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KS3 Science · Year 9Chapter 9 · Energy, power and efficiency
Year 9 · Chapter 9

Energy, power and efficiency

By the end of this chapter you will be able to

  • Name the energy stores and the transfers in a simple system
  • Calculate power from energy and time, and convert between W and kW
  • Calculate efficiency as a percentage of useful output over total input
  • Use the kinetic and gravitational potential energy formulae in simple cases (extension)
  • Use conservation of energy to find a missing energy value

You should already know

  • Energy stores and transfers, Sankey diagrams (Year 8 Science, Chapter 11)
  • Units of energy in the domestic context (Year 7 and Year 8 Science)

Where this leads

  • Electrical circuits in Chapter 10, where power and energy are used for lamps and resistors

National Curriculum for England, Key Stage 3 science, Year 9. Content: 9P1 energy stores and transfers revisited (deepens Year 8, Chapter 11), 9P1 power as the rate of energy transfer, in watts (W) and kilowatts (kW), 9P1 efficiency = useful energy output / total energy input, as a percentage, 9P1 energy calculations in simple cases; kinetic and gravitational potential energy in simple cases (EXTENSION: formulae flagged), 9P1 conservation of energy in all transfers.

Exercise P  Do you remember?

1
FWhat is 2 x 300? Write the number.
2
FHow many seconds are there in 5 minutes? Write the number.
3
FWhich energy store does a moving object have? Write the words.
4
FWhat is the unit of energy? Write the word.
5
FWhat is 100 - 35? Write the number.
9.1

Energy stores and transfers, revisited

Year 9
9P1: energy stores and transfers revisited (deepens Year 8, Chapter 11)
Video lesson: Energy stores and transfers, revisitedComing soon
Story. A pupil lifts a book, then lets it fall. “Where is the energy when the book is high up?” she asks. Her teacher explains that the energy moves between stores: from the store of the lifted book, to the kinetic store as it falls, and to the thermal store of the floor when it lands.

Energy is stored in stores, and moves between them by transfers. Common stores are the kinetic store (movement), the gravitational potential store (height), the thermal store (temperature), the chemical store (fuels and food) and the elastic store (stretched or squashed objects).

A transfer can happen by heating, by a force moving an object, by an electrical current, or by radiation such as light. Energy is not used up in a transfer; it is spread out.

Key ideas

  • Stores: kinetic, gravitational potential, thermal, chemical, elastic.
  • A transfer moves energy from one store to another.
  • Energy is conserved in every transfer.
  • Energy spreads out to the surroundings as it is transferred.
Worked example 9.1.1
A lifted book is high up. Which energy store does it have? Write the words.

Method. Think about the height.

  1. Think. An object high above the ground has energy because of its height.
    because of its height
  2. Name it. This is the gravitational potential store.
    gravitational potential store
  3. Write the answer.
    gravitational potential store

Check. Height gives gravitational potential energy. ✓

Worked example 9.1.2
As the book falls, which store gains energy? Write the words.

Method. Think about the movement.

  1. Think. The falling book is moving faster as it falls.
    moving faster
  2. Name it. Its kinetic store gains energy.
    kinetic store
  3. Write the answer.
    kinetic store

Check. The gravitational store falls as the kinetic store rises. ✓

Worked example 9.1.3
When the book hits the floor, which store gains energy? Write the words.

Method. Think about what the impact does.

  1. Think. The impact warms the book and the floor a little.
    warms
  2. Name it. The thermal store of the surroundings gains energy.
    thermal store
  3. Write the answer.
    thermal store

Check. Some energy is spread out as sound too. ✓

Watch out

Watch out: energy is never used up. Say that energy is transferred between stores, not that it is “used”.

Exam tip

Exam tip. In a transfer, name the store that falls and the store that rises.

Try it (with your teacher, or a grown-up at home). With your teacher, hold a rubber ball and drop it onto the bench from a low height. Describe the stores and transfers from the moment you let go to the moment it bounces back. Use a small, safe height only.

