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Conservation of energy, energy transfers, conversions & efficiency
IGCSE AQA GCSE Physics Edexcel GCSE Physics OCR GCSE
Gateway Science Physics OCR GCSE 21st Century Science Physics
Doc Brown's school physics revision notes: GCSE
physics, IGCSE physics, O level physics, ~US grades 8, 9 and 10
school science courses or equivalent for ~14-16 year old students of
physics
Examples, calculations, Sankey diagrams, wasted energy
This page will answer many questions e.g.
What do we mean by efficiency in energy
transfer? How do you calculate efficiency? What is the
formula for efficiency? What does a Sankey diagram tell you? How do you draw and interpret a Sankey diagram?
Sub-index for this page
(a)
Law of
conservation of energy and a closed system
(b)
Types of energy transfer:
What do energy conversions involve?
(c)
Some 'domestic' energy
transfers in the home
(d)
More varied examples of
conservation - energy transfers between energy stores
(e)
Energy transfer and
efficiency - useful work output
(f)
Sankey diagrams and wasted
energy and energy analysis of using electrical appliances
(g)
Costs, efficiency and pay-back time for a variety of energy
strategies
(h)
Examples of reducing unwanted energy transfers - friction and air resistance
(i)
Examples of how to solve
and work
out efficiency calculation questions
See also
Types of energy - a comparison with examples explained,
energy store calculations gcse physics
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(a) Energy conservation and a
closed system
Know and understand that energy can be transferred
usefully from one form to another, or stored, or dissipated, but energy cannot be created or destroyed.
This is the law of
conservation of energy.
Another way of stating the law is to say
the ...
'total energy of a system remains
constant no matter what energy conversions take place'.
However, energy is only useful
if it can be converted from one form to another.
Examples - from a suitable
energy source ==> useful form (plus waste in most cases)
Energy stores have been described in
Types of energy store - a comparison with examples explained
Here we are interested in how
efficient are energy transfers to produce useful energy.
What do we mean by conservation of energy and a closed system?
A system is an object or objects
involved in a particular situation which can be described in its own context
without any energy being exchanged with its surroundings - the system does not
absorb energy from, or lose energy too, the surroundings.
If energy is gained or lost by the
system, it cannot be closed.
However, you can make an existing system
into a closed system by including other things as part of it.
e.g. a car and its kinetic energy is
limited because energy is being lost by friction (wheel-road) and air
resistance (car body-air), but if you include the air around it and the road
(the environment) you have 'constructed' a closed system.
Theoretically, irrespective of form, if
the total energy at the start of a process doesn't equal the total energy at
the end, that process can't happen.
You can use the work (E = Fd) and power
(P = E/t) formulae to calculate an energy transfer-conversion from one
energy store to another, but the formulae do not explain why the transfer
takes place, nor does it tell you how much of the energy involves useful
work or wasted energy. E can represent energy or work done - its all the
same!
See
Types of energy store - a comparison with examples explained,
mechanical work done and power calculations
If there are no frictional forces
operating, the work done on the object equals the work done = the energy is
transferred to a useful energy store.
However, this is rarely the case
since resistive forces are often present e.g. surfaces scraping against
each other, air resistance etc.
Work must be done against these
resistive forces which causes energy to be wasted - dissipated to the
surroundings as heat due to friction - increasing the thermal energy
store of the surroundings.
Under these circumstances, the energy
transferred to the useful energy store as useful work, will be less than
that transferred from the original energy store.
If work is done by the object itself,
the work done does actually equal the energy transferred from the objects
useful energy store.
See
Types of energy store - a comparison with examples explained,
mechanical work done and power calculations
Reminders:
Law of conservation of energy -
energy cannot be created or destroyed.
BUT, not all the energy in a system
is useful, there is always some wasted or dissipated energy and their
relative values can be quite different.
TOP OF PAGE and
sub-index
(b)
Types of energy transfer:
What do energy transfers-conversions involve?
You need to be a bit more specific than just
saying 'energy transferred' from x energy store to y energy store!
Energy is transferred
electrically
when a moving electrical charge (the current) is doing work against a
resistance.
e.g. a battery providing electrical
energy via the circuit to light a torch bulb.
Operating any electrical appliance or
device from mains circuit electricity.
Energy is transferred by
heating when
a hotter object or material transfers heat energy to a colder object or material.
e.g. boiling water in an electric kettle
- the hot element transfers heat to the water.
When you first put something to bake
in an oven, heat is transferred from the hot air to the colder baking
tin and contents.
Using a soldering iron to make an
electric circuit link.
Energy is transferred
mechanically
when a force acts on an object to move it or change its shape e.g. pushing,
pulling, stretching-expanding or squashing-compressing.
e.g. kicking a football - the force you
exert from your leg accelerates the football and give it kinetic energy.
A car engine moving the wheels of a
car.
Cutting a piece of cake!
Energy is transferred by
radiation,
usually the waves of electromagnetic radiation.
e.g. The Earth receives visible light,
infrared and ultraviolet radiation from the Sun.
Infrared radiation from an electric
fire.
Radio waves from a transmitter to a
receiver.
TOP OF PAGE and
sub-index
(c)
Some 'domestic' examples of energy transfers
Cooking 1: Our electricity supply is initially powered
from either a fossil fuel chemical energy store, a nuclear energy store or a
renewable energy store (hydroelectric, wind or solar etc.).
The initially energy store decreases and the
kinetic energy store of the turbine blades and generator increases.
The generator converts the kinetic energy
into electrical energy, which becomes thermal energy in a toasted sandwich maker the heat is
transferred to the bread by conduction.
The electrical energy is converted into
heat/thermal energy by the insulated electrical resistors in the iron cased
toaster (iron is a good conductor of heat) - the thermal store of the heating
elements is increased.
The thermal energy is transferred by
conduction to the iron grill and the sandwich, increasing both their energy
stores and cooking the sandwich.
