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GCSE Physics AQA
1.1 Energy Changes in a System
CONTENTS
1.1.1 Energy Stores & Transfers
1.1.2 Examples of Energy Transfer
1.1.3 Kinetic Energy
1.1.4 Gravitational Potential Energy
1.1.5 Elastic Potential Energy
1.1.6 KE, GPE & EPE
1.1.7 Thermal Energy
1.1.8 Required Practical: Investigating Specific Heat Capacity
1.1.9 Changes in Energy
1.1.10 Power
1.1.11 Conservation & Dissipation of Energy
1.1.12 Wasted Energy
1.1.13 Conduction of Heat
1.1.14 Required Practical: Investigating Insulation
1.1.15 Efficiency
1.1.16 Improving Efficiency
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1.1.1 Energy Stores & Transfers
Systems in Physics
In physics, a system is defined as:
An object or group of objects
An apple sitting on a table can be defined as a system
Defining the system in physics is a way of narrowing the parameters to focus only on what
is relevant to the situation being observed
When a system is in equilibrium, nothing changes and so nothing happens
When there is a change in a system, things happen, and when things happen energy is
transferred
If the table is removed, the apple will fall
As the apple falls, energy is transferred
Energy is measured in units of joules (J)
A thermodynamic system can be isolated, closed or open
An open system allows the exchange of energy and matter to or from its surroundings
A closed system can exchange energy but not matter to or from its surroundings
An isolated system does not allow the transfer of matter or energy to or from its
surroundings
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A system can be open, closed or isolated
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Energy Stores & Transfers
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Energy Stores
Energy is stored in objects
When a change happens within a system, energy is transferred between objects or
between stores
The principle of conservation of energy states that:
Energy cannot be created or destroyed, it can only be transferred from one store to
another
This means that for a closed system, the total amount of energy is constant
There are many different energy stores that objects can have, these are shown in the table
below:
Energy Stores Table
Energy Transfer Pathways
Energy is transferred between stores via transfer pathways
Examples of these are:
Mechanically
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Electrically
By heating
By radiation
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These are described in the table below:
Energy Transfer Pathway Table
An example of an energy transfer is a hot coffee heating up cold hands
Energy is transferred from the hot coffee to the mug to the cold hands
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Worked Example
Describe the energy transfers in the following scenarios:
a) A battery powering a torch
b) A falling object
a)
Step 1: Determine the store that energy is being transferred away from,
within the parameters described by the defined system
For a battery powering a torch
The system is defined as the energy transfer from the battery to the
torch, so this is the transfer to focus on
Therefore, the energy began in the chemical store of the cells of the
battery
Step 2: Determine the store that energy is transferred to, within the
parameters described by the defined system
When the circuit is closed, the bulb lights up
Therefore, energy is transferred to the thermal store of the bulb
Energy is then transferred from the bulb to the surroundings, but this
is not described in the parameters of the system
Step 3: Determine the transfer pathway
Energy is transferred by the flow of charge around the circuit
Therefore, the transfer pathway is electrical
Energy is transferred electrically from the chemical store of the battery to
the thermal store of the bulb
b)
Step 1: Determine the store that energy is being transferred away from,
within the parameters described by the defined system
For a falling object
In order to fall, the object must have been raised to a height
Therefore, it began with energy in its gravitational potential store
Step 2: Determine the store that energy is transferred to, within the
parameters described by the defined system
As the object falls, it is moving
Therefore, energy is being transferred to its kinetic store
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Step 3: Determine the transfer pathway
For an object to fall, a resultant force must be acting on it, and that
force is weight, and it acts over a distance (the height of the fall)
Therefore, the transfer pathway is mechanical
Energy is transferred from the gravitational store to the kinetic store of the
object via a mechanical transfer pathway