Exercise 9A  Energy stores and transfers, revisited

1
FWhat is the name of the energy store of a stretched elastic band? Write the word.
2
FWhich energy store holds energy in a battery? Write the word.
3
FWhat is the name of the store that depends on temperature? Write the word.
4
FName a way in which energy can be transferred by electricity. Write the word.
5
FWhat is the name of the transfer by light or heat without touching? Write the word.
6
FDoes energy get used up in a transfer? Write yes or no.
7
FA toy car rolls down a slope. Which store does it gain energy in as it moves faster? Write the words.
8
PSA kettle transfers electrical energy to the water. Which store gains energy? Write the word.
9
PSA ball is thrown up and rises. As it rises, which store gains energy? Write the words.
10
RExplain why a moving object slows down, using stores. Write one sentence. Accept any sentence saying kinetic energy is transferred to the thermal store of the surroundings by friction.
11
RChallenge: explain why a dropped ball bounces less high each time. Accept any sentence saying some energy is transferred to the thermal store and sound each bounce, so less kinetic energy is left.
9.2

Power: the rate of energy transfer

Year 9
9P1: power as the rate of energy transfer, in watts (W) and kilowatts (kW)
Video lesson: Power: the rate of energy transferComing soon
Story. A kettle is rated at 2000 W, and a lamp at 60 W. A pupil asks: “Which one uses more energy?” Her teacher says that power tells us how fast energy is transferred, and that the time must also be known before the total energy can be found.

Power is the rate at which energy is transferred. It is measured in watts, W. One watt is one joule of energy transferred each second. The equation is power = energy transferred / time, or P = E / t. One kilowatt (kW) is 1000 W.

Energy transferred is found by multiplying power by time: E = P x t. Time must be in seconds to give energy in joules.

AppliancePower (W)Time used (s)Energy transferred (J)
kettle2000300600000
lamp6060036000
fan501206000
Power, time and energy transferred for three appliances

Key ideas

  • Power = energy transferred / time (W = J per second).
  • Energy transferred = power x time, with time in seconds.
  • 1 kW = 1000 W.
  • Convert minutes to seconds before using the equation.
Worked example 9.2.1
A device transfers 60 J of energy in 2 s. What is its power, in watts? Write the number.

Method. Use P = E / t.

  1. Write. P = 60 / 2.
    60 / 2
  2. Calculate. So the power is 30 W.
    60 / 2 = 30
  3. Write the answer.
    30

Check. 30 W x 2 s = 60 J. ✓

Worked example 9.2.2
A kettle has a power of 2 kW. What is its power in watts? Write the number.

Method. Multiply the kilowatts by 1000.

  1. Write. 1 kW = 1000 W, so 2 kW = 2 x 1000.
    2 x 1000
  2. Calculate. So the power is 2000 W.
    2 x 1000 = 2000
  3. Write the answer.
    2000

Check. 2000 / 1000 = 2 kW. ✓

Worked example 9.2.3
A 2000 W kettle runs for 300 s. How much energy does it transfer, in joules? Write the number.

Method. Use E = P x t.

  1. Write. E = 2000 x 300.
    2000 x 300
  2. Calculate. So the energy is 600 000 J.
    2000 x 300 = 600000
  3. Write the answer.
    600000

Check. 600000 / 300 = 2000 W. ✓

Watch out

Watch out: convert minutes to seconds first. 5 minutes is 300 seconds, not 5 seconds.

Exam tip

Exam tip. Write the equation, then the numbers with units, then the answer with its unit.

Try it (with your teacher, or a grown-up at home). With your teacher, use a 60 W lamp and a stopwatch to see how long a fully charged battery or a timer takes to run. Discuss which of these two numbers is power and which is energy.

Exercise 9B  Power: the rate of energy transfer

1
FWhat is the unit of power? Write the symbol.
2
FWhat is power the rate of? Write the words.
3
FHow many watts are in 1 kilowatt? Write the number.
4
FWrite the equation for power. Write the words.
5
PSA device transfers 100 J in 4 s. What is its power, in watts? Write the number.
6
PSA lamp has a power of 60 W. How much energy does it transfer in 10 s, in joules? Write the number.
7
PSA fan has a power of 50 W and runs for 120 s. How much energy does it transfer, in joules? Write the number.
8
PSA heater has a power of 2.5 kW. What is its power in watts? Write the number.
9
PSA motor transfers 3000 J in 60 s. What is its power? Write the number, in watts.
10
PSA kettle is rated 2 kW and is used for 5 minutes. How much energy does it transfer, in joules? Write the number. (Use 1 kW = 1000 W and 1 minute = 60 s.)
11
RTwo appliances are used for the same time. The kettle is 2000 W and the lamp is 60 W. Which transfers more energy? Write the word.
12
RChallenge: a pupil says a 60 W lamp uses more energy than a 2000 W kettle if it is left on for longer. Is this possible? Write yes or no, and explain why in one sentence. Accept yes, with a reason that energy is power multiplied by time.
9.3

