coil providing 3,600 J/min is required when the p.d across it is 24 V. Calculate the length of the wire making the coil given that its cross-sectional area is 1 × 10^-7 m² and resistivity 1 × 10^-6 Ω m.

Solution

E = P t hence P = E / t = 3,600 / 60 = 60 W

P = V² / R therefore R = (24 × 24)/ 60 = 9.6 Ω

R = ρ l/ A, l = (RA) / ρ = (9.6 × 1 × 10^-7) / 1 × 10^-6 = 0.96 m

 

Electrical energy and power

In summary, electrical power consumed by an electrical appliance is given by;

P = V I

            P = I² R

            P = V² / R

The SI unit for power is the watt (W)

1 W = 1 J/s and 1kW = 1,000 W.

Examples

1. What is the maximum number of 100 W bulbs which can be safely run from a 240 V source supplying a current of 5 A?

Solution

Let the maximum number of bulbs be ‘n’. Then 240 × 5 = 100 n

So ‘n’ = (240 × 5)/ 100 = 12 bulbs.

1. An electric light bulb has a filament of resistance 470 Ω. The leads connecting the bulb to the 240 V mains have a total resistance of 10 Ω. Find the power dissipated in the bulb and in the leads.

Solution

R_eq = 470 + 10 = 480 Ω, therefore I = 240 / 480 = 0.5 A.

Hence power dissipated = I² R = (0.5)² × 470 = 117.5 W (bulb alone)

For the leads alone, R = 10 Ω and I = 0.5 A

Therefore power dissipated = (0.5)² × 10 = 2.5 W.

 

Applications of heating of electrical current

1. Filament lamp – the filament is made up of tungsten, a metal with high melting point (3.400 ⁰C). It is enclosed in aglass bulb with air removed and argon or nitrogen injected to avoid oxidation. This extends the life of the filament.
2. Fluorescent lamps – when the lamp is switched on, the mercury vapour emits ultra violet radiation making the powder in the tube fluoresce i.e. emit light. Different powders emit different colours.

 

 

 

 

 

 

 

 

1. Electrical heating – electrical fires, cookers e.tc. their elements are made up nichrome ( alloy of nickel and chromium) which is not oxidized easily when it turns red hot.

 

 

 

 

 

 

 

1. Fuse – this is a short length of wire of a material with low melting point (often thinned copper) which melts when current through it exceeds a certain value. They are used to avoid overloading.

 

 

 

 

CHAPTER NINE

QUANTITY OF HEAT

 

Heat is a form of energy that flows from one body to another due to temperature differences between them.

Heat capacity

Heat capacity is defined as the quantity of heat required to raise the temperature of a given mass of a substance by one degree Celsius or one Kelvin. It is denoted by ‘C’.

Heat capacity, C = heat absorbed, Q / temperature change θ.

The units of heat capacity are J / ⁰C or J / K.

Specific heat capacity.

S.H.C of a substance is the quantity of heat required to raise the temperature of 1 kg of a substance by 1 ⁰C or 1 K. It is denoted by ‘c’, hence,

c = Q / m θ where Q – quantity of heat, m – mass andθ – change in temperature.

The units for ‘c’ are J kg^-1 K^-1. Also Q = m c θ.

Examples

1. A block of metal of mass 1.5 kg which is suitably insulated is heated from 30 ⁰C to 50 ⁰C in 8 minutes and 20 seconds by an electric heater coil rated54 watts. Find;

1. The quantity of heat supplied by the heater
2. The heat capacity of the block
3. Its specific heat capacity

Solution

1. Quantity of heat = power × time = P t

= 54 × 500 = 27,000 J

1. Heat capacity, C = Q / θ = 27,000 / (50 – 30) = 1,350 J Kg^-1 K^-1
2. Specific heat capacity, c = C / m = 1,350 / 1.5 = 900 J Kg^-1 K^-1

1. If 300 g of paraffin is heated with an immersion heater rated 40 W, what is the temperature after 3 minutes if the initial temperature was 20 ⁰C? (S.H.C for paraffin = 2,200 J Kg^-1 K^-1).