Exam Tip
Don't worry too much about the parameters of the system. They are there to help
you keep your answers concise so you don't end up wasting time in your exam.
If you follow any process back far enough, you would get many energy transfers
taking place. For example, an electric kettle heating water. The relevant energy
transfer is from the thermal store of the kettle to the thermal store of the water, with
some energy dissipated to the surroundings. But you could take it all the way back
to how the electricity was generated in the first place. This is beyond the scope of
the question. Defining the system gives you a starting point and a stopping point for
the energy transfers you need to consider.
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1.1.2 Examples of Energy Transfer
Energy Transfer Examples
Different types of energy transfers occur all the time in various everyday circumstances
Some common situations include
When an object is projected upwards
When a moving object hits an obstacle
When an object is accelerated by a constant force
When a vehicle speeds up or slows down
When water is brought to a boil in an electric kettle
An Object Projected Upwards
Before the ball is thrown upwards, the person holding the ball has energy in their chemical
store
When the ball is thrown, some of that energy is transferred to the kinetic store of the ball as
it begins to move upwards
As the height of the ball increases, energy from the kinetic store of the ball is transferred to
its gravitational potential store
A Moving Object Hitting an Obstacle
When an object, such as a car, is moving, energy in the chemical store of the fuel is
transferred to the kinetic store of the car
If the object hits an obstacle, such as the car hitting a wall, the speed of the car will
decrease very quickly
Therefore, the energy in its kinetic store will decrease
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In this scenario, most of the energy from its kinetic store is transferred to the thermal store
of the surroundings (dissipated)
Energy is transferred mechanically to the thermal store of the wall (the force of the car on
the wall)
Energy is also transferred by heating to the thermal store of the car, the wall and to the
thermal store of the air as the sound waves transfer energy away from the system (causing
the air particles to vibrate)
A Vehicle Being Accelerated by a Constant Force
When a vehicle is stationary, it has energy in the chemical store of the fuel
When the vehicle speeds up or accelerates, the energy is transferred to the kinetic store of
the car
A Vehicle Slowing Down
When a vehicle is moving, it has energy in its kinetic store
As it slows down or decelerates, energy is transferred to the thermal store of the
surroundings (dissipated)
This energy is transferred by heating due to friction between the tyres on the ground, and
due to friction between the brakes and the brake pads
Energy is also transferred by heating as the sound waves transfer energy away from the
system (making the air particles vibrate)
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Boiling Water in a Kettle
When an electric kettle boils water, energy is transferred by electrical working from the
mains to the thermal store of the heating element inside the kettle
As the heating element gets hotter, energy is transferred by heating to the thermal store of
the water
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1.1.3 Kinetic Energy
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Kinetic Energy
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Energy in the kinetic store is defined as:
The amount of energy an object has as a result of its mass and speed
This means that any object in motion has energy in its kinetic store
If an object speeds up, energy is transferred to its kinetic store
If an object slows down, energy is transferred away from its kinetic store
Kinetic energy can be calculated using the equation:
Ek = ½ × m × v2
Where:
Ek = kinetic energy in joules (J)
m = mass of the object in kilograms (kg)
v = speed of the object in metres per second (m/s)
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Worked Example
Calculate the kinetic energy stored in a vehicle of mass 1200 kg moving at a
speed of 27 m/s.
Step 1: List the known quantities
Mass of the vehicle, m = 1200 kg
Speed of the vehicle, v = 27 m/s
Step 2: Write down the equation for kinetic energy
EK = ½ mv2
Step 3: Calculate the kinetic energy
EK = ½ × 1200 × (27)2
EK = 437 400 J
Step 4: Round the final answer to 2 significant figures
EK = 440 000 J
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Exam Tip
When performing calculations using the kinetic energy equation, always doublecheck that you have squared the speed. Forgetting to do this is the most common
mistake that students make.
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1.1.4 Gravitational Potential Energy
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What is Gravitational Potential Energy?
Energy in the gravitational store of an object is defined as:
The energy an object has due to its height in a gravitational field
This means:
If an object is lifted up, energy is transferred to its gravitational potential store
If an object falls, energy will be transferred away from its gravitational potential store
Gravitational Potential Energy Equation
The gravitational potential energy, Ep, of an object can be calculated using the equation:
Ep = m × g × h
Where:
Ep = gravitational potential energy, in joules (J)
m = mass, in kilograms (kg)
g = gravitational field strength in newtons per kilogram (N/kg)
h = height in metres (m)
Gravitational Field Strength
The gravitational field strength (g) on the Earth is approximately 9.8 N/kg
The gravitational field strength on the surface of the Moon is less than on the Earth
This means it would be easier to lift a mass on the Moon than on the Earth
The gravitational field strength on the surface of the gas giants (eg. Jupiter and Saturn) is
more than on the Earth
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This means it would be harder to lift a mass on the gas giants than on the Earth
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Some values for g on the different objects in the Solar System
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Worked Example
A man of mass 70 kg climbs a flight of stairs that is 3 m higher than the floor.
Gravitational field strength is approximately 9.8 N/kg. Calculate the energy
transferred to the man's gravitational potential energy store.
Step 1: List the known quantities
Mass of the man, m = 70 kg
Gravitational field strength, g = 9.8 N/kg
Height, Δh = 3 m
Step 2: Write down the equation for gravitational potential energy
ΔEP = mgΔh
Step 3: Calculate the gravitational potential energy
ΔEP = 70 × 9.8 × 3
ΔEP = 2058 J