See also
The Usefulness of electricity, transferring
electrical energy and cost calculations gcse physics revision notes
 Gas
fire appliance: The
natural gas (methane) is a chemical energy store.
On combustion the fuel's chemical energy
store decreases and the heat/thermal energy store of the waste gases increases.
The hot gases from a gas fire will always
rise due to the immediate formation of a rising convection current which carries
the heat around the room.
The decrease in the chemical energy store of
the fuel gas therefore increases the thermal energy of the contents of the room,
mainly by convective heat transfer.
The heat is also transferred by infrared
radiation emitted from the hot flame - from the higher temperature flame to the
lower temperature room.
Car headlamp
A car battery is a potential chemical
energy store. When using the car, the chemical energy store of the battery
decreases as electrical energy is produced to operate lights (visible EM
radiation), ignition systems (heat), wipers (KE) etc.,
In the case of the headlamps the thermal
energy store of the metal filament is increased (not LED lamp)
so some of the thermal energy becomes visible light and
infrared radiation ...
... hence an early morning case of infrared radiation! Unlike 'modern'
LED bulbs, 'old fashioned' filament bulbs emit quite a bit of IR heat
radiation (from the increased thermal energy store of the filament). You can detect this with a frosty car where the central portion
of the ice has melted on the transparent headlamp cover. Filament bulbs only
convert ~10% of the electrical energy into visible light energy, most of the
rest is converted into infrared EM radiation. The ice absorbs infrared
equivalent to the latent heat of fusion (melting) and changes to liquid
water. You can see this (in the above photographs) after the
headlamps have been switched on for a few minutes on a frosty morning. The
concentrated IR beam increases the thermal energy store of the plastic cover
and the ice and the central part of the lamp cover warms up first
melting the ice.
Energy store changes: The chemical
energy store of the battery decreases as it is converted into
electrical energy. The electrical energy increases the thermal
energy store of the metal filament of the bulb. The thermal energy
store of the filament decreases as it emits visible and infrared EM
radiation. The absorbed EM radiation increases the thermal energy
store of the headlamp cover and ice - causing the latter to melt.
Eventually all the energy involved from the battery increases the
thermal energy store of the surroundings.
A 'green' note: If there
is, and its happening now in the UK and other countries, a change
from very inefficient filament light bulbs to very efficient low
energy LED light bulbs, there will be quite a reduction in the
domestic demand for electricity. This reduced demand will help, on
closure fossil fuel power stations, reduce CO2 emissions,
reducing the greenhouse effect, and allow renewable energy resources
to take over more of our electricity generation.
From the efficiency of light production old
fashioned tungsten filament bulbs used in the home are very
inefficient - ~5% of the electrical energy is transferred as visible
light energy. The other ~95% of the energy ends up as thermal energy
i.e. increase the thermal energy store of the room and its contents.
 |
 |
Cooking 2: The initial energy store to produce
electricity has already been described with the toaster (and elsewhere on
this page). The electrical current does work on the resistance convert
electrical energy into heat energy - increasing its thermal energy store.
The electrical resistance elements of a cooker ring or a toaster
become hot enough to emit a strong beam of infrared radiation to heat
the contents of a pan or grill the toast.
Electrical energy is converted
into heat/thermal energy which increases the thermal energy store of the
heating elements and then increases the thermal energy store of the pan and
contents or bread being toasted.
Eventually all the heat is
wasted/dissipated to the surroundings, slightly heating up the kitchen.
See also
The Usefulness of electricity, transferring
electrical energy and cost calculations gcse physics revision notes
Using a mobile phone
The battery is a chemical energy
store (after charging).
The chemical energy is transferred as
electrical energy.
The electrical energy is converted
into light energy and sound energy.
There is also a little wasted thermal
energy from the electrical circuits operating the phone.
A HiFi system
Electrical energy is converted into
kinetic energy as the cones in the speakers are made to vibrate - their
kinetic energy stores are increased.
The kinetic energy of the vibrating
cones causes waves of sound energy to spread into the room.
Sound waves are vibrations in the
air - a sort of kinetic energy.
Much of the sound energy is absorbed
by objects in the room, so it dissipated-wasted as heat energy.
A small % of the sound energy
vibrates your ear drums, increasing their kinetic energy store, and the
ear 'system' sends electrical signals to the brain.
TOP OF PAGE and
sub-index
(d)
More varied examples of
conservation & energy transfers between energy stores
In all these examples you must treat them as
far as possible as a closed system (so include the surroundings) and be able to
account for all the energy transfers involved.
To put it as simply as possible:
Total energy input = Useful energy
output + Wasted (dissipated) energy
There is a separate section on
EFFICIENCY -
calculations and Sankey diagrams which deals with numerical
calculations and details of useful input/output data.
1.
When a gun fires, chemical energy
is converted into heat energy, sound energy, light energy, but mainly into
the kinetic
energy store of the bullet by way off the rapidly expanding hot gases from
the explosion.
When the bullet fires, the thermal
energy store of the gases produced is increased.
When the bullet embeds itself into some material the kinetic energy
of movement is converted into some sound energy, but mainly increases the
thermal energy store of the material it hits.
| Chemical
energy store of bullet |
== heat - hot gases ==> |
== mechanical
conversion ==> |
KE store of
bullet (and recoiling gun) |
== mechanical conversion
==> |
heat
energy - thermal store of material |
+ |
sound,
light, friction and heat losses to surroundings |
2.
Photovoltaic
solar panels convert light energy directly into electrical energy
which may be stored in a battery.
The Sun's nuclear energy and thermal
energy stores are decreasing and the energy is transferred by radiation to
the solar panel.
The chemical potential energy store of the battery is
increased by the transfer of energy in the electrical charge of current.
3.
TV and mobile phone: We
use a large number of electrical devices in the home e.g.