Solution

Energy = P t = m c θ = Q = quantity of heat.

P t = 40 × 180 = 7,200 J

m = 0.30 kg c = 2,200, θ = ..?

Q = m c θ, θ = Q / m c = 7,200 / (0.3 × 2,200) = 10.9 ⁰C

1. A piece of copper of mass 60 g and specific heat capacity 390 J Kg^-1 K^-1 cools from 90 ⁰C to 40 ⁰C. Find the quantity of heat given out.

Solution

Q = m c θ, = 60 × 10^-3 × 390 × 50 = 1,170 J.

 

Determination of specific heat capacity

A calorimeter is used to determine the specific heat capacity of a substance. This uses the principle of heat gained by a substance is equal to the heat lost by another substance in contact with each other until equilibrium is achieved. Heat losses in calorimeter are controlled such that no losses occur or they are very minimal.

 

 

 

 

 

 

 

 

 

 

 

 

 

Examples

1. A 50 W heating coil is immersed in a liquid contained in an insulated flask of negligible heat capacity. If the mass of the liquid is 10 g and its temperature increases by 10 ⁰C in 2 minutes, find the specific heat capacity of the liquid.

Solution

Heat delivered (P t) = 50 × 2 × 60 = 2,400 J

Heat gained              = 0.1 × c × 10 J

Therefore ‘c’              = 2,400 / 0.1 × 10 = 2,400 J Kg^-1 K^-1

1. A metal cylindermass 0.5 kg is heated electrically. If the voltmeter reads 15V, the ammeter 0.3A and the temperatures of the block rises from 20 ⁰C to 85 ⁰C in ten minutes. Calculate the specific heat capacity of the metal cylinder.

Solution

Heat gained = heat lost, V I t = m c θ

15 × 3 × 10 × 60 = 0.5 × c × 65

c = (15 × 3 × 600)/ 0.5 × 65 = 831 J Kg^-1 K^-1

 

Fusion and latent heat of fusion

Fusion is the change of state from solid to liquid. Change of state from liquid to solid is called solidification. Latent heat of fusion is the heat energy absorbed or given out during fusion. Specific latent heat of fusion of a substance is the quantity of heat energy required to change completely 1 kg of a substance at its melting point into liquid without change in temperature. It is represented by the symbol (L), we use the following formula,

Q = m L_f

Different substances have different latent heat of fusion.

Factors affecting the melting point

1. Pressure
2. Dissolved substances

Specific latent heat of vaporization is the quantity of heat required to change completely 1 kg of a liquid at its normal boiling point to vapour without changing its temperature. Hence

Q = m L _v

The SI unit for specific latent heat of vaporization is J / Kg.

Example

An immersion heater rated 600 W is placed in water. After the water starts to boil, the heater is left on for 6 minutes. It is found that the mass of the water had reduced by 0.10 kg in that time. Estimate the specific heat of vaporization of steam.

Solution

Heat given out by the heater = P t = 600 × 6 × 60

Heat absorbed by steam         = 0.10 × L _v

Heat gained = heat lost, therefore, 600 × 6 × 60 = 0.10 × L _v = 2.16 × 10⁶ J / Kg

Evaporation

Factors affecting the rate of evaporation

1. Temperature
2. Surface area
3. Draught (hot and dry surrounding)
4. Humidity

Comparison between boiling and evaporation

Evaporation                                                                            Boiling

1. Takes place at all temperature – takes place at a specific temperature
2. Takes place on the surface (no bubbles formed)- takes place throughout the liquid ( bubbles formed)
3. Decrease in atmospheric pressure increases the rate –decreases as atmospheric pressure lowers

Applications of cooling by evaporation

1. Sweating
2. Cooling of water in a porous pot
3. The refrigerator

 

 

CHAPTER TEN

THE GAS LAWS

Pressure law

This 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”. The comparison between Kelvin scale and degrees Celsius is given by; θ⁰ = (273 + θ) K, and T (K) = (T – 273) ⁰C.