Exam Tip
When doing calculations involving gravitational field strength, g, always use the
value of 9.8 N/kg unless you are told otherwise in your exam question. You will be
expected to remember the value of g for your exam!
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1.1.5 Elastic Potential Energy
Elastic Potential Energy
What is Elastic Potential Energy?
Energy in the elastic potential store of an object is defined as:
The energy stored in an elastic object when work is done on the object
This means that any object that can change shape by stretching, bending or compressing
(eg. springs, rubber bands)
When a spring is stretched (or compressed), work is done on the spring which results
in energy being transferred to the elastic potential store of the spring
When the spring is released, energy is transferred away from its elastic potential
store
How to determine the extension, e, of a stretched spring
How to Calculate Elastic Potential Energy
The amount of elastic potential energy stored in a stretched spring can be calculated using
the equation:
Ee = ½ × k × e2
Where:
Ee = elastic potential energy in joules (J)
k = spring constant in newtons per metre (N/m)
e = extension in metres (m)
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The above elastic potential energy equation assumes that the spring has not been
stretched beyond its limit of proportionality
The spring on the right has been stretched beyond the limit of proportionality
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Worked Example
A mass is attached to the bottom of a hanging spring with a spring constant of
250 N/m. It stretches from 10.0 cm to 11.4 cm.
Calculate the elastic energy stored by the stretched spring.
Step 1: Determine the extension of the spring
Step 2: List the known quantities
Spring constant, k = 250 N/m
Extension, e = 1.4 cm = 0.014 m
Step 3: Write out the elastic potential energy equation
Ee = ½ ke2
Step 4: Calculate the elastic potential energy
Ee = ½ × 250 × (0.014)2
Ee= 0.0245 J
Step 5: Round the answer to 2 significant figures
Ee = 0.025 J
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Exam Tip
Look out for units! If the question gives you units of cm for the length you MUST
convert this into metres for the calculation to be correct.
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1.1.6 KE, GPE & EPE
KE, GPE & EPE
When a mass on a vertical spring oscillates up and down, energy is transferred between
stores
Although the total energy of the mass-spring system will remain constant, it will have
changing amounts of energy in its:
Elastic potential energy (EPE) store
Kinetic energy (KE) store
Gravitational potential energy (GPE) store
Energy changes when a spring is stretched
At position A:
The spring has some energy in its elastic potential store since it is slightly
compressed
The spring has zero energy in its kinetic store since it is stationary
The amount of energy in its gravitational potential store is at a maximum because the
mass is at its highest point
At position B:
The spring has some energy in its elastic potential store since it is slightly stretched
The energy in its kinetic store is at a maximum as it passes through its resting position
at its maximum speed
The spring has some energy in its gravitational potential store since the mass is still
above its lowest point in the oscillation
At position C:
The energy in the elastic potential store of the spring is at its maximum because it is at
its maximum extension
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The spring has zero energy in its kinetic store since it is stationary
The energy in the gravitational potential store of the spring is at a minimum because it
is at its lowest point in the oscillation
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Worked Example
The diagram below shows a student before and after a bungee jump. The
bungee cord has an unstretched length of 30.0 m.
The mass of the student is 60.0 kg. The gravitational field strength is 9.8 N / kg.
Calculate:
a) The change in gravitational potential energy of the student at 30.0 m
b) The maximum change in the gravitational potential energy of the student
c) The speed of the student after falling 30.0 m if 90% of the energy in the
student's gravitational potential store is transferred to the student's kinetic
store
d) The spring constant of the bungee cord if all the energy in the gravitational
potential store of the student is transferred to the elastic potential store of the
bungee cord
Part (a)
Step 1: List the known quantities
Mass of the student, m = 60.0 kg
Gravitational field strength, g = 9.8 N/kg
Change in height, h = 30.0 m
Step 2: Write out the equation for gravitational potential energy
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E P = mgh
Step 3: Calculate the change in gravitational potential energy
E P = 60 × 9 . 85 × 30
E P = 17 640 J
Part (b)
Step 1: List the known quantities
Mass of the student, m = 60.0 kg
Gravitational field strength, g = 9.8 N/kg
Maximum change in height, h = 75.0 m
Step 2: Calculate the maximum change in gravitational potential energy
E P max = mgh max
E P max = 60 × 9 . 8 × 75
E P max = 44 100 J
Part (c)
Step 1: List the known quantities
Mass of the student, m = 60.0 kg
E P at 30.0 m = 17 640 J
Step 2: Determine 90% of the E P at 30.0 m
E K = 90% of E P
E K = 0 . 9 × 17 640
E K = 15 876 J
Step 3: Write out the equation for KE
EK =
1
mv 2
2
Step 4: Rearrange to make speed the subject
Multiply both sides by 2:
mv 2 = 2 × E K
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Divide both sides by m:
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v2
=
2 × EK
m
Take the square root of both sides:
2 × EK
v=
m
Step 5: Calculate the speed
2 × 15 876
60
v=
v = 23. 0 m/s
Part (d)
Step 1: List the known quantities
E P max = 44 100 J
E e at 75.0 m = E e max
Step 2: Determine the extension of the bungee cord
e = 75. 0 − 30. 0
e = 45. 0 m
Step 3: Write out the equation for elastic potential energy
Ee =
1 2
ke
2
Step 3: Rearrange to make spring constant, k, the subject
Multiply both sides by 2:
ke2 = 2 × E e
Divide both sides by e2 :
k=
2 × Ee
e2
Step 4: Calculate the spring constant
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k=
2 × 44 100
452
k = 43. 6 N/ m