A TV converts electrical energy
into useful light and sound, but some waste heat from the electrical
circuits is produced. Eventually all the electrical energy is dissipated
in some way to the surroundings increasing its thermal energy store.
 In
charging a mobile phone battery
you convert mains electrical energy into useful chemical potential energy.
The electrical energy store decreases and the chemical potential energy
store increases.
When using your mobile phone the
useful chemical energy store decreases as it produces electrical energy, which in turn is converted
into useful light and sound energy when using the phone. However, there is
some wasted thermal energy added directly to the surroundings - you can
detect this wasted heat as your phone warms up as you are using it.
 4.
Wind
turbines convert kinetic energy into electrical energy. The kinetic
energy store of the wind decreases, the kinetic energy store of the turbine
blades increases.
This kinetic energy is converted into electrical energy by a
generator.
The turbine does work in turning the generator and this kinetic
energy is converted into electrical energy.
Some energy is wasted due to friction
of moving parts - energy dissipated to increase the thermal energy store
of the surroundings.
 5.
When
you wind up a clock you are converting chemical energy from your body
to mechanically create kinetic energy to increase the elastic potential
energy store of the clock spring.
The potential energy store of the spring
decreases as it moves the hands around giving them kinetic energy.
Suppose
instead of a spring you have a falling weight?
In this case the winding up
involves using kinetic energy to increase the gravitational potential energy
of the clock weight.
As the weight falls the GPE store decreases.
Although using the term 'kinetic
energy' seems ok, what you should appreciate that in winding up the
clock and when the clock is freely working, a force is acting through a
distance.
Since work = force x distance, your
bodies chemical energy used = work done in winding up clock = work done
in working the clock.
 6.
In
some hydroelectric power schemes, excess 'off-peak' electricity is
used to pump water back up into the reservoir.
This is mechanically using
electrical energy to increase the kinetic energy of the pumped-water to move
it upwards against the force of gravity.
The gravitational potential energy
store is
initially increased as the water builds up behind the
dam and then decreased when the water flows down through the generators.
At peak demand times, extra water is released,
accelerated by gravity, and so the dam's GPE energy store decreases and the
kinetic energy (KE) store of the water increases.
The KE store of the
water then decreases as it is mechanically converted into the kinetic energy
of the generator which converts its KE into electrical energy (with some
loss in sound and heat from friction).
The 'peak time' energy store changes
can be expressed in a simple diagram
| GPE store of water |
== gravitational
acceleration - mechanical conversion ==> |
KE store of
the flowing water |
== KE of rotating generator -
mechanical conversion ==> |
electrical energy |
+ |
friction
and heat losses to surroundings |
7. When you are cooking you are
converting electrical energy (electric cooker) or chemical energy (gas
cooker) into thermal energy to increase the thermal energy stores of the
cooker ring and then the pan and
its contents.
There will be heat energy losses due to convection, conduction
or radiation to increase the thermal energy store of the surrounding air.
8. When you
brake to slow down a moving
car and bring it to a halt, the kinetic energy store of the car is
decreased and energy is lost as thermal energy (heat), created by the friction between the
brake pads and the discs on the wheels.
This is an example of a mechanical
transfer between energy stores - resulting in initially increasing the
thermal energy store of the brake pads.
Eventually this excess heat
increases the thermal energy store of the surrounding air.
You are
mechanically using your chemical energy (from food) to create the force of
friction and the brakes mechanically convert the KE of the car into thermal
energy - work is being done against the forces of friction.
A little sound energy is also involved - adding to the waste energy
dissipated to the surroundings.
If you just take your foot of the
accelerator, on a level road, the car will eventually come to a halt due
to friction between the wheels and the road and the moving parts of the
engine, and also, air resistance as the air brushes over the car body.
BUT, the KE store of the car still decreases to the same amount as if
you were braking and the thermal energy store of the environment
increases the same amount too.
If a vehicles crashes into a
stationary object, the contact force causes energy to be
mechanically transferred from the vehicle's kinetic energy store to
elastic potential energy store of the crushed vehicle parts, the
thermal energy stores of the vehicle, object crashed into and the
surrounding air (including some sound energy too - which also ends up as
thermal energy!).
See also
Reaction times, stopping distances, safety
aspects. calculations including F=ma
gcse physics notes
9. When a
cricketer hits a cricket ball,
there are all sorts of energy changes going on. The bodies chemical energy
store is decreased as energy is used in the bodies muscles mechanical motion
on swinging the bat. Therefore the chemical energy is converted into increasing the kinetic energy store of
the bat as it is swung at the ball. When the ball is hit the kinetic energy store of the bat decreases
and the kinetic energy store of the moving ball is increased. However, some
of the kinetic energy of the 'bat and ball' is converted (wasted)
into sound and thermal energy - this eventually increases the thermal energy store of the
environment.
However, the wasted energy is NOT
wasted on the 3rd umpire in test cricket! The Umpire Decision
Review System is a technology-based system used in cricket to help the
match officials with their decision-making. The two on-field umpires or
players can choose to consult with the third umpire to consider a
decision of the on-field umpires. The technology used includes
microphones to detect small sounds (due to friction, from KE of
ball) made as the ball
hits bat or pad (or neither), and infra-red thermal imaging to detect temperature changes as
the ball hits bat or pad (heat from friction, from KE of ball).
If there is no contact between bat/glove & ball or ball & pad, there is
no increase above the background sound level and there is no 'hot spot'
due to friction,
The sound effect is mainly used in
the system these days?, so meet ...
... SNICKO the snickometer !!! The
sound (if any) of the 'snick' is detected by a sensitive microphone in
one of the cricket stumps.
The sound sequence of the movement of
the batsman and bat is then portrayed electronically on an
oscilloscope or a computer screen
linked to a piece of music technology software.
The sound trace is also synchronised
with a slow motion replay of the batsman's stroke.