Examples

1. A gas in a fixed volume container has a pressure of 1.6 × 10⁵ Pa at a temperature of 27 ⁰ What will be the pressure of the gas if the container is heated to a temperature of 277⁰C?

Solution

Since law applies for Kelvin scale, convert the temperature to kelvin

T₁ = 27⁰C = (273 + 27) K = 300 K

T₂ = 227⁰C = (273 + 277) = 550 K

P₁ / T₁ = P₂ / T₂, therefore P₂ = (1.6 × 10⁵) × 550 / 300 = 2.93 × 10⁵ Pa.

2. At 20⁰C, the pressure of a gas is 50 cm of mercury. At what temperature would the pressure of the gas fall to 10 cm of mercury?

Solution

P / T = constant, P₁ / T₁ = P₂ / T₂, therefore T₂ = (293 × 10) / 50 = 58.6 K or (– 214.4 ⁰C)

 

 

 

 

Charles law

Charles law states that “the volume of a fixed mass of a gas is directly proportional to its absolute temperature (Kelvin) provided the pressure is kept constant”. Mathematically expressed as follows,

V₁ / T₁ = V₂ / T₂

Examples

1. A gas has a volume of 20 cm³ at 27⁰C and normal atmospheric pressure. Calculate the new volume of the gas if it is heated to 54⁰C at the same pressure.

Solution

Using, V₁ / T₁ = V₂ / T₂, then V₂ = (20 × 327) / 300 = 21.8 cm³.

1. 0.02m³ of a gas is at 27 ⁰C is heated at a constant pressure until the volume is 0.03 m³. Calculate the final temperature of the gas in ⁰C.

Solution

Since V₁ / T₁ = V₂ / T₂, T₂ = (300 × 0.03) / 0.02 = 450 K 0r 177⁰C

 

Boyle’s law

Boyle’s law states that “the pressure of a fixed mass of a gas is inversely proportional to its volume provided the temperature of the gas is kept constant”. Mathematically expressed as,

P₁ V₁ = P₂ V₂

Examples

1. A gas in a cylinder occupies a volume of 465 ml when at a pressure equivalent to 725 mm of mercury. If the temperature is held constant, what will be the volume of the gas when the pressure on it is raised to 825 mm of mercury?

Solution

Using, P₁ V₁ = P₂ V₂, then V₂ = (725 × 465) / 825 = 409 ml.

 

 

 

1. The volume of air 26 cm long is trapped by a mercury thread 5 cm long as shown below. When the tube is inverted, the air column becomes 30 cm long. What is the value of atmospheric pressure?

 

 

 

 

 

 

 

 

 

 

Solution

Before inversion, gas pressure = atm. Pressure + h p g

After inversion, gas pressure = atm. Pressure – h p g

From Boyle’s law, P₁ V₁ = P₂ V_2, then let the atm. Pressure be ‘x’,

So (x + 5) 0.26 = (x – 5) 0.30

0.26x + 1.30 = 0.3x – 1.5, x = 2.8/ 0.04 = 70 cm.

 

A general gas law

Any two of the three gas laws can be used derive a general gas law as follows,

P₁ V₁ / T₁ = P₂ V₂ / T₂or

P V / T = constant – equation of state for an ideal gas.

Examples

1. A fixed mass of gas occupies 1.0 × 10^-3 m³ at a pressure of 75 cmHg. What volume does the gas occupy at 17.0 ⁰C if its pressure is 72 cm of mercury?

Solution

P V / T = constant so V₁ = (76 × 1.0 × 10^-3 × 290) / 273 ×72 = 1.12 × 10^-3 m³.

1. A mass of 1,200 cm³ of oxygen at 27⁰C and a pressure 1.2 atmosphere is compressed until its volume is 600 cm³ and its pressure is 3.0 atmosphere. What is the Celsius temperature of the gas after compression?

