6508
/www/nrich/html/content/id/6508/
1
2011-02-01T00:00:01
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<mdoxml version="1.0"><ul id="stemLinks">
<li><a href="http://nrich.maths.org/7500">Warm-up</a></li>
<li><a href="http://nrich.maths.org/6453">Try this next</a></li>
<li><a href="http://nrich.maths.org/6505">Think higher</a></li>
<li><a href="http://plus.maths.org/content/restaurants-climate-change">Read: mathematics</a></li>
<li><a href="http://environmentalresearchweb.org/cws/article/news/39408">Read: science</a></li>
<li><a href="http://plus.maths.org/content/facing-climate-challenge">Explore further</a></li>
</ul>
<div> </div>
<br></br>
<p><span style="font-weight: bold;">Being green is a good thing, but how are we to know what the greenest choices to make are? Why not make up your own mind by analysing some of the following statements yourself?</span><br></br>
<br></br>
<span style="font-style: italic;">At the foot of the question we provide you with lots of data taken from the internet. This isn't necessarily all of the data needed to complete the investigation, but a set of data which appears to be relevant to the problem. Some of the sources are given at the foot of the problem. You may, in your work, find that you need more data or question what the data, as
presented, might really mean. Use your common sense to try to decide what the most important factors are</span>.<br></br>
<br></br>
<span style="font-weight: bold;">Questions to consider</span></p>
<br></br>
<ol>
<li>Would it be better for commuters to catch the bus to work, or to go by car?</li>
<li>Is it better to buy locally produced goods or goods imported from overseas?</li>
<li>Is it better to go on a holiday by boat, train and car or by plane?</li>
</ol>
<div style="font-weight: bold;">Suggested approach</div>
<div style="font-weight: bold;"> </div>
<div>You can make sensible comparisons by working out the mass of carbon needed to complete each activity.</div>
<br></br>
<div style="font-weight: bold;">Thoughts on the data</div>
<div style="font-weight: bold;"> </div>
<div>Perhaps the activity might make you question the way in which some of the 'standard' data below is calculated, or what it really means. What questions are raised? To analyse these questions fully, what experiments or measurements would you need to make?</div>
<br></br>
<br></br>
<table style="" border="">
<tbody>
<tr>
<td>1 gallon of petrol produces $8.87$kg of CO2</td>
<td> </td>
</tr>
<tr>
<td>A round trip, economy class, from London to New York produces $760.22$kg of CO2 per person</td>
<td> </td>
</tr>
<tr>
<td>Efficiency of a car ranges from about $25$ miles per gallon to $50$ miles per gallon</td>
<td> </td>
</tr>
<tr>
<td>An efficient small car produces about 120g per km of CO2</td>
<td> </td>
</tr>
<tr>
<td>An efficient large car produces about 140g per km of CO2</td>
<td> </td>
</tr>
<tr>
<td>An efficient empty delivery truck produces about 220 g per km of CO2</td>
<td> </td>
</tr>
<tr>
<td>Locally produced food travels an average of about 200 miles from farm to shop</td>
<td> </td>
</tr>
<tr>
<td>Environmental CO2 output from shipping is twice as much as airlines</td>
<td> </td>
</tr>
<tr>
<td>The distance from London to New York is about 2000 miles.</td>
<td> </td>
</tr>
<tr>
<td>An empty bus emits seven times more CO2 per km than an empty car</td>
<td> </td>
</tr>
<tr>
<td>Short haul air freight emissions are 1580 g CO2 per tonne kilometre</td>
<td> </td>
</tr>
<tr>
<td>Long haul air freight emissions are 570 g CO2 per tonne kilometre</td>
<td> </td>
</tr>
<tr>
<td>Freight in a medium truck produces 85 g CO2 per tonne kilometre</td>
<td> </td>
</tr>
<tr>
<td>Freight in a large transport ship produces 10 g CO2 per tonne kilometre.</td>
<td> </td>
</tr>
<tr>
<td>An average man weighs about 80 or 90 kg</td>
<td> </td>
</tr>
<tr>
<td>Bus journeys can take longer than car journeys</td>
<td> </td>
</tr>
<tr>
<td>On average, rail journeys produce 0.0602 kg of CO2 per passenger km</td>
<td> </td>
</tr>
<tr>
<td>On average, bus journeys produce 0.0891 kg of CO2 per passenger km</td>
<td> </td>
</tr>
<tr>
<td>Journeys in slow moving traffic can dramatically reduce fuel efficiency.</td>
<td> </td>
</tr>
<tr>
<td>Buses, taking into account stops, use an average of $39$ litres of fuel per $100$km</td>
<td> </td>
</tr>
</tbody>
</table>
<br></br>
<br></br>
<p>You might also want to challenge other commonly accepted green ideas or the impact of various green activities. For example, what is the relative impact of these green measures? What mass of carbon do these various common activities use up?</p>
<ol>
<li>Washing clothes at $30^\circ$ degrees instead of $40^\circ$.</li>
<li>Shutting your computer down every night.</li>
<li>Using low-energy light bulbs instead of regular light bulbs.</li>
<li>Switching off the television instead of leaving it on standby</li>
<li>Boiling only 1 cup of water at a time, instead of a whole kettle.</li>
<li>Disposable nappies are less green then washable nappies.</li>
</ol>
<br></br>
<br></br>
<br></br>