10. Electrical machines that lift objects:
When a crane lifts an object, the motor usefully, and mechanically, converts
electrical energy into kinetic energy to lift the object. The lifted object
has increased its gravitational potential energy store. There will be
various losses due to - friction in the moving parts of the machine
producing heat and sound, heat losses from the resistance of the electrical
circuits (electrical store to thermal energy store).
| input of
electrical energy |
== electric motor -
mechanical conversion ==> |
useful KE
of motor lifting object |
== useful GPE store of object
increased - mechanical conversion |
+ |
heat and
sound losses to surroundings |
11. As a
parachutist is
dropped from an aircraft, the person has its maximum gravitational potential
energy (GPE) store.
As the person falls, so does their
GPE store as the GPE is mechanically converted into kinetic energy.
However, other energy conversions
take place to. Some of the GPE is converted into heat and sound by
air resistance. This happens both before and after the parachute is
opened.
On landing on the ground the
parachutist's GPE is reduced to zero and the rest of the kinetic energy
is converted to heat and sound.
The energy conversions are:
The descent: GPE ====>
heat + sound + kinetic energy
On landing: kinetic energy
====> heat + sound
12.
A road vehicle
A non-electric car
Fuel (oil, diesel, hydrogen) is a
store of chemical potential energy.
The chemical potential energy is
converted to thermal energy when its burned in the engines
cylinders.
The thermal energy store of the
engine expands gas to drive the moving engine parts to increase
their kinetic energy store - so the car moves!
There will be thermal energy
losses from friction to the thermal energy store of the surrounding
air (via air resistance) and moving part and road surface frictions.
Wasted or dissipated thermal
energy which cannot be used or reclaimed.
An electric car
When the batteries are charged
with electrical energy they become a chemical potential energy
store.
When an electric car moves, the
chemical energy store is converted into electrical energy.
The electrical energy drives a
motor to move the car whose kinetic energy store is increased.
There will be thermal energy
losses from friction to the thermal energy store of the surrounding
air (via air resistance) and moving part and road surface frictions.
Wasted or dissipated thermal
energy which cannot be used or reclaimed.
The electric car has less
moving parts than a conventional fossil fuelled car, so the
thermal energy loss due to friction should be less.
TOP OF PAGE
and sub-index
(e) Energy transfer and efficiency
- useful work output and wasted energy
Introduction- reminders
via a 'car' example:
Law of conservation of energy - energy
cannot be created or destroyed.
BUT, not all the energy in a system is
useful, there is always some wasted or dissipated energy and their relative
values can be quite different.
In practical terms:
Energy input =
Useful output (useful work) + wasted (dissipated) energy
e.g. an electric car can have an
efficiency of over 80%, that is over 80% of the stored electrical energy
actually gets used to move the car. Most energy loss is from friction from
moving parts and air resistance.
However, the electricity must be
generated - if its from fossil fuels, the efficiency of electricity
production drops to ~35%, but from renewable energy resources like wind
turbines the overall efficiency is much higher.
However, for a petrol/diesel fuelled car
the efficiency is less than 20%, meaning over 80% of the chemical energy
store of the fuel is lost as heat from the engine and friction from the
moving parts (more so than in an electric car) and air resistance.
In many cases the wasted or
dissipated energy increases the thermal energy store of the
surroundings.
So, ....
-
Know and understand that when energy is transferred
only part of it may be usefully transferred, the rest is ‘wasted’.
-
Know and understand that wasted energy is eventually
transferred to the surroundings, which will become warmer - increasing its
thermal energy store.
-
Be able to calculate the
efficiency of a device using the equations:
-
Efficiency can be expressed as a decimal fraction from 0.0
to 1.0, but it is usually quoted as a percentage.
-
The equation is quite simple and can be
calculated from energy or power data.
-
efficiency = useful energy out / total energy in
-
efficiency = useful power out / total power in
-
So, expressed as a percentage from 0 to
100
-
With the x100 the
efficiency has a value between 0% and 100%.
-
There are other ways to express the
efficiency formula e.g.
-
efficiency = useful energy
transferred to device / total energy supplied to the device
-
You must be able to calculate
efficiency as a decimal fraction (i.e. omit the x 100) or as a percentage
(0-100%).
-
-
The efficiency formula
triangle if you need to rearrange the equation to calculate energy in or
energy out.
-
It should be pointed out
that virtually no device is 100% efficient, there is no such device as a
perfect machine.
-
Friction is one of the principal ways
in which energy is wasted when machines are operating.
-
This is because when any work is done
mechanically, friction forces must be overcome because moving parts
are rubbing against each other.
-
Work is done against the
resistive force of friction.
-
The friction produces thermal energy (things
heat up, and often
some sound too) which is lost to increase the thermal energy store of
the machine and its surroundings.
-
This wasted energy, by definition,
cannot contribute to the useful work output.
-
The heat may be conducted
away or radiated away to increase the thermal energy store of the
surroundings - the machine itself or surrounding air.
-
Wherever possible, lubricants like
oil and grease, which flows easily, are used to minimise the friction between
moving parts that touch each other - bicycles, cars and locomotives are
good examples of the application of lubrication.
-
Without the use of lubricants on
moving parts, any machine can overheat causing damage - very expensive!
-
So, more useful work is done, less
wasted energy, efficiency increased and money save on fuel and repairs!
A good example is oiling the gears
and axles on a mountain bike.
The same arguments apply to any
moving machinery where one surface has contact with another.
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sub-index
(f)
Sankey diagrams and efficiency - wasted energy
and energy analysis of using electrical appliances
These are quantitative diagrams to show
how the energy is distributed in two or more ways - useful and waste energy.
A generalised Sankey diagram
E = the energy input, U = useful
work or energy output, W = wasted (dissipated) energy
From the law of conservation of
energy: E = W + U
(Remember W is usually one form of
energy, but U could involve several forms of energy.)
Be able to interpret and draw a Sankey diagram.