Solution

Since P₁ V₁ / T₁ = P₂ V₂ / T₂, then T₂ = (3 × 600 × 300) / 1.2 × 1,200 = 375 K or 102 ⁰C.

 

 

 

 

 

 

 

 

 

===== THE END =====

 

CBC Grade 7 CRE Schemes of Work Free Editable Word, PDF Downloads

SCHOOL	GRADE	LEARNING AREA	TERM	YEAR
	7	CRE	3

 

WEEK	LESSON	STRAND	SUB-STRAND	SPECIFIC LEARNING OUTCOME	LEARNING EXPERIENCES	KIQ	LEARNING RESOURCES	ASSESSMENT METHOD	REFLECTION
1	1	Christian Living.	Human Sexuality.	By the end of the lesson, the learner should be able to: (a).Define the term human sexuality. (b).Outline and discuss the physical, mental, emotional, social and spiritual changes that boys and girls experience as adolescents. (c). Prepare a PowerPoint presentation on the changes boys and girls experience as adolescents. (d). Acknowledge the different changes boys and girls experience as adolescents.	In groups,learners are guided to: mention some of the bodily changes boys and girls undergoes during adolescent. discuss the meaning of human sexuality. conduct an internet search on the physical, mental, social, emotional and spiritual changes that boys and girls experience as adolescents. Prepare a PowerPoint presentation on the changes boys and girls experience as adolescents.	What are the bodily changes that adolescents experience during puberty? What is human sexuality?	Digital devices. Top Scholar CRE pg 116-117.	Oral questions. Assessment rubric. Written tests.
	2	Christian Living.	Human Sexuality -Healthy and Unhealthy Relationships.	By the end of the lesson, the learner should be able to: (a). State the meaning of healthy and unhealthy relationship. (b). Outline and discuss the indicators of healthy and unhealthy relationship among young people. (c). Prepare flashcards showing the life skills needed to maintain healthy relationship. (d).Desire to have and maintain a healthy relationship among the peers.	In groups,pairs,learners are guided to: explain the meaning of healthy and unhealthy relationship. discuss the examples or indicators of healthy and unhealthy relationship among young people. search and discuss the life skills needed to maintain healthy relationships. Prepare flashcards showing the life skills needed to maintain healthy relationship. Prepare a one week journal on how you can promote healthy relationship and avoid unhealthy relationship.	How can you overcome unhealthy relationship? What are some of the examples of healthy and unhealthy relationship among young people?	Top Scholar CRE pg 118-119. Flashcards. Digital devices.	Assessment rubric. Journal. Oral questions. Written tests.
2	1	Christian Living.	Human Sexuality.	By the end of the lesson, the learner should be able to; (a). Identify the circumstances that lead to an unhealthy relationship among peers. (b). Discuss the circumstances that lead to unhealthy relationship. (c). Summarize the points on circumstances that lead to unhealthy relationship in their exercise books. (d). Recognize circumstances that may lead to unhealthy relationship among his/her peers.	In groups,pairs,learners are guided to: read the story in learner’s book and identify the circumstances that lead to unhealthy relationship among peers. discuss the circumstances that lead to unhealthy relationships among peers/young people. summarize the points in their exercise books.	What leads to an unhealthy relationship among peers?	Top Scholar CRE pg 120.	Observation. Assessment rubric. oral questions. Checklists.
	2	Christian Living.	Human Sexuality.	By the end of the lesson, the learner should be able to: (a).Define the term Sexual temptation. (b). Discuss the circumstances that can lead to sexual temptation among young people. (c). Sort out circumstances that can lead to sexual temptation. (d). Summarize the points on circumstances that lead to sexual temptation on charts. (e). Acknowledge the circumstances that can lead to sexual temptations.	In groups,pairs,learners are guided to; brainstorm the meaning of sexual temptation. identify and discuss the circumstances that lead to sexual temptation among the young people. Prepare charts showing circumstances that lead to sexual temptation and display in class.	What is sexual temptation? What circumstances can lead to sexual temptation?	Top Scholar CRE pg 121. Charts. Digital devices.	Assessment rubric. Checklists. Written tests. Oral questions.
