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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.
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
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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
A Sankey diagram for a cooling fan (above and below) presented in terms of
absolute energy values in kJ or % useful output and % wasted energies.
The Sankey diagram for an electric motor.
SET A Questions - 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?
Answers to set A
questions
| 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?
Answers to set A
questions
| 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?
Answers to set A
questions
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?
Answers to set A
questions
| 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?
Answers to set A
questions
| 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?
Answers to set A
questions
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?
Answers to
set A questions
| 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?
Answers to
set A questions
| 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?
Answers to
set A questions
| 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?
Answers to
set A questions
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?
Answers to
set A questions
| 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?
Answers to
set A questions
| 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?
Answers to
set A questions
Set B Questions - 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
Set B
Questions on efficiency and energy transfer analysis
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?
(b) What was the measured power rating of
the electric kettle.
(c) What was the useful power output of
the electric kettle?
ANSWERS to Set B Questions
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?
(b) If the appliance runs for two minutes
how many joules of energy are wasted?
(c) If the motor of another electrical
appliance transfers 120 J of useful energy for every 150 J of electrical
energy supplied.
What is the efficiency of the
motor?
ANSWERS to Set B Questions
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?
(b) If the toy runs for 20 seconds, what
is the actual useful working power of the toy?
ANSWERS to Set B Questions
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?
(b) How much electrical energy is
transferred to the machine in 5.0 minutes?
(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?
ANSWERS to Set B Questions
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?
(b) What has happened to the rest of
the energy?
ANSWERS to Set B
Questions
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?
(b) How much chemical energy from a
fossil fuel energy store is needed to provide a car with 450 kJ of kinetic
energy?
ANSWERS to Set B Questions
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?
ANSWERS to Set B Questions
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?
ANSWERS to Set B Questions
Q9
based on the 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?
(b) What is the % efficiency of
the cooling 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?
(d) What is the rate of energy
loss due to sound vibrations in J/s?
(e) How can the energy losses be
minimised.
(f) What is the power rating of
the fan?
ANSWERS to Set B Questions
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.
(b) Why is the efficiency much less than
100%?
ANSWERS to Set B Questions
For more power calculations see
Types of energy & stores and calculations of
mechanical work done and power
More
examples of Sankey diagrams
A Sankey diagram for an electric motor
Sankey diagram for an electric cooling fan
INDEX of notes on
conservation of energy, costs and wasted energy
Keywords, phrases and learning objectives
on energy conservation
Be able to do e
nergy transfer efficiency calculations by
interpreting Sankey diagrams in terms of joules (kJ) of energy or
percentage (%) energy output from a 100% input.
Be able to describe and discuss the useful
work compared with wasted energy from a Sankey diagram or give data.