-
You should be able to use a Sankey diagram to calculate the
efficiency of an appliance.
-
From a Sankey diagram you can
see quite clearly in a visual way what happens to the energy input into a
device ie what proportion of energy was useful and how much energy was
wasted.
-
The breadth of the base of each arrow
is proportional to the percentage of that energy output.
-
The greater the width of the
'arrow' the greater proportion of energy it represents.
-
-
Sankey diagram for an electric motor e.g. in a domestic appliance.
-
An electric motor illustrates
the idea of a Sankey diagram.
-
You will find an electrical
motor in devices such as an electric drill, washing machine, food mixer,
electric car etc. etc. A lot of our lives runs on electrical power!
-
The Sankey diagram above analyses what
happens to every 100 J of electrical energy that is used by the electric
motor.
-
This electric motor only has an efficiency of 56%
useful energy out as kinetic energy with losses of 17% sound from
friction-vibration and 27% heat energy loss from moving parts friction or
warm electrical wiring in the motor.
-
In this example the numbers are easy, but whatever the
numbers are, from the Sankey diagram, you need to be able to get to the
proportion of useful energy and covert it to a percentage of the total
energy input.
-
Sankey diagram for a cooling fan
-
The Law of conservation of energy
states that energy cannot be created but only changes from one form to
another.
-
Know that appliances transfer energy but
they rarely transfer all of the energy to the place we want, but whatever
happens to the energy, its neither lost nor gained, but not all of it is
usefully transferred.
-
The Sankey style diagram above illustrates how
you can represent what happens to the energy when some kind of energy
consuming device is in operation.
-
The input energy quantity indicated by the
purple arrow (left) must equal the useful energy output of the blue arrow
(right) plus the wasted energy
output of the red arrow (down).
-
If you can decrease the energy wasted
you can increase the efficiency of the device.
-
Appreciate that we need to know the efficiency
of appliances so that we can choose between them, including how cost
effective they are, and how to improve them.
-
Devices eg industrial machines,
household appliances, light bulbs etc. can only be useful if they can
efficiently transform one form of 'source' energy ('total input') into an
appreciable percentage of a 'useful' energy ('useful output').
-
Such devices should be designed
to 'waste' as little energy as possible, the less waste energy, the greater
the efficiency of the device.
-
See the energy flow diagram and
efficiency formula 'triangle' above and the calculation of efficiency and
Sankey diagram further down the page.
-
It should be pointed out
that virtually no device is 100% efficient, there is no such device as a
perfect machine.
-
Whether of not the energy
outputs are useful or waste, most of the energy input in a device ultimately
ends up as heat energy.
-
The most useful energy sources
are in a sense 'highly concentrated' like a battery or a fuel like petrol,
but as the energy is used you cannot recover the waste energy - it
has been dissipated to the surroundings and become useless heat energy
in this 'diluted' form.
-
See
Methods of reducing heat transfer eg in a house
and investigating insulating properties of materials
Further examples of energy transfer analysis
(BUT not using a Sankey diagram, the problems are
set out as a data table to solve using the law of conservation of
energy)
Q1 is
based on using a hair dryer
| electrical |
energy => |
useful/wasted
energy outputs |
| energy input |
transfers as a |
3 J/s of wasted sound energy |
| of 600 J/s to |
hair dryer |
590 J/s of useful heat energy |
| the appliance |
is being used |
? J/s of ? energy |
Q1 (a) The table above summarises what happens to the
energy input and output of an electrical appliance.
What is the most likely missing quantity and form of output energy when the
hair dryer is in use?
Answer:
7 J/s of useful
kinetic energy
Comment: A fan has to operate to blow
the warm air out.
| electrical |
energy => |
useful/wasted
energy outputs |
| energy input |
transfers as a |
5 J/s of useful kinetic energy |
| of 400 J/s to |
hair dryer |
393 J/s of useful heat energy |
| the appliance |
is being used |
? J/s of ? energy |
Q1 (b) The table summarises what happens to the energy input and output of an electrical appliance.
What is the most likely missing quantity and form of output energy when the
hair dryer is in use?
Answer:
2 J/s of wasted
sound energy
Comment: Sound is of no obvious use.
| electrical |
energy => |
useful/wasted
energy outputs |
| input energy |
transfers as a |
4 J/s of useful kinetic energy |
| of 300 J/s to |
hair dryer |
1 J/s of wasted sound energy |
| the appliance |
is being used |
95
J/s of wasted heat energy |
| |
? J/s of ? energy |
Q1 (c) The table summarises what happens to the energy input and output of an electrical appliance.
What is the most likely missing quantity and form of output energy when the
hair dryer is in use?
Answer:
200 of J/s of useful
heat energy Comment: There will be
losses due to friction of the moving parts e.g. the electric
motor and fan blower
Q2 is
based on using a food mixer
| electrical |
energy => |
useful/wasted energy outputs |
| input energy |
transfers as a |
50 J/s of wasted sound energy |
| of 1000 J/s to |
food mixer |
400 J/s of useful kinetic energy |
| the appliance |
is being used |
? J/s of ? energy |
Q2 (a) The table summarises what happens to the energy input and output of an electrical appliance.
What is the most likely missing quantity and form of output energy when the
food mixer is in use?
Answer:
550 J/s of wasted
heat energy
Comment: Friction of the moving parts of
the mixture - sticky food mix will increase it.
| electrical |
energy => |
useful/wasted energy outputs |
| input energy |
transfers as a |
80 J/s of wasted sound energy |
| of 1200 J/s to |
food mixer |
620 J/s of wasted heat energy |
| the appliance |
is being used |
? J/s of ? energy |
Q2 (b) The table summarises what happens to the energy input and output of an electrical appliance.
What is the most likely missing quantity and form of output energy when the
food mixer is in use?