Exam Tip
If a question asks you to "state" a value, you do not need to carry out a calculation:
The answer will almost certainly be a number either from a previous answer or which
was given somewhere in the question.
For example, if you have just calculated the gravitational potential energy of an
object and are then asked to state the kinetic energy a moment later, the answers
are very likely to be the same.
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1.1.7 Thermal Energy
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Thermal Energy
Energy in the thermal store of an object is responsible for its temperature
Energy can be transferred to or transferred from an object or system
The amount of energy needed to raise the temperature of a given mass of a substance by a
given amount can be calculated using the equation:
ΔE = mcΔθ
Where:
ΔE = change in energy, in joules (J)
m = mass, in kilograms (kg)
c = specific heat capacity, in joules per kilogram per degree Celsius (J/kg °C)
Δθ = change in temperature, in degrees Celsius (°C)
The specific heat capacity of a substance is defined as:
The amount of energy required to raise the temperature of 1 kg of a substance by 1
°C
Different substances have different specific heat capacities
If a substance has a low specific heat capacity, it heats up and cools down quickly
It takes less energy to change its temperature
If a substance has a high specific heat capacity, it heats up and cools down slowly
It takes more energy to change its temperature
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Low v high specific heat capacity
Specific heat capacity is mainly used for liquids and solids
The specific heat capacity of different substances determines how useful they would be
for a specific purpose eg. choosing the best material for kitchen appliances
Good electrical conductors, such as copper and lead, are excellent thermal
conductors due to their low specific heat capacity
On the other hand, water has a very high specific heat capacity, making it ideal for
heating homes as the water remains hot in a radiator for a long time

Exam Tip
This equation will be given on your equation sheet, so don't worry if you cannot
remember it, but it is important that you understand how to use it. You will always be
given the specific heat capacity of a substance, so you do not need to memorise
any values.
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1.1.8 Required Practical: Investigating Specific Heat Capacity
Required Practical 1: Investigating Specific Heat Capacity
Aims of the Experiment
The aim of the experiment is to determine the specific heat capacity of a substance, by
linking the amount of energy transferred to the substance with the rise in temperature of
the substance
Variables:
Independent variable = Time, t
Dependent variable = Temperature, θ
Control variables:
Material of the block
Current supplied, I
Potential difference supplied, V
Equipment List
Resolution of measuring equipment:
Thermometer = 1 °C
Stopwatch = 0.01 s
Voltmeter = 0.1 V
Ammeter = 0.01 A
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Method
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Apparatus to investigate the specific heat capacity of the aluminium block
1. Start by assembling the apparatus, placing the heater into the top of the block
2. Measure the initial temperature of the aluminium block from the thermometer
3. Turn on the power supply and start the stopwatch
4. Whilst the power supply is on, the heater will heat up the block. Take several periodic
measurements, eg. every 1 minute of the voltage and current from the voltmeter and
ammeter respectively, calculating an average for each at the end of the experiment up to 10
minutes
5. Switch off the power supply, stop the stopwatch and leave the apparatus for about a
minute. The temperature will still rise before it cools
6. Monitor the thermometer and record the final temperature reached for the block
An example table of results might look like this:
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Analysis of Results
The thermal energy supplied to the block can be calculated using the equations:
E = QV and Q = It
Where:
E = thermal energy, in joules (J)
Q = Charge, in coulombs (C)
I = current, in amperes (A)
V = potential difference, in volts (V)
t = time, in seconds (s)
Combining the equations:
Rearrange to make Q the subject
E = QV ⇒ Q =
E
V
Substitute into the Q = It equation
Q = It
E
= It
V
Rearrange to make E the subject
E = IVt
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The change in thermal energy is defined by the equation:
∆ E = mc ∆ θ
Where:
ΔE = change in energy, in joules (J)
m = mass, in kilograms (kg)
c = specific heat capacity, in joules per kilogram per degree Celsius (J/kg °C)
Δθ = change in temperature, in degrees Celsius (°C)
Rearranging for the specific heat capacity, c:
c=
∆E
m ∆θ
To calculate Δθ:
∆θ = θ f − θ i
Where:
θ f = final temperature
θ i = initial temperature
To calculate ΔE:
∆ E = IVθ f − IVθ i
Where:
I = average current, in amperes (A)
V = average potential difference (V)
θf = final time, in seconds (s)
θi = initial time, in seconds (s)
These values are then substituted into the specific heat capacity equation to calculate the
specific heat capacity of the aluminium block
Evaluating the Experiment
Systematic Errors:
Make sure the voltmeter and ammeter are initially set to zero, to avoid zero error
Random Errors:
Not all the energy transferred from the heater will be transferred to the block, some will be
dissipated to the surroundings into the surroundings and some will be transferred to the
thermometer (also part of the surroundings)
This means the measured value of the specific heat capacity is likely to be higher than
what it actually is
To reduce this effect, make sure the block is fully insulated
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A joulemeter could be used to calculate energy directly
This would eliminate errors from the voltmeter, ammeter and the stopwatch
Make sure the temperature value is read at eye level from the thermometer, to avoid
parallax error
The experiment can also be repeated with a beaker of water of equal mass, the water
should heat up slower than the aluminium block
Safety Considerations
Make sure never to touch the heater whilst it is on, otherwise, it could burn skin or set
something on fire
Run any burns immediately under cold running water for at least 5 minutes
Allow time for all the equipment, including the heater, wire and block to cool before packing
away the equipment
Keep water away from all electrical equipment
Wear eye protection if using a beaker of hot water
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1.1.9 Changes in Energy
Changes in Energy
Changes make things happen. When there is a change in a system, energy is transferred
Energy can be transferred via different pathways:
Heating by particles
Heating by radiation
Mechanical work done by forces
Electrical work done when a current flows
Heating
Energy transfers by heating increase the energy in the kinetic store of the particles that
make up that system, which increases the energy in the thermal store of the object
This either raises the system's temperature or, produces a change of state (eg. solid to
liquid)
An example of an energy transfer by heating is warming a pan on a hob
Energy is transferred electrically from the mains supply to the thermal store of the hob
which is then transferred by heating to the thermal store of the pan
Energy is transferred by heating from the thermal store of the hob to the thermal store of the
pan
Work Done by Forces
Mechanical work is done when a force acts over a distance
For example, when a person pushes a box across the floor
Energy is transferred mechanically from the kinetic store of the person to the kinetic store
of the box
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Energy transfers taking place when a box is pushed across the floor
If the system is defined as the man and the box, energy is transferred mechanically from
the kinetic store of the person to the kinetic store of the box
If the system is defined as the box and the floor, energy is transferred by heating from
the kinetic store of the box to the thermal store of the floor (due to friction) and
by heating to the thermal store of the surroundings as the sound waves transfer energy
away from the system and cause the air particles to vibrate
Work Done When a Current Flows
Current is the flow of charge
A current flows when there is a potential difference applied to the circuit
This is provided by the power supply or a cell
Energy is transferred electrically from the power supply to the components in the circuit
This is the electrical work done by the power supply when a current flows
Energy from the chemical store of the cell is transferred electrically to the thermal store of
the lamp as the filament heats up
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Energy is transferred from the thermal store of the lamp by heating and by radiation (light)
to the thermal store of the surroundings
Energy is also transferred by heating to the thermal store of the wires (due to resistance)
Energy transfers taking place in an electrical circuit