Efficiency

Year 9
9P1: efficiency = useful energy output / total energy input, as a percentage
Video lesson: EfficiencyComing soon
Story. A motor uses 200 J of electrical energy. It lifts a box, and produces 150 J of useful energy. The rest is spread out as thermal energy. The class asks: “How good is the motor?” The answer is found by its efficiency.

Efficiency is the fraction of the energy input that becomes useful energy output. It is found by:

efficiency = useful energy output / total energy input x 100%

An efficiency of 100% would mean all of the energy is useful. In practice, some energy is always wasted, usually as thermal energy in the surroundings. A good device has a high efficiency, so less energy is wasted.

Energy input and output (electric motor, 200 J in)useful 150 Jwasted 50 Jinput: 200 J; the bar shows how the energy is sharedefficiency = 150 / 200 x 100% = 75%
A bar showing 200 J input, split into useful and wasted energy
DeviceEnergy in (J)Useful energy out (J)Efficiency (%)
electric motor20015075
light bulb (energy as light)1001010
kettle50045090
Energy in, useful energy out and efficiency for three devices

Key ideas

  • Efficiency = useful energy output / total energy input x 100%.
  • Wasted energy = total input minus useful output.
  • Efficiency is always less than 100%.
  • A higher efficiency means less energy is wasted.
Worked example 9.3.1
A motor has 200 J of input and 150 J of useful output. What is its efficiency, as a percentage? Write the number.

Method. Divide the useful output by the input, then multiply by 100.

  1. Divide. 150 / 200 = 0.75.
    150 / 200 = 0.75
  2. Convert. 0.75 x 100 = 75%.
    0.75 x 100 = 75
  3. Write the answer.
    75

Check. 75% of 200 J is 150 J. ✓

Worked example 9.3.2
A light bulb takes in 100 J and gives 10 J of light. How much energy is wasted? Write the number, in joules.

Method. Subtract the useful output from the input.

  1. Subtract. 100 - 10 = 90 J.
    100 - 10
  2. Write. So 90 J is wasted.
    90
  3. Write the answer.
    90

Check. 10 + 90 = 100 J. ✓

Worked example 9.3.3
A kettle is 90% efficient and takes in 500 J. How much useful energy is output? Write the number, in joules.

Method. Find 90% of the input.

  1. Convert. 90% = 90 / 100 = 0.9.
    0.9
  2. Multiply. 0.9 x 500 = 450 J.
    0.9 x 500 = 450
  3. Write the answer.
    450

Check. 450 / 500 = 0.9, which is 90%. ✓

Watch out

Watch out: efficiency is a percentage of the input, not of the output. Divide by the input.

Exam tip

Exam tip. Always write the efficiency formula first, then substitute the useful output and the total input.

Try it (with your teacher, or a grown-up at home). With your teacher, compare how much energy a battery-powered torch or a small fan wastes as heat when it runs. Use a thermometer on the case, and say which part of the device gets warm, and why this is wasted energy.

Exercise 9C  Efficiency

1
FWhat is the efficiency formula? Write the words.
2
FCan an efficiency be 100%? Write yes or no.
3
FWhat is the name of the energy that is usually wasted? Write the word.
4
PSA device has a useful output of 40 J and an input of 80 J. What is its efficiency, as a percentage? Write the number.
5
PSA device has an input of 300 J and a useful output of 120 J. What is its efficiency, as a percentage? Write the number.
6
PSAn electric motor is 75% efficient and takes in 200 J. How much useful energy is output? Write the number, in joules.
7
PSA device takes in 500 J and outputs 100 J of useful energy. How much energy is wasted? Write the number, in joules.
8
PSA kettle is 90% efficient and takes in 500 J. How much energy is wasted? Write the number, in joules.
9
PSWhich device is the most efficient: a motor with 75%, a light bulb with 10%, or a kettle with 90%? Write the word.
10
RExplain why a light bulb with 10% efficiency is not a good choice for lighting. Write one sentence. Accept any sentence saying most of the energy is wasted as thermal energy, not used as light.
11
RChallenge: a pupil says a 90% efficient kettle has 10% of its energy lost. Is this correct? Write yes or no, and give the reason in one sentence. Accept yes, with a reason that the 10% that is not useful is wasted.
9.4