3	1	Christian Living.	Human Sexuality.	By the end of the lesson, the learner should be able to; (a).State ways to avoid temptations and tempting places. (b). Discuss the different ways or activities that helps in avoiding temptations and tempting areas in the community. (c).Role play how to overcome tempting situations. (d). Appreciate the different ways/activities that helps in avoiding temptations and tempting areas.	In groups,pairs,learners are guided to; brainstorm the ways or activities that may help a person to avoid temptations and tempting areas. discuss the ways of avoiding temptations and tempting areas. summarize the points in exercise books. role play how to overcome tempting situations in life and record themselves.	How do one avoid temptations and tempting places?	Top Scholar CRE pg 122. Digital devices.	Observation. Written texts. Role plays. Checklists. Anecdotal.
	2	Christian Living.	Human Sexuality.	By the end of the lesson, the learner should be able to: (a).Read the different biblical texts. (b). Discuss the biblical teachings on Sexual temptations. (c). Summarize the biblical teachings on charts and present in class. (d). Apply the biblical teachings in their lifes.	In groups,pairs,learners are guided to: Take turns in reading the Bible texts;1st Corinthians 6:9,18,Phillipians 4:8-9, Galatians 5:23,1st Thessalonians 4:3. identify and discuss the biblical teachings from the texts on sexual temptations. summarize their points on charts and share with other groups for assessment.	What are the biblical teachings on sexual temptations?	Good News Bible. Flashcards. Charts. Top Scholar CRE pg 122-123.	Oral questions. Checklists. Written texts. Assessment rubric.
4	1	Christian Living.	Human Sexuality.	By the end of the lesson, the learner should be able to: (a).State reasons why young people should engage in sex before marriage (b,). Conduct an internet search on the consequences of engaging in sex before marriage. (c). Develop PowerPoint slides for presentations on the consequences of sex before marriage. (d). Acknowledge the consequences of engaging in sex before marriage.	In groups, learners are guided to: state reasons why young people should not engage in sex before marriage. use digital devices to search the internet on the consequences of sex before marriage to an individual. discuss the consequences of engaging in sex before marriage. develop PowerPoint slides for presentation on the consequences of engaging in sex before marriage.	What are the consequences of engaging in sex before marriage?	Top Scholar CRE pg 123-124. Digital devices.	Assessment rubric. Checklists. Written test. oral questions.
	2	Christian Living.	Human Sexuality.	By the end of the lesson, the learner should be able to: (a). Interview a resource person and identify the values that guide good morals (b). Discuss the values needed by boys and girls to lead a chaste life. (c). Prepare flashcards showing the values needed by boys and girls to lead a chaste life. (d).Desire to develop the values needed by boys and girls to lead chaste lives.	In groups,learners are guided to; interview a resource person, identify and discuss the values that guide good morals. discuss values needed by boys and girls to lead a chaste life. make flashcards showing the values needed to lead a chaste life. compose a song on “Lord help me overcome temptations”	Which values are needed by boys and girls to lead chaste lives?	Top Scholar CRE pg 124-126. Flashcards. Digital devices. Songs.	Assessment rubric. Observation. Checklists. Oral questions. Written test. Interviewing.
5	1	Christian Living.	Christian Marriage and Family.	By the end of the lesson, the learner should be able to: (a).Define the terms marriage and family. (b). Mention and discuss the types of families in the community. (c).Make charts with information on the types of families in the community. (d). Appreciate the different types of families in the community.	In groups, learners are guide to; brainstorm the meaning of marriage and family. mention and discuss the types of families in the community. Prepare charts with information on the types of families in the community.	What is the difference between marriage and family? What are the different types of families in Kenya?	Top Scholar CRE pg 127-128. Charts. Digital devices. Dictionaries.	Assessment rubric. oral questions. Checklists. Written tests.
