A2 Science In Society 3.5
Teacher Notes
Introduction
This short activity introduces students to some of the units used for
energy and power. The approach is based on that adopted by
Professor David Mackay in his e-book Sustainable energy –without the
hot air which is available free on a web site (www.withouthotair.com).
It is worth referring to pages 24 - 28 (pdf files 37 – 41) in Professor
David MacKay’s book called: Sustainable energy – without the hot air
which is freely available on line as a pdf file from this web address:
http://www.withouthotair.com/. This book will be the basis of an activity
about renewable energy in this set of resources.
David MacKay has recently (September 2009) been appointed as the
UK Government's Energy Adviser in the Department of Energy.
Science explanations
Oe Energy from fuels and other
resources can be measured in
Joules (J) or Megajoules (MJ), in
kilowatt hours (KWh) or in million
tonnes of oil equivalent (toe).
Oj The efficiency of a process is the
percentage of the energy originally
available which ends up where you
want it to be. In many processes,
energy is wasted and ends up
heating pats of the system or its
surroundings.
You may prefer to use parts of this activity at the start of the class
which requires the particular units rather than doing so many calculations all together.
The activity
Energy
1. A kilowatt hour is a unit of energy. How many joules of energy are equivalent to 1 kWh?
1 kW = 1000 W = 1000 J/s
1 hour = 60  60 s = 3600 s
1 kWh = 3 600 000 J
Power
2. A desk lamp has a 40 watt bulb. What is the power of this bulb (to the nearest whole number)
measured in kWh/day?
Power = 40  24  1000  1 kWh/day
3. A hair drier has a power of 2 kilowatts (kW). What is the power of the drier measured in kWh/d?
Power = 2  24  48 kWh/day
4. A typical mobile phone charger has a power of about 0.5 W when connected to the mains but not
being used to charge a phone. Estimate the power saving for the UK in kWh/day per person if
everyone unplugged their chargers when not in use. Comment on the value you get.
Power = 0.5  24  1000 kWh/day
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©The Nuffield Foundation, 2009
Copies may be made for UK in schools and colleges
A2 Science In Society 3.5
Teacher Notes
Assume that on average every person in the UK has a phone and charger. Assume that they all
leave their chargers plugged in when not in use and the time the charger is actually used is relatively
small.
Power = 0.5  24  1000 kWh/day per person
 0.01 kWh/day per person
This is a trivial power compared to the total energy use of 140 kWh/day per person (see question 6).
We are not going to solve our environmental problems by unplugging mobile phone chargers – even
if everyone could be persuaded to do so. As David Mackay points out the energy saved in switching
off the charger for one year is equal to the energy needed to heat a single hot bath.
5
Waste incinerators are used to generate electricity. In the UK (population 60 million) waste
incineration delivers a total power of 7 TWh per year. In Denmark (population 5.5 million) waste
incineration delivers 10 TWh per year. 1 TWh (one terawatt-hour) is equal to one billion kWh.
Calculate the kWh/day per person of power from waste incinerators in the two countries and
comment on the values.
UK: power per person = 7  109  (365  60  106) kWh/day per person
= 0.3 kWh/day per person
Denmark: power per person = 10  109  (365  5.5  106) kWh/day per person
= 5 kWh/day per person
So, per capita, the Danes generate about 13 times more energy per person from waste that we do in
the UK. This illustrates the advantage of working in the power units kWh/day per person
Power and energy
6 In 2007, the total energy used, for all purposes, in the UK was 250 million tonnes of oil equivalent.
What was the power in kWh/day per person?
Total energy used = 250  106 x 12 000 kWh
Power = (250  12 000 x 109)  (365  60  106) kWh/day per person
 140 kWh/day per person
Efficiency
7 Efficiency of the power station = (1.2  3.45)  100% = 35%
8
(a) Efficiency of the power station = (30  98)  100% = 31%
(b) Overall efficiency of the conventional system = (75  154)  100% = 49%
(c) Efficiency of generating electricity only in the CHP scheme = (30  100)  100% = 30%
(d) Overall efficiency of the CHP system = (75  100)  100% = 75%
(e) CHP schemes can only give the full efficiency gains if there is a steady demand for the heating as
well as the electricity. This means that they work well in industrial contexts where there is a steady
demand for hot steam. Where there is seasonal demand for heating they are less efficient than these
figures show – and they generate electricity less efficiently.