Exam Tip
Don't worry too much about the parameters of the system. They are there to help
you keep your answers concise so you don't end up wasting time in your exam.
If you follow any process back far enough, you would get many energy transfers
taking place. For example, an electric kettle heating water. The relevant energy
transfer is from the thermal store of the kettle to the thermal store of the water, with
some energy dissipated to the surroundings. But you could take it all the way back
to how the electricity was generated in the first place. This is beyond the scope of
the question. Defining the system gives you a starting point and a stopping point for
the energy transfers you need to consider.
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1.1.10 Power

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Power
YOUR NOTES
Machines, such as car engines, transfer energy from one energy store to another
constantly over a period of time
The rate of this energy transfer, or the rate of work done, is called power
Time is an important consideration when it comes to power
Two cars transfer the same amount of energy, or do the same amount of work to
accelerate over a distance
If one car has more power, it will transfer that energy, or do that work, in a shorter amount
of time
Two cars accelerate to the same final speed, but the one with the most power will reach that
speed sooner
Power is defined as
Energy transferred per unit time
Therefore, power can be calculated using the equation
P=
E
t
Where:
P = power in watts (W)
E = energy transferred in joules (J)
t = time in seconds (s)
Since
energy transferred = work done
Power can also be calculated using the equation
P=
W
t
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Where:
P = power in watts (W)
W = work done in joules (J)
t = time in seconds (s)

This equation can be rearranged with the help of a formula triangle:
Work, power and time formula triangle
How to Use Formula Triangles
Formula triangles are really useful for knowing how to rearrange physics equations
To use them:
1. Cover up the quantity to be calculated, this is known as the 'subject' of the equation
2. Look at the position of the other two quantities
If they are on the same line, this means they are multiplied
If one quantity is above the other, this means they are divided - make sure to keep the
order of which is on the top and bottom of the fraction!
In the example below, to calculate speed, cover-up 'speed' and only distance and time are
left
This means it is equal to distance (on the top) ÷ time (on the bottom)
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How to use formula triangles
Power ratings are given to appliances to show the amount of energy transferred per unit
time
Common power ratings are shown in the table below:
Power Ratings Table
Power and power ratings are useful because power describes how fast the energy is
transferred from one store to another
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Two identical cars accelerating to the same final speed will both transfer the same amount
of energy. But if one of them does it in a shorter time, it will have a greater power

Worked Example
Calculate the energy transferred when an iron with a power rating of 2000 W is
used for 5 minutes.
Step 1: List the known values
Power, P = 2000 W
Time, t = 5 minutes = 5 × 60 = 300 s
Step 2: Write down the relevant equation
P=
E
t
Step 3: Rearrange for energy transferred, ΔE
E = Pt
Step 4: Substitute in the known values
E = 2000 × 300
E = 600 000 J

Exam Tip
Think of power as “energy per second”. Thinking of it this way will help you to
remember the relationship between power and energy
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The Watt
YOUR NOTES
The watt is the unit of power
Since power is energy transferred per second, the watt can also be defined as 1 joule per
second

1 W=1 J/s
1 kilowatt (1 kW) is equal to 1000 watts, or 1000 joules of energy transferred per second (1 kJ
/ s)

Exam Tip
One way to remember this unit is it remember the saying “watt is the unit of power?”
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Comparing Power Outputs
YOUR NOTES

