Modeling Your Carbon Footprint. (Student handouts)
What is a model?
What do you think of when you hear the word model? If you are like most
people, you think of model cars and model airplanes, which are made of plastic and look
almost exactly like the real life vehicles, even though they are not usually functionally
similar (they do not run off of gasoline, etc.).
If you happen to be asked about models in a classroom, your answer may be more
focused on teaching models, to include models such as a globe, ball and stick models of
an atom, or plastic models of a person, cell, etc. In many respects, these models are much
the same as the vehicle models above. They are often different in size (like a globe is
smaller than the earth or a cell model is larger than the cell) but make attempts to look as
much like the thing that they represent as possible. These models are physical models,
because you can pick them up and “play” with them physically.
However, there is another type of model that is very important in science. This
kind of model is a mathematical model. Today, we will examine several different models
dealing with calculating your carbon footprint, and tomorrow, we will try to make our
own.
A mathematical model:
A mathematical model takes several pieces of information (data) about several
factors (variables) that might influence some other result and calculates a result from this
information. When a mathematical model is made on a computer, one can quickly
change one piece of information and see what affect this change has on the outcome, sort
of like testing variables in a scientific method. In fact, the model is like a hypothesis (or
theory or law) representing how the scientists who created the model thinks that these
various factors are related. Although outside of science class we think primarily about
how a model looks, one of the most powerful uses of models