Answer:
500 J/s of useful
kinetic energy
Comment: Useful energy to do the mixing.
| electrical |
energy => |
useful/wasted energy outputs |
| input energy |
transfers as a |
370 J/s of useful kinetic energy |
| of 800 J/s to |
food mixer |
400 J/s of wasted heat energy |
| the appliance |
is being used |
? J/s of ? energy |
Q2 (c) The table summarises what happens to the energy input and output of an electrical appliance.
What is the most likely missing quantity and form of output energy when the
food mixer is in use?
Answer:
30 J/s of wasted
sound energy
Comment: Sound energy is of no use.
Q3 is
based on using a CD-HiFi system
| electrical |
energy => |
useful/wasted energy outputs |
| input energy |
transfers as a |
2 J/s of useful kinetic energy |
| of 200 J/s |
CD-HiFi system |
192 J/s of wasted heat energy |
| to the |
is being |
5 J/s of useful sound energy |
| appliance |
used |
? J/s of ? energy |
Q3 (a) The table summarises what happens to the energy input and output of an electrical appliance.
What is the most likely missing quantity and form of output energy when the
CD-HiFi system is in use?
Answer:
1 J/s of useful
light energy
Comment: You need to be able to see what
is going on!
| electrical |
energy => |
useful/wasted energy outputs |
| input energy |
transfers as a |
4 J/s of useful kinetic energy |
| of 500 J/s |
CD-HiFi system |
2 J/s of useful light energy |
| to the |
is being |
464 J/s of wasted heat energy |
| appliance |
used |
? J/s of ? energy |
Q3 (b) The table summarises what happens to the energy input and output of an electrical appliance.
What is the most likely missing quantity and form of output energy when the
CD-HiFi system is in use?
Answer:
30 J/s of useful
sound energy
Comment: Needed to hear the output
| electrical |
energy => |
useful/wasted energy outputs |
| input energy |
transfers as a |
3 J/s of useful kinetic energy |
| of 400 J/s |
CD-HiFi system |
1 J/s of useful light energy |
| to the |
is being |
20 J/s of useful sound energy |
| appliance |
used |
? J/s of ? energy |
Q3 (c) The table summarises what happens to the energy input and output of an electrical appliance.
What is the most likely missing quantity and form of output energy when the
CD-HiFi system is in use?
Answer:
376 J/s of wasted
heat energy
Comment: There is usually heat losses in
electrical circuits.
| electrical |
energy => |
useful/wasted energy outputs |
| input energy |
transfers as a |
287.5 J/s of wasted heat energy |
| of 300 J/s |
CD-HiFi system |
0.5 J/s of useful light energy |
| to the |
is being |
10.0 J/s of useful sound energy |
| appliance |
used |
? J/s of useful ? energy |
Q3 (d) The table summarises what happens to the energy input and output of an electrical appliance.
What is the most likely missing quantity and form of output energy when the
CD-HiFi system is in use?
Answer:
2.0 J/s of useful
kinetic energy
Comment: The CD needs to rotate.
Q4 is
based on using a washing machine
| electrical |
energy => |
useful/wasted energy outputs |
| input energy |
transfers as a |
1200 J/s of useful kinetic energy |
| of 3000 J/s to |
washing machine |
10 J/s of wasted sound energy |
| the appliance |
is being used |
? J/s of ? energy |
Q4 (a) The table summarises what happens to the energy input and output of an electrical appliance.
What is the most likely missing quantity and form of output energy when the
washing machine is in use?
Answer:
1300 J/s of useful
heat energy and 490 J/s of wasted heat energy
Comment: You need kinetic energy to do the wash by rotating
the drum and clothes, but heat energy loss from friction in
moving parts, also conduction out of machine - though should
be well insulated
| electrical |
energy => |
useful/wasted energy outputs |
| input energy |
transfers as a |
5 J/s of wasted sound energy |
| of 2000 J/s to |
washing machine |
1485 J/s of useful/wasted heat energy |
| the appliance |
is being used |
? J/s of ? energy |
Q4 (b) The table summarises what happens to the energy input and output of an electrical appliance.
What is the most likely missing quantity and form of output energy when the
washing machine is in use?
Answer:
510 J/s of useful
kinetic energy
Comment: You need kinetic energy to
rotate the drum and clothes to do the wash.
| electrical |
energy => |
useful/wasted energy outputs |
| input energy |
transfers as a |
900 J/s of kinetic energy |
| of 2500 J/s to |
washing machine |
1593 J/s of useful/wasted heat energy |
| the appliance |
is being used |
? J/s of ? energy |
Q4 (c) The table summarises what happens to the energy input and output of an electrical appliance.
What is the most likely missing quantity and form of output energy when the
washing machine is in use?
Answer:
7 J/s of wasted
sound energy Comment: sound is of
no use and indicates the machine is vibrating, difficult to
avoid this loss.
TOP OF PAGE and
sub-index
(g) Costs, efficiency and pay-back time for a variety of energy
strategies
TOP OF PAGE and
sub-index
(h)
Examples of reducing unwanted energy transfers - friction and air resistance
A system consists of an object or objects
and the total energy in a system is constant - one expression of the law
of conservation of energy - energy cannot be created or destroyed.
e.g. no mechanical device cannot work
perfectly, there are always energy losses.
When anything moves, in most cases there
is a friction force operating which causes energy to be lost.
When things rub together, work is
done against the resistive force of friction raising the temperature
of the system.
This also includes air resistance
- so in a moving car you get resistance as it moves through air as
well as all the friction associated with the moving parts of the car
(engine and wheels) and friction between the tyre and road surfaces.
This work generates thermal energy
which is lost and spread out into the surrounding thermal energy store -
dissipated, and is therefore not useful energy - waste energy
can't be used during the overall energy transfer .
This raises the temperature of the
surrounding thermal energy store e.g. air, water or road surface etc.
and you cannot extract or reclaim this lost thermal energy
There are several ways you can reduce
wasted energy i.e. energy lost from a useful energy store to a useless
energy store e.g.