Kinetic and gravitational potential energy (extension)

Year 9
9P1: kinetic and gravitational potential energy in simple cases (EXTENSION: the formulae are not in the programme text; flagged)
Video lesson: Kinetic and gravitational potential energy (extension)Coming soon
Story. A pupil rolls a toy car down a ramp. The car goes faster the higher it starts, and it has more energy when it is raised. Her teacher offers two formulae for the energy stores: one for the moving car, and one for the raised car. These are an extension for this class.

Extension (not in the KS3 programme text). The kinetic energy of a moving object is KE = 0.5 x m x v2, where m is the mass in kilograms and v is the speed in metres per second. The gravitational potential energy of an object raised above the ground is GPE = m x g x h, where g is the gravitational field strength (10 N/kg here) and h is the height in metres.

Both are in joules. In a simple system with no losses, the GPE lost as an object falls is equal to the KE gained.

Key ideas

  • Extension: KE = 0.5 x m x v2, with m in kg and v in m/s.
  • Extension: GPE = m x g x h, with g = 10 N/kg and h in metres.
  • Both give energy in joules (J).
  • With no losses, GPE lost = KE gained.
Worked example 9.4.1
A 2 kg object moves at 3 m/s. Calculate its kinetic energy, in joules. (Extension.) Write the number.

Method. Use KE = 0.5 x m x v2.

  1. Square the speed. 32 = 9.
    3 x 3 = 9
  2. Multiply. KE = 0.5 x 2 x 9 = 9 J.
    0.5 x 2 x 9 = 9
  3. Write the answer.
    9

Check. Check: 0.5 x 2 = 1, and 1 x 9 = 9. ✓

Worked example 9.4.2
A 5 kg object is raised 4 m above the ground. Calculate its GPE, in joules. (Extension.) Write the number.

Method. Use GPE = m x g x h, with g = 10 N/kg.

  1. Write. GPE = 5 x 10 x 4.
    5 x 10 x 4
  2. Calculate. So GPE = 200 J.
    5 x 10 x 4 = 200
  3. Write the answer.
    200

Check. 200 / 10 / 4 = 5 kg. ✓

Worked example 9.4.3
A 50 kg child is raised 2 m. How much GPE is gained, in joules? (Extension.) Write the number.

Method. Use GPE = m x g x h.

  1. Write. GPE = 50 x 10 x 2.
    50 x 10 x 2
  2. Calculate. So the GPE gained is 1000 J.
    50 x 10 x 2 = 1000
  3. Write the answer.
    1000

Check. 1000 / 10 / 2 = 50 kg. ✓

Watch out

Watch out: kinetic energy uses the speed squared, so doubling the speed makes KE four times as large.

Exam tip

Exam tip. Square the speed before multiplying. Use metres for height and metres per second for speed.

Try it (with your teacher, or a grown-up at home). With your teacher, roll a toy car down a short ramp from two different heights, and measure the distance it rolls on the bench. Say which store gained energy at the top, and which store had the energy at the bottom. This is an extension activity.

Exercise 9D  Kinetic and gravitational potential energy (extension)

1
FWhich energy store does a moving object have? Write the words.
2
FWhich energy store does a raised object have? Write the words.
3
FIn the formula KE = 0.5 x m x v2, which quantity is squared? Write the letter.
4
FWhich value of g does the programme use for calculations on Earth? Write the number, in N/kg. (Extension.)
5
PSA 2 kg object moves at 4 m/s. Calculate its kinetic energy, in joules. (Extension.) Write the number.
6
PSA 3 kg object moves at 2 m/s. Calculate its kinetic energy, in joules. (Extension.) Write the number.
7
PSA 5 kg object is raised 4 m. Calculate its GPE, in joules. (Extension.) Write the number.
8
PSA 10 kg object is raised 3 m. Calculate its GPE, in joules. (Extension.) Write the number.
9
PSIf a 2 kg object at 3 m/s has KE = 9 J, what would its KE be at 6 m/s? (Extension.) Write the number.
10
RA ball falls from a height, and loses 20 J of GPE. Assuming no losses, how much KE does it gain? (Extension.) Write the number.
11
RExplain why a fast car has much more kinetic energy than a slow car of the same mass. Write one sentence. Accept any sentence saying kinetic energy depends on the square of the speed.
12
RChallenge: a 4 kg object falls 5 m, and then has 200 J of KE just before landing. Is energy conserved if no energy is lost? Write yes or no. (Extension.) Accept yes, with a reason that GPE = 4 x 10 x 5 = 200 J.
9.5