<div style="font-weight: bold;">NOTES AND BACKGROUND</div>
<br></br>
<div>Making sense of the mass of data available on the internet is immensely tricky. Getting to the truth of the matter is very difficult. Scientists and statisticians need to bring a healthy sceptical view to data. This is why good, scientifically sound documents will contain references in which the exact meaning of the figures presented will be given. The scientist or statistician can then make
an informed judgement based on the evidence. Of course, we do not have time to make informed judgements about everything, but it helps to be aware that data and facts are hardly ever simply black or white.</div>
<br></br>
<br></br>
<br></br>
<br></br>
<p>Sources</p>
<ol>
<li>International Civil Aviation Organisation http://www2.icao.int/public/cfmapps/carbonoffset/carbon_calculator.cfm</li>
<li>buycarbon.org http://www.buycarbon.org/</li>
<li>http://www.guardian.co.uk/environment/2007/mar/03/travelsenvironmentalimpact.transportintheuk</li>
<li>http://www.sustainweb.org/</li>
<li>http://directgov.transportdirect.info/Downloads/TransportDirectCO2Data.pdf</li>
<li>http://www.naei.org.uk/ (National Atmospheric Emissions Inventory)</li>
<li>http://actonco2.direct.gov.uk/index.html</li>
<li>http://www.safeclimate.net/</li>
<li>http://www.dft.gov.uk/pgr/roads/environment/research/cqvcf/economicsofbusdrivelines?page=8</li>
<li>http://www.bbc.co.uk/bloom/actions/trainandbus.shtml</li>
</ol>
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<span class="editorial">Masood, Akeel, and Dolapo from Wilson's
School sent us their analysis:</span><br></br>
<br></br>
An efficient small car produces about 120g per km of CO2.<br></br>
An empty bus emits seven times more CO2 than a car per km.<br></br>
So taking this into account, an empty bus emits 840g per km of
CO2.<br></br>
On average a normal commuter would travel 5km to get to work. So an
efficient small car would emit 600g of CO2 when a bus would emit
about 4200g. However there are more than seven people using a bus
so altogether a bus is better than a car to travel to work.<br></br>
<br></br>
If you were somehow able to travel to New York by train, you would
be travelling 2000 miles.<br></br>
On average, rail journeys produce 0.0602 kg of CO2 per passenger
km<br></br>
2000 miles is approximately 3200km.<br></br>
So travelling to New York by train would emit $0.0602 \times 3200 =
192.64$ kg of CO2 for one person.<br></br>
Travelling by plane, the figure given is 760.22kg of CO2
per person for a round trip, which is 380.11kg of CO2 each way, so
travelling by train would be better if it were
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<h3>Why do this problem?</h3>
<a href="http://nrich.maths.org/public/viewer.php?obj_id=6508&part=">
This problem</a> offers a good opportunity to discuss some of the
maths behind the issue of carbon emissions. It is a chance for
students to use some maths to support their viewpoint, and to equip
themselves with the skills needed to analyse critically what they
see in the media about climate change. There is real scope for
making cross-curricular links through this problem. It is almost
certain to raise surprising realisations about the sheer volume of
carbon produced by everyday activities.<br></br>
<h3>Possible approach</h3>
One way of approaching this problem with a class is to divide them
into groups and provide each group with a copy of the data given in
the problem, which can be found <a href="/content/id/6508/Carbon%20footprints.doc">here.</a> Allocate
one of the questions for consideration to each group, and give them
plenty of time to discuss which pieces of information are useful to
them in answering the question. Each group could prepare a
presentation or poster to present to the rest of the class
explaining their answer to the question and stating any assumptions
they have made. Students could also consider questions of their
own, and could use some of the links provided at the bottom of the
problem to find other useful information needed in order to answer
the questions.<br></br>
<h3>Key questions</h3>
<div>Which pieces of information are useful in answering each
question?</div>
<div>What assumptions need to be made in order to answer the
questions?</div>
<h3>Possible extension</h3>
Students could be encouraged to think about what extra information
would help them better to answer these questions, and could seek
out this extra information.<br></br>
<h3>Possible support</h3>
Suggest starting with common-sense reasoning and then look for the
numbers to back up what their common sense suggests.<br></br>
<br></br>
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Clearly, this problem is rather involved and designed to get you
thinking.<br></br>
<br></br>
The only hint is that you ask questions and then try to locate the
data to answer them!<br></br>
<br></br>
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Carbon footprints
Is it really greener to go on the bus, or to buy local?
Using, Applying and Reasoning about Mathematics
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