In the case of moving machinery an
application of oil and grease considerably reduces the friction and
therefore the waste heat energy generated by surfaces rubbing together.
The lubricant smoothes the surfaces
so they rub against each other with less friction.
The lubricant must be liquid (e.g. oil)
or semi-liquid (eg grease) so that it spreads easily over the contact
surfaces so that the two surfaces move smoothly over each other e.g. wheel bearings
on a car axle or the pistons in the a engine's cylinder.
lubrication helps anything that moves
on wheels to move more slowly - less friction - less energy wasted and
lost to the surroundings - heat energy is dissipated to the thermal
energy store of the surrounding air.
For examples of reducing energy losses
in the home see ...
More on methods of reducing heat transfer eg in a house
and investigating insulating properties of materials
For examples of reducing water friction and air
resistance see ...
Acceleration,
friction, drag effects and terminal velocity experiments
gcse physics revision notes
and in these examples you are
reducing the loss from a kinetic energy store to the surrounding
air/water thermal energy store
TOP OF PAGE and
sub-index
(i)
Examples of how to solve work out efficiency calculation
questions
(see also
Types of energy store,
mechanical work done and power calculations
You need to use other formulae apart from the
equation for efficiency.
e.g. energy transferred = worked
done E (J) = force (N) x distance (m)
power (W) = energy transferred
(J) / time taken (s)
Exemplar 'efficiency' questions worked out
for you
Q1
An electric kettle transfers 50 000 J of electrical energy into an electric
kettle in 40 seconds.
Measurements of the temperature rise,
mass of water and its specific heat capacity enable you to calculate that 40 000
J of energy were added to the water's thermal energy store.
(See
Specific heat capacity: How to determine it, use of data,
calculations and thermal energy stores)
(a) What was the percentage efficiency of
the electric kettle?
% Efficiency = 100 x useful energy
output / total energy input
%
Efficiency = 100 x 40 000 / 50
000 =
80%
(b) What was the measured power rating of
the electric kettle.
power = work done / time taken =
energy transferred (J) / time taken (s)
Power
in watts = 50 000 / 40 =
1250
W (1.25 kW)
(c) What was the useful power output of
the electric kettle?
Efficiency = 100 x useful power
output / total power input
useful power output = efficiency x
total power input / 100
useful power output = 80 x 1250 / 100
= 0.8 x 1250 = 1000 W
Q2
An electrical appliance includes an electric motor, is found to be 75% efficient.
If the appliance has a maximum power
input of 800 W
(a) What is the useful power output?
Efficiency = 100 x useful power
output / total power input
useful power output = efficiency x
total power input / 100
Efficiency = 100 x useful power
output / total power input
useful power output = 75 x 800 / 100
= 0.75 x 800 =
600 W
(b) If the appliance runs for two minutes
how many joules of energy are wasted?
power = 800 W = 800 J/s
energy input for 2 minutes = 800 x 2
x 60 = 96,000 J
since the appliance is 75% efficient,
then 25% of the energy is wasted
therefore energy wasted = 25 x 96,000
/ 100 = 0.25 x 96,000 =
24,000 J
'useless' energy
(c) If the motor of another electrical
appliance transfers 120 J of useful energy for every 150 J of electrical
energy supplied.
(i) What is the efficiency of the
motor?
% Efficiency = 100 x useful energy
output / total energy input
% efficiency =
100 x 120 / 150 =
80%
Q3
After winding up, a clockwork toy car stores 400 J of elastic potential energy.
When allowed to run, 320 J of the toy's
energy store is released as useful kinetic energy.
(a) What is the % efficiency of the
clockwork motor of the toy car?
% efficiency = 100 x useful energy
output / total energy input
% efficiency = 100 x 320 / 400
= 80%
(b) If the toy runs for 20 seconds, what
is the actual useful working power of the toy?
power = useful work done / time taken
power = 320 / 20 =
16 W
(If you ignore energy loss due to
friction, the original maximum power output would be 400 / 20 = 20 W)
Q4 An electrical machine has a useful power
output of 3.0 kW from a total power input of 4.0 kW
(a) What is the efficiency of the
machine?
% efficiency = 100 x useful energy
output / total energy input
% efficiency = 100 x 3.0 / 4.0
= 75% (0.75
as a decimal fraction)
(b) How much electrical energy is
transferred to the machine in 5.0 minutes?
P = E / t, E = P x t, P = 4.0 kW =
4000 J/s, t = 5 x 60 = 300 s
therefore E transferred = P x t =
4000 x 300 = 120,000 J =
120
kJ
(c) If, in a given time, 6.0 x 106
J of electrical energy are transferred to the machine, how many joules of
useful work are obtained in that same time?
efficiency = useful energy output /
total energy input
useful energy output = efficiency x
total energy input
useful energy output = 0.75 x 6.0 x
106 = 4.5 x 106
J
Q5 A sprinter's
body applies a force of 80 N for a sprint distance of 100 m.
In the process the runner used 50 000 J
of chemical energy from the body's food store.
(a) What is the efficiency of the
sprinter?
useful work done = applied force x
distance
work done = 80 x 100 = 8000 J
% efficiency = 100 x useful
energy output / total energy input
% efficiency = 100 x 8000 / 50 000 =
16%
(b) What has happened to the rest of
the energy?
When you take exercise, your body
becomes temporarily hotter. A lot of the chemical energy being
transferred ends up increasing the thermal energy store of your
body.
Q6
Suppose (i) an electrical car is 80% efficient in its use of electrical energy
and (ii) the electricity is generated from a fossil fuelled power station with
an efficiency of 30%.
(a) What is the overall efficiency of the
energy transfer of original chemical energy into the kinetic energy store of
the car?
The answer is basically 80% of 30%
Overall efficiency is
30 x 100 / 80 =
24%
(b) How much chemical energy from a
fossil fuel energy store is needed to provide a car with 450 kJ of kinetic
energy?