	2	Christian Living.	Christian Marriage and Family.	By the end of the lesson, the learner should be able to: (a).Read biblical texts: Genesis 2:23-24 and Ephesians 5:25-33. (b). Discuss the biblical teachings on marriage and family to develop positive attitudes. (c). Summarize the biblical teachings on marriag and family on charts. (d). Appreciate the biblical teachings on marriage and family.	In groups,learners are guided to; take turns in reading the Bible texts: Genesis 2:23-24, Ephesians 5:25-33, Exodus 20:12, Psalms 127:3-5 & Ephesians 6:4. identify and discuss the biblical teachings on marriage from Genesis 2:23-24 & Ephesians 5:25-33. identify and discuss the biblical teachings on family from Exodus 20:12, Psalms 127:3-5 & Ephesians 6:4.	What are the requirements of a Christian marriage? Why should children respect their parents?	Good News Bible. Top Scholar CRE pg 129-130.	Reading and explaining biblical teachings. Assessment rubric. oral questions. Written tests.
6	1	Christian Living.	Christian Marriage and Family.	By the end of the lesson, the learner should be able to: (a). Explain ways through which christians promote values among young people before marriage. (b). Discuss reasons why it is important for marriages and families to have harmonious relationships. (c). Prepare PowerPoint presentation on the importance of families and marriages having harmonious relationship. (d). Appreciate the importance of marriages and families in a community.	In groups,learners are guided to; interact with a religious leader or resource person to find out ways through which christians promote values among young people before marriage. search the internet on the importance of families and marriages to have harmonious relationship. discuss their findings and prepare PowerPoint presentation.	Why is it important for families and marriages to have harmonious relationship?	Digital devices. Resource Person. Top Scholar CRE pg 131-132.	Oral questions. Written tests Assessment rubrics. Questionnaires.
	2	Christian Living.	Christian Marriage and Family.	By the end of the lesson, the learner should be able to: (a). Identify the skills required to sustain and support stable families in the society. (b). Discuss how the skills can contribute towards stable families. (c).Role play a stable common family and record it using digital devices. (d). Appreciate the skills that contribute towards stable families in the society.	In groups,learners are guided to; conduct an internet inquiry on skills young people need to contribute to stable families. discuss how each of the identified skill contribute towards stable families. role play a stable common family. compose poems on ‘God is the center for stable families.	Which skills do young people need to contribute towards stable families?	Top Scholar CRE pg 133-134. Digital devices.	Anecdotal. Assessment rubric. Written test. oral questions.
7	1	Christian Living.	Alcohol,Drugs and Substance Use.	By the end of the lesson, the learner should be able to: (a).List the commonly abused drugs in Kenya today. (b). Discuss reasons why people abuse drugs today. (c). Search the internet on the effects of abusing drugs and alcohol on an individual and families. (d). Prepare PowerPoint presentation on the effects of abusing alcohol,drugs and substance on individuals and families.	In groups,learners are guided to: mention the types of drugs commonly abused in Kenya today. explain reasons why people abuse drugs today. use digital devices to search the internet on the effects of abusing drugs, alcohol on individuals and families. prepare PowerPoint presentation on the effects of abusing drugs and alcohol on individuals and families in the Kenya.	Which are the commonly abused drugs in Kenya today? Why do people abuse drugs today? What are the effects of abusing drugs on individuals and families?	Digital devices. Top Scholar CRE pg 136-140. Flashcards.	Assessment rubric. Written tests. Oral questions. Checklists.
	2	Christian Living.	Alcohol,Drugs and Substance Use.	By the end of the lesson, the learner should be able to: (a).Read biblical texts: Ephesians 5:18, Proverbs 20:1,1st Corinthians 3:17,6:9-10. (b). Identify and discuss the biblical teachings on alcohol, drug and substance use. (c). Identify skills and values that would help avoid alcohol,drugs and substance use. (d). Prepare flashcards with details on skills and values that would help avoid drug, alcohol and substance use. (e). Apply the values and skills to avoid drug, substance and alcohol use in life.	In groups,learners are guided to: read the bible and identify the biblical teachings on drug, alcohol and substance use. explain the biblical teachings on drug, alcohol and substance use from the Bible verses. identify and discuss the values and skills that would help an individual to avoid drug, substance and alcohol use.	Which values and skills can help a person avoid drug, alcohol and substance use?	Top Scholar CRE pg 140-143. Flashcards. Good News Bible.	Assessment rubric. Checklists. Written tests. Oral questions. Reading and explaining biblical teachings.