9
(a) Efficiency = (53  110)  100% = 48%
(b) Average power of the panel = 40  12 W.
Power of the panel per square metre = (40  12 W) 25 m2 = 19.2 W/m2  20%
Efficiency = (20  110)  100% = 18% (so about 20%)
July 2009
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©The Nuffield Foundation, 2009
Copies may be made for UK in schools and colleges
A2 Science In Society 3.5
Student sheets
There is a summary of the scientific units of energy and power in the box on page 137 of your text book.
Note the unfortunate errors in the key terms box in the first printing of the textbook on page 138. 1 Mtoe
translates to about 42 million GJ (42  106 GJ) or 12000 GWh.
It is important to distinguish between energy and power.
The energy unit on electricity and gas bills is the kilowatt hour (kWh). Most choices we make each day
that involve amounts of energy involve small numbers of kilowatt-hours.
Power is the rate at which energy is supplied or used. In his e-book Sustainable energy –without the hot
air, David Mackay uses the kilowatt hour per day as his measure of power. He uses this unit for all types
of power: Not just electrical power but also the power for heating homes or running motor vehicles.
He suggests that this is a unit on a human scale. He points out that one kilowatt-hour per day is roughly
the power you could get from one human servant. So the number of kilowatt-hours per day you use is
thus the effective number of servants you have working for you.
A power of 1 kWh per day is the same as 40 W.
Getting a measure of the units
In these rough and ready conversions you should only quote your answers to one (or at most two)
significant figures.
Energy
1
A kilowatt hour is a unit of energy. How many joules of energy are equivalent to a 1 kWh?
Power
2
A desk lamp has a 40 watt bulb. What is the power of this bulb (to the nearest whole number)
measured in kilowatt hour per day kWh/day?
3
A hair drier has a power of 2 kilowatts (kW). What is the power of the drier measured in kWh/d?
4
A typical mobile phone charger has a power of about 0.5 W when it is connected to the mains but not
being used to charge a phone. Estimate the power saving for the UK in kWh/day per person if
everyone unplugged their chargers when not in use. Comment on the value you get.
5
Waste incinerators are used to generate electricity. In the UK (population 60 million) waste
incineration delivers a total power of 7 TWh per year. In Denmark (population 5.5 million) waste
incineration delivers 10 TWh per year. 1 TWh (one terawatt-hour) is equal to one billion kWh.
Calculate the kWh/day per person of power from waste incinerators in the two countries and
comment on the values.
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©The Nuffield Foundation, 2009
Copies may be made for UK in schools and colleges
A2 Science In Society 3.5
Student sheets
Power and energy
6 In 2007, the total energy used in the UK, for all purposes, was 250 million tonnes of oil equivalent.
What was the power in kWh/day per person?
Efficiency
7 A coal fired power station converts 3.45 MW of energy from burning coal into 1.2 MW of electrical
energy. What is the efficiency of the power station?
8
The diagram compares methods of producing heat and electricity from burning fossil fuels. The
conventional process involves two quite separate systems, the combined heat and power uses waste
heat from the power station to generate the steam. The steam can be used for many industrial
processes and for warming homes and workplaces. (Adapted from
http://www.epa.gov/chp/basic/methods.html).
(a) What is the efficiency of the conventional power station in producing electricity?
(b) What is the overall efficiency of the conventional system for producing electricity and steam in
two separate processes?
(c) What is the efficiency of the CHP scheme with respect to generating electricity?
(d) What is the overall efficiency of the combined head and power (CHP) system for producing
electricity and steam?
(e) Suggest reasons why CHP schemes are not as widely used in the UK as might be expected.
9 Taking into account the latitude and the length of time that the sun shines in a year, The average
power, throughout the year, of sunshine per square metre of south-facing roof in Britain is roughly
110 W/m2.
(a) A 3 m2 hot-water panel installed on a test house in Britain produced, on average, 53 W/m2.
What was the efficiency of the panel in converting the energy from sunlight into hot water.
(b) A 25 m2 solar photovoltaic panel on a roof in Cambridgeshire in 2006 produced an average of 12
kWh per day in 2006.
What was the power per square metre of panel?
What was the efficiency of the conversion of energy from sunlight into electrical energy?
Page 2
©The Nuffield Foundation, 2009
Copies may be made for UK in schools and colleges