450 kJ only represents 24% of the
energy from the fossil fuel.
You therefore need to scale up by
a factor of 100/24.
Therefore energy required from the
fossil fuel chemical energy store = 450 x 100 / 24 =
1875 kJ
(just as a check, as in maths
lessons!, 24% of 1875 = 24 x 1875 / 100 = 450 kJ)
Q7 An electric
motor is supplied with 2000 J of electrical energy per minute.
If 500 J of the electrical energy is lost
as thermal energy from the circuits to the surroundings, what is the
efficiency of the electric motor?
If 500 J is wasted energy, 2000 - 500
= 1500 J of useful work per minute.
Efficiency = useful work / total
energy input = 1500 / 2000 =
0.75 (or
75% efficiency)
Q8
An LED lamp has an efficiency of 0.90.
If the LED lamp is supplied with 500 J of
electrical energy, how much energy is converted to light energy?
Efficiency = useful energy output /
total energy input
Rearranging gives: Useful light
energy output = Efficiency x Total energy input
Light energy output
= 0.90 x 500
= 450
J
Q9
Sankey diagram for a cooling fan
Above is the Sankey diagram for the
energy input and outputs for a working cooling fan.
Assume 6000 J of electrical energy
is supplied to the fan every minute.
(a) How much useful energy is
transferred per minute?
From the scale of the Sankey
diagram you can see that:
10 squares equals the total
input = 100 %
≡
6000 J/min
On the right the useful
kinetic energy driving the fan around is equal to 8 squares.
Therefore useful energy out
put = 6000 x 8 /10 =
4800 J/min
(b) What is the % efficiency of
the cooling fan?
% efficiency = 100 x useful energy
transferred to device / total energy supplied to the device
Therefore the
efficiency of this device
= 100 x 4800 / 6000
= 80%
In other words 80% of the
electrical energy input is transferred to the kinetic energy store
of the rotating fan.
(c) (i) What % of the input energy is
wasted through a heating effect? (ii) What is this loss in J/min?
(iii) What causes the friction and what happens to the energy?
(i) The energy loss as thermal
energy equals 1.5 squares on the Sankey diagram.
The % wasted energy = 100 x
1.5/10 =
15%
(ii) This equates to 6000 x 15 /
100 =
900 J/min
(iii) What causes the friction
and what happens to the wasted energy?
There are two sources of
friction.
Friction between moving parts
in the fan motor.
Friction between the fan and
the air it is passing through.
In both cases work is done
against the force of friction.
The energy lost from friction
increases the thermal energy store of the surrounding air -
wasted - dissipated. (Strictly speaking this includes the sound
energy too)
(d) What is the rate of energy
loss due to sound vibrations in J/s?
The energy loss due to sound is
0.5 of a square on the Sankey diagram.
Therefore the loss of energy =
6000 x 0.5 / 10 = 300 J/min = 300 / 60 =
5 J/s
(The sound vibrations are caused
by friction as the surfaces of moving parts rub against each other.
This energy is eventually dissipated as thermal energy.
(e) How can the energy losses be
minimised.
Quite simply, a drop of oil on
the fan axle.
This allows surfaces to rub over
each other more smoothly, reducing the friction effects.
The lubricant reduces friction
and increases the output of useful energy, less wasted as heat or
sound.
(f) What is the power rating of
the fan?
6000 J is supplied per min. time
1 min = 60 s, power of 1 W = 1 J/s
Power = energy transferred (J) /
time (s) = 6000 / 60 =
100 W
Q10 An electric motor in a toy train does 0.2 J of work to accelerate
it to a speed of 25 cm/s.
(a) If the toy train has a mass of 3500
g, what is the efficiency of the motor?
First calculate the kinetic energy
store of the train.
mass = 3500/1000 = 3.50 kg, speed =
(25/100) = 0.25 m/s
KE = 1/2mv2
= 0.5 x 3.5 x 0.252 = 0.1094 J
Efficiency = useful
energy out / total energy input = 0.1094 / 0.20 =
0.55 (2
s.f.)
Efficiency = 0.55 x
100 =
55% (2 s.f.)
(b) Why is the efficiency much less than
100%?
Apart from a little sound, most
energy is lost (dissipated) from the friction of the moving parts of the
electric motor and friction between the wheels and the rails - all
energy lost ends up increasing the thermal energy store of the
surroundings.
For more power calculations see
Types of energy & stores and calculations of
mechanical work done and power
(see KS3 questions)
and Q9 GCSE on this page
TOP OF PAGE and
sub-index
Energy resources, and
transfers, work done and
electrical power supply revision notes index
Types of energy & stores - examples compared/explained, calculations of
mechanical work done and power
Chemical *
Elastic
potential energy *
Electrical
& electrostatic
*
Gravitational potential
energy
Kinetic
energy store *
Nuclear
energy store *
Thermal
energy stores *
Light energy *
Sound energy
Conservation of energy,
energy transfers-conversions, efficiency - calculations and
Sankey diagrams gcse physics
Energy resources: uses, general survey & trends,
comparing renewables, non-renewables, generating electricity
Renewable energy (1) Wind power and
solar power, advantages and disadvantages gcse physics revision
notes
Renewable energy (2) Hydroelectric power and
geothermal power,
advantages and disadvantages
gcse physics
Renewable energy (3) Wave power and tidal barrage power,
advantages and disadvantages
gcse physics
See also
Renewable energy - biofuels & alternative fuels,
hydrogen, biogas, biodiesel gcse chemistry notes
Greenhouse
effect, global warming, climate change,
carbon footprint from fossil fuel burning gcse chemistry
The absorption and emission of radiation by
materials - temperature & surface factors including global warming
The Usefulness of Electricity gcse
physics electricity revision notes
and
The 'National Grid' power supply, mention of small
scale supplies, transformers gcse
physics notes
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