Two electric motors:
lift the same weight
by the same height
but one motor lifts it faster than the other
The motor that lifts the weight faster has more power
Two motors with different powers
Maths Tip
GCSE physics equations will mostly require fractions
These are made up of the numerator (the top number) and the denominator (the
bottom number)
If the denominator decreases and the numerator stays the same, the whole fraction
increases
If the denominator increases and the numerator stays the same, the whole fraction
decreases
This is known as inverse proportionality
If the denominator stays the same and the numerator increases, the whole fraction
increases
If the denominator stays the same and the numerator decreases, the whole fraction
decreases
This is known as direct proportionality
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How to know whether the value of a fraction increases or decreases
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Worked Example
Two electric motors transfer 40 J of energy to lift a load. Motor A does this in 10
seconds, motor B does this is in 20 seconds.
Determine which motor is more powerful, and by how much.
Step 1: List the known quantities
Energy transferred for both motors, E = 40 J
Time for motor A, tA = 10 s
Time for motor B, tB = 20 s
Step 2: Write down the equation for power
P=
E
t
Step 3: Calculate the power for both motors by substituting values into the
power equation
For motor A:
PA =
E
tA
PA =
40
10
PA = 4 W
For motor B:
PB =
E
tB
PB =
40
20
PB = 2 W
Step 4: Determine which motor is more powerful
Motor A is twice (4 ÷ 2 = 2) as powerful as motor B
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1.1.11 Conservation & Dissipation of Energy

Conservation of Energy
The law of conservation of energy states that:
Energy cannot be created or destroyed, it can only be transferred from one store to
another
This means the total amount of energy in a closed system remains constant
Energy can be transferred from store to store usefully (to do work)
Or energy can be dissipated to the thermal store of the surroundings
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Examples of Energy Conservation
Conservation of energy applies to all energy transfers
Example 1: A bat hitting a ball
The moving bat has energy in its kinetic store
Some of that energy is transferred usefully to the kinetic store of the ball
Some of that energy is dissipated by heating to the thermal store of the bat, the ball, and
the surroundings
The impact of the bat and the ball cause the particles of the bat and ball to vibrate
The sound wave causes the air particles to vibrate
Conservation of energy: a bat hitting a ball
Example 2: An electric heater
Energy is transferred electrically from the mains supply to the thermal store of the heating
element
Some of that energy is usefully transferred to the thermal store of the surroundings by
heating the air particles in the room
Some of that energy is dissipated to the thermal store of the surroundings by radiation
(light)
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Conservation of energy: electric heater
Example 3: Rollercoasters
The roller coaster has energy in its gravitational potential store when it is on an elevated
piece of track
Energy is transferred usefully to the kinetic store as the rollercoaster gains speed as it
descends
Energy is transferred from the kinetic store to the gravitational store as the rollercoaster
climbs again
And energy is transferred usefully to the kinetic store as descends again
Energy is dissipated to the thermal store of the surroundings by heating due to friction
heating the wheels and track, and due to sound waves vibrating the air particles
As the rollercoaster in the diagram travels from A to D, the useful energy transfers that take
place are:
gravitational potential store → kinetic store → gravitational potential store → kinetic store
This is sometimes also described as
GPE ➝ KE ➝ GPE ➝ KE
Example 4: Trampoline
Whilst jumping, the person has energy in their kinetic store
When the person lands on the trampoline, most of that energy is transferred to the elastic
potential store of the trampoline
That energy is transferred usefully back to the kinetic store of the person as they bounce
upwards
Energy is transferred from the kinetic store of the person to the gravitational potential
store of the person as they gain height
Some of the energy is dissipated by heating to the thermal store of the surroundings (the
person, the trampoline and the air)
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
The useful energy transfers taking place are:
elastic potential energy ➝ kinetic energy ➝ gravitational potential energy
Useful energy transfers: person on a trampoline

Worked Example
Describe the energy transfers in the following scenarios:
a) A falling object
b) A battery powering a torch
c) A mass on a spring
Part (a)
For a falling object:
Energy is transferred mechanically from the gravitational potential store of the object to the
kinetic store of the object
Part (b)
For a battery powering a torch:
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Energy is transferred electrically from the chemical store of the cell to the thermal store of the
bulb
Part (c)
For a mass on a spring:
Energy is transferred mechanically from the elastic potential store of the spring to the kinetic
store of the mass
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1.1.12 Wasted Energy
Wasted Energy
In practice, most systems tend to be open systems
When energy transfers occur that are not useful, these are described as energy being
dissipated to the surroundings
Dissipated just means spread out
This is considered to be wasted energy
Often these less useful energy transfers often involve heating, light and sound
When energy is transferred to the thermal stores of the objects, the temperature of the
objects increases
The particles that make up the objects vibrate more, hence the transfer pathway is by
heating (of the particles)
Visible light is electromagnetic radiation
Therefore, when light is produced, energy is transferred by radiation
When sound is produced, the sound waves make the air particles vibrate as the wave
carries energy away
This increases the energy in the thermal store of the air, hence the transfer pathway is
by heating (of the particles)
Useful energy can be defined as:
The energy that is transferred from store to store and used for an intended purpose
Wasted energy can be defined as:
The energy that is not useful for the intended purpose and is dissipated to the
surroundings
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Worked Example
A student uses an electric motor to lift a load.
The motor turns a mechanism that lifts the load. Some of the energy transfers
are useful and the rest of the energy is wasted.
a) State the useful energy transfer occurring in this system.
b) State the wasted energy transfer occurring in this system.
Part (a)
The motor turns the mechanism that lifts the load
Therefore, the useful transfer is:
Energy in the kinetic store of the motor is transferred to the
gravitational potential store of the load
Part (b)
As the motor operates, friction causes a rise in the temperature of the
components and the surroundings
In this case, the energy transfer from the kinetic store of the motor to the
thermal store of the motor and the surroundings is not useful, hence it is a
wasted energy transfer
Energy is dissipated, by heating, to the surroundings