Conservation of energy in all transfers

Year 9
9P1: conservation of energy in all transfers; energy calculations in simple cases
Video lesson: Conservation of energy in all transfersComing soon
Story. A lamp is powered by a battery. The energy in the battery is transferred to light and thermal energy. The class checks whether the energy out equals the energy in, and finds the missing value.

The law of conservation of energy says the total energy before a change equals the total energy after it. Energy is only transferred or stored in other stores. In a transfer, the total of all the useful and wasted energy outputs equals the total energy input.

To find a missing value, add the known outputs and subtract from the input.

Key ideas

  • Total energy in = total energy out (useful plus wasted).
  • Missing energy = total in minus the known outputs.
  • Energy is never created or destroyed.
  • Energy spreads out, so it becomes harder to use.
Worked example 9.5.1
A battery gives 300 J. A lamp gives out 120 J of light, and the rest as heat. How much energy is given out as heat? Write the number, in joules.

Method. Subtract the light from the input.

  1. Subtract. 300 - 120 = 180 J.
    300 - 120
  2. Write. So 180 J is given out as heat.
    180
  3. Write the answer.
    180

Check. 120 + 180 = 300 J. ✓

Worked example 9.5.2
A machine takes in 400 J. It outputs 250 J of useful energy and some as sound. The sound is 50 J. How much is wasted as heat? Write the number, in joules.

Method. Subtract every known output from the input.

  1. Subtract. 400 - 250 - 50 = 100.
    400 - 250 - 50
  2. Write. So 100 J is wasted as heat.
    100
  3. Write the answer.
    100

Check. 250 + 50 + 100 = 400 J. ✓

Worked example 9.5.3
A kettle is 80% efficient. It takes in 1000 J. How much energy is wasted? Write the number, in joules.

Method. Find the useful output, then subtract.

  1. Useful. 80% of 1000 = 800 J.
    0.8 x 1000 = 800
  2. Wasted. 1000 - 800 = 200 J.
    1000 - 800 = 200
  3. Write the answer.
    200

Check. 800 + 200 = 1000 J. ✓

Watch out

Watch out: a missing value is found by subtraction. Do not add the outputs to the input.

Exam tip

Exam tip. Write the energy in and the energy out as a sum, then solve for the missing value.

Try it (with your teacher, or a grown-up at home). With your teacher, use a low-voltage battery pack, a bulb and a small fan. Describe where the energy goes in each device, and which output is useful. Do not connect mains electricity.

Exercise 9E  Conservation of energy in all transfers

1
FWhat is the law that says energy is never created or destroyed? Write the words.
2
FIn a transfer, is the total energy out equal to the total energy in? Write yes or no.
3
FWhat is the name of the energy that is wasted in most devices? Write the word.
4
PSA battery gives 300 J. A lamp gives out 120 J of light and the rest as heat. How much energy is given out as heat? Write the number, in joules.
5
PSA machine takes in 500 J and outputs 300 J as useful energy and 100 J as sound. How much is wasted as heat? Write the number, in joules.
6
PSA fan takes in 150 J and gives 120 J of useful kinetic energy. How much is wasted? Write the number, in joules.
7
PSA kettle is 90% efficient and takes in 2000 J. How much useful energy is output? Write the number, in joules.
8
PSA kettle is 90% efficient and takes in 2000 J. How much energy is wasted? Write the number, in joules.
9
PSA device takes in 80 J and wastes 20 J. What is its efficiency, as a percentage? Write the number.
10
RExplain why the energy in a bulb is the same as the energy out, even though it looks like energy is lost. Write one sentence. Accept any sentence saying the energy is transferred to the surroundings as light and thermal energy.
11
RChallenge: a pupil says energy is lost when a machine warms up. Write one sentence to correct her. Accept any sentence saying the energy is transferred to the thermal store of the machine and surroundings, so it is conserved but spread out.