8	1	Christian Living.	Gambling as a form of addiction.	By the end of the lesson, the learner should be able to: (a).Define the term gambling and identify the types of gambling in society. (b). Explain the biblical teachings on addictions. (c). Search the internet and discuss the causes of gambling in the society. (d).Make charts with information on causes of gambling in the society.	In groups,pairs,learners are guided to: brainstorm the meaning of term gambling and identify the types of gambling in the society. read bible verses: Proverbs 13:11;28:20-22;1st Timothy 6:9. explain the biblical teachings on addictions. search the internet for the causes of gambling in the society. summarize the findings on charts and display them in class.	What is gambling? Why do people engage in gambling?	Top Scholar CRE pg 144-147. Digital devices. Charts. Good News Bible.	Assessment rubric. Oral questions. Written tests. Reading and explaining biblical teachings.
	2	Christian Living.	Gambling as a form of addiction.	By the end of the lesson, the learner should be able to: (a). Outline the effects of gambling on individuals and families. (b). Discuss the measures taken by christians and government to help young people overcome gambling. (c). Identify and prepare flashcards on the skills and values that help a person avoid gambling. (d).Desire to live an addiction free life.	In groups,pairs,learners are guided to; outline the effects of gambling on an individual and families. identify and discuss the measures taken by Christians and government to help young people overcome gambling. identify and prepare flashcards showing the values and skills that would help one to avoid gambling. draw a value tree and place the values on different parts of the tree.	What are the effects of gambling to an individual and families? Which measures can be taken to help young people overcome gambling in the society?	Top Scholar CRE pg 148-152. Flashcards. Digital devices. Good News Bible.	Assessment rubric. Oral questions. Written tests. Checklists.
9	1	Christian Living.	Social Media.	By the end of the lesson, the learner should be able to: (a).Define the term Social media platforms. (b).List the social media platforms used by young people today. (b). Outline and discuss ways of using the social media responsibly. (c). Prepare PowerPoint slides on the precautions that one need to exercise as he/she engages on social media platforms. (d). Acknowledge the dangers of chatting or meeting with online strangers.	In groups, pairs,learners are guided to: define the term social media platform. list the commonly used social media platforms by young people. discuss the ways of using social media responsibly. sort and write safety precautions to exercise as one engage on social media platforms. prepare PowerPoint presentation on the precautions to exercise when engaging in social media platforms.	Which are the commonly used social media platforms by young people in Kenya? Which dangers can one get involved in when chatting with online strangers?	Top Scholar CRE pg 154-157. Pictures. Digital devices.	Assessment rubric. Written tests. Oral questions. Checklists.
	2	Christian Living.	Social Media.	By the end of the lesson, the learner should be able to; (a). Outline ways in which social media is misused today. (b). Define cyber bullying and give examples. (c). Discuss ways of responding of responding to cyber bullying. (d). Design posters and write skills one should use when using social media platforms. (e). Apply Christian values while using different social media platforms.	In groups,pairs,learners are guided to: explain the ways in which social media is misused today. search the meaning of cyber bullying and cite examples. identify and discuss ways of responding to cyber bullying. identify the christian values and skills to apply while using different social media platforms. design posters and write skills to apply while using social media platforms.	How is social media misused today? What is cyber bullying? How should one respond to cyber bullying? Which skills and values can one apply when using social media platforms?	Top Scholar CRE pg 159-161. Posters. Digital devices.	Assessment rubric. Oral questions. Written tests. Checklists.
10	ASSESSMENT AND CLOSURE OF SCHOOL