Exam Tip
Make sure you are able to identify "useful" and "wasted" energy as this is commonly
tested in exams! When describing wasted energy, make sure to say the energy is
dissipated to the surroundings, if you say the energy is simply "lost", this will not
gain you the mark as it implies energy is not conserved.
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Reducing Energy Loss
YOUR NOTES
Mechanical processes can become wasteful when they cause a rise in temperature
These processes often involve friction
When friction acts, it has the effect of transferring energy from the kinetic store by
heating to the objects and the surroundings
This energy cannot be used in a useful way, therefore it is called wasted energy
Energy that is transferred to the surrounding is said to be dissipated (spread out) to
the surroundings

Lubrication
Friction is a major cause of wasted energy in machines
For example, the gears on a bike can become hot if the rider has been cycling for a long time
Energy is wasted as it is transferred from the kinetic energy store of the bike to the
thermal energy store of the gears and the chain
This friction makes them become hot and transfers energy by heating to the thermal
energy store of the surrounding air
This wasted energy can be reduced if the amount of friction can be reduced
This can be achieved by lubricating the parts that rub together
Lubrication helps reduce friction in the parts of a cycle
Insulation
In many situations, the energy transferred by heating is wanted. For example:
When heating a home
When boiling a kettle
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If this energy can be prevented from dissipating, then less energy will be needed to replace
the wasted energy
This can be achieved by surrounding the appliance with insulation
The effectiveness of insulation depends upon:
How well the insulation conducts heat
How thick the insulation is
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1.1.13 Conduction of Heat

Conduction of Heat
Thermal conduction is the process where energy is transferred by vibrating particles in a
substance
The vibrating particles transfer energy from their kinetic store to the kinetic store of
neighbouring particles
The direction of energy transfer is always from hot to cold
The higher the thermal conductivity of a material, the higher the rate of energy transfer by
conduction across the material
Materials with high thermal conductivity heat up faster than materials with low thermal
conductivity
Materials with high and low thermal conductivity
Examples of substances with high thermal conductivity include:
Diamond
Aluminium
Graphite
Examples of substances with low thermal conductivity include:
Air
Steel
Bronze
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Factors Affecting Conduction
An insulator is a substance that is a poor thermal conductor
Examples include wool, plastic, wood
Insulators are used to reduce energy transfers, for example, to keep a house warm or build a
soundproof room
This is why in cold weather, a woollen jumper is worn to retain body heat and keep warm
The energy transfer through a layer of insulating material depends on:
The temperature difference across the material - the greater the temperature
difference, the more conduction
The thickness of the material - the thicker the material, the less energy will be
transferred by conduction
The thermal conductivity of the material - the higher the thermal conductivity, the
more energy will be transferred by conduction
Therefore, good insulators which keep the energy transfer through them as low as possible
have:
A low thermal conductivity
Layers that are as thick as possible
Insulation in the Home
Insulating the loft of a house lowers its rate of cooling, meaning less energy is lost to the
outside
The insulation is often made from fibreglass (or glass fibre)
This is a reinforced plastic material composed of woven material with glass fibres laid
across and held together
The air trapped between the fibres makes it a good insulator
It has a much lower thermal conductivity than the roof material
Several layers of insulation make it very thick and therefore decrease the rate of cooling
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Less heat is lost from a building with the help of insulation (filled cavity in walls)
Another aspect that affects the cooling of buildings is the walls
Houses in cold countries are fitted with cavity wall insulation which is made from blown
mineral fibre filled with gas
This lowers the conduction of heat through the walls from the inside to the outside
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1.1.14 Required Practical: Investigating Insulation
Required Practical 2: Investigating Insulation
Aim of the Experiment
The aim is to investigate the effectiveness of different materials as thermal insulators and
the factors that may affect the thermal insulation properties of a material
Variables:
Independent variable = Type of material
Dependent variable = Temperature, T (°C)
Control variables:
Volume of water
The temperature of the water at the start of the experiment
The thickness of each material
Equipment List
Resolution of measuring equipment:
Thermometer = 1 °C
Stopwatch = 0.01 s
Method
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1. Set up the apparatus by placing a small beaker inside the larger beaker
2. Fill the small beaker with boiling water from a kettle
3. Place a piece of cardboard over the beakers as a lid. It should have a hole suitable for a
thermometer and place the thermometer through this hole and into the water in the small
beaker
4. Record the temperature of the water in the small beaker and start the stopwatch
5. Record the temperature of the water every 2 minutes for 20 minutes, or until the water
reaches room temperature
6. Repeat the experiment, each time changing the cardboard for another insulating material
(in any order) and also without any insulation at all
An example of a table of results may look like this:
Analysis of Results
Plot a graph of temperature against time and draw a curve of best fit
Plot all the curves for each material on the same axis
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An example graph might look like this:

The graphs should show that the temperature falls quickly at high temperatures, then more
slowly (shown by the graph levelling out)
When the water is at a high temperature, there is a greater temperature difference
between it and room temperature. Therefore there is a greater energy transfer by
heating
When the water is at a low temperature, there is less temperature difference between
it and room temperature. Therefore, there is a lesser energy transfer by heating
The curve which takes the longest time for the temperature to drop is the shallowest
This material is the best insulator
Evaluating the Experiment
Systematic Errors:
Make sure the starting temperature of the water is the same for each material since this will
cool very quickly
It is best to do this experiment in pairs to coordinate starting the stopwatch and
immersing the thermometer
Only the top of the beaker is covered, so that energy is transferred by conduction through
the glass
An alternative to this experiment could be:
Putting the insulating materials around the beaker as well as on top of it
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Using one material with different thicknesses. This will show that the thicker the
material, the better the insulation
Use a data logger connected to a digital thermometer to get more accurate readings
Random Errors:
Make sure the hole for the thermometer isn't too big, otherwise, energy will be transferred
through the hole
Take repeated readings for each insulator
Read the values on the thermometer at eye level, to avoid parallax error
Safety Considerations
Keep water away from all electrical equipment
Make sure not to touch the hot water directly
Run any burns immediately under cold running water for at least 5 minutes
Do not overfill the kettle
Place the small beaker inside the large beaker first before pouring water in, since the small
beaker will become very hot
Make sure all the equipment is in the middle of the desk, and not at the end to avoid
knocking over the beakers
Carry out the experiment only whilst standing, in order to react quickly to any spills
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1.1.15 Efficiency

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Efficiency
YOUR NOTES
The efficiency of a system is a measure of the amount of wasted energy in an energy
transfer
Efficiency is defined as:
The ratio of the useful energy output from a system to its total energy input
If a system has high efficiency, this means most of the energy transferred is useful
If a system has low efficiency, this means most of the energy transferred is wasted
Efficiency can be represented as a decimal or as a percentage
The equations for efficiency are:
efficiency =
useful output energy transfer
total input energy transfer
efficiency =
useful power output
total power input
Since power is the energy transferred per unit time, power can also be used to calculate
efficiency
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YOUR NOTES
Worked Example
An electric motor has an efficiency of 35%. It lifts a 7.2 kg load through a height of 5
m in 3 s.
Calculate the power of the motor.
Answer:
Step 1: Write down the efficiency equation
Efficiency =
useful power output
× 100%
total power input
Step 2: Rearrange to make power input the subject
power input =
power output
power output × 100
OR power input =
efficiency ÷ 100
efficiency
Step 3: Calculate the power output
power output =
E
t
ΔE is equal to the change in gravitational potential energy as the load is lifted
∆ E P = mg ∆ h
∆E P = 7 . 2 × 9 . 8 × 5
∆ E P = 352 . 8 J
Therefore, power output =
352 . 8
3
power output = 117 . 6 W
Step 4: Substitute the values into the power input equation
power input =
117 . 6
117 . 6 × 100
OR power input =
0 . 35
35
power input = 336 W
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
YOUR NOTES
Exam Tip
Efficiency can be given in a ratio (between 0 and 1) or percentage format (between 0
and 100 %)
If the answer is required as a percentage, remember to multiply the ratio by 100 to
convert it: if the ratio = 0.25, percentage = 0.25 × 100 = 25 %
Remember that efficiency has no units
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1.1.16 Improving Efficiency
Improving Efficiency (HT only)
The efficiency of a device can be improved by reducing wasted energy transfers
Machines waste energy due to:
Friction between their moving parts
Air resistance
Electrical resistance
Sound
Reducing Friction
In a mechanical system, for example, there is often friction between the moving parts of
the machinery
This results in unwanted energy transfers by heating to the machinery and the
surroundings
Friction can be reduced by:
Adding bearings to prevent components from directly rubbing together
Lubricating parts
Lubricating parts of a bicycle to reduce friction
Reducing Electrical Resistance
In electric circuits, there is resistance as current flows through the wires and components
This results in unwanted energy transfers by heating to the wires, components and the
surroundings
Resistance can be reduced by:
Using components with lower resistance
Reducing the current
Reducing Air Resistance
Air resistance causes a frictional force between the moving object and the air that
opposes its motion
This results in unwanted energy transfers by heating to the object and the surroundings
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Air resistance can be reduced by:
Streamlining the shapes of moving objects

For example, a racing cyclist adopts a more streamlined posture to reduce the effects of
air resistance
Also, the bicycle, clothing and helmet are designed to allow them to go as fast as
possible
Many factors such as posture, clothes and bicycle shape must be considered when trying
to reduce air resistance
Reducing Noise
Sound is often created by moving parts of machinery
This results in unwanted energy transfers by heating to the surroundings as sound waves
cause the particles in the air and nearby objects to vibrate
Sound can be reduced by:
Tightening loose parts to reduce vibration
Lubricating parts

Exam Tip
When answering questions about improving efficiency, it is helpful to identify the
useful energy transfers and the wasted energy transfers. Remember, the efficiency
of a device is improved by increasing the useful energy transfers
and reducing the wasted energy transfers.
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