Chapter summary

SkillMethod
Stores and transfersEnergy moves between stores (kinetic, gravitational potential, thermal, chemical, elastic); it is conserved.
PowerPower = energy transferred / time, in W; energy = power x time (time in s); 1 kW = 1000 W.
EfficiencyUseful output / total input x 100%; wasted energy = input minus useful output.
Kinetic energy (extension)KE = 0.5 x m x v2, in joules, with m in kg and v in m/s.
Gravitational potential energy (extension)GPE = m x g x h, with g = 10 N/kg and h in metres.
ConservationTotal energy in equals total energy out, including the wasted energy.

Can you…?

  • I can name the energy stores and describe the transfers in a simple system
  • I can calculate power from energy and time, and convert between W and kW
  • I can calculate efficiency as a percentage of useful output over total input
  • I can use the kinetic and gravitational potential energy formulae in simple cases (extension)
  • I can use conservation of energy to find a missing energy value

Key terms

energy store
a place where energy is held, such as kinetic, thermal or chemical
energy transfer
the movement of energy from one store to another
power
the rate at which energy is transferred, in watts
watt
a unit of power: one joule per second
efficiency
the percentage of the energy input that becomes useful output
useful energy output
the energy that is transferred to where it is wanted
wasted energy
the energy transferred to stores that are not wanted, usually thermal
kinetic energy
the energy of a moving object (extension: 0.5 x m x v squared)
gravitational potential energy
the energy of an object raised above the ground (extension: m x g x h)
joule
the unit of energy

Exercise 9Z  Check-up

1
What is the unit of power? Write the symbol.
2
A device transfers 100 J in 4 s. What is its power, in watts? Write the number.
3
A heater has a power of 3 kW. What is its power in watts? Write the number.
4
A lamp is 60 W and is used for 10 s. How much energy does it transfer, in joules? Write the number.
5
A device has an input of 200 J and a useful output of 150 J. What is its efficiency, as a percentage? Write the number.
6
A kettle is 90% efficient and takes in 500 J. How much energy is wasted, in joules? Write the number.
7
Name the energy store of a raised object. Write the words.
8
A battery gives 300 J, and a lamp gives out 120 J of light. How much is given out as heat, in joules? Write the number.
9
Is energy created or destroyed in a transfer? Write yes or no.
10
Explain why no device is 100% efficient. Write one sentence. Accept any sentence saying some energy is always wasted, usually as thermal energy.

Total 22 marks. Allow about 22 minutes.

Exercise 9X  Practice test questions

1
FWhat is the unit of energy? Write the symbol.[1 mark]
2
PSA device transfers 60 J in 2 s. What is its power, in watts? Write the number.[1 mark]
3
PSHow many watts are in 2.5 kW? Write the number.[1 mark]
4
FWrite the equation for efficiency as a percentage. Write the words.[2 marks]
5
PSA 2 kW kettle runs for 300 s. How much energy does it transfer, in joules? Write the number.[2 marks]
6
PSA motor takes in 400 J and outputs 300 J as useful energy. What is its efficiency, as a percentage? Write the number.[2 marks]
7
PSA device has 80% efficiency and takes in 250 J. How much energy is wasted, in joules? Write the number.[2 marks]
8
PSA 3 kg object moves at 4 m/s. Calculate its kinetic energy, in joules. (Extension.) Write the number.[3 marks]
9
RExplain why a device with a higher efficiency wastes less energy. Write one sentence. Accept any sentence saying a bigger share of the input becomes useful output, so less is wasted.[2 marks]
10
PSA 5 kg object is raised 4 m. Calculate its gravitational potential energy, in joules, using g = 10 N/kg. (Extension.) Write the number.[3 marks]
11
RA device takes in 500 J, outputs 350 J as useful energy, and the rest as heat. Find the energy wasted as heat, and explain why energy is conserved. Write the number, then one sentence. Accept any answer giving 150 J with a sentence saying the input equals the useful plus wasted energy.[3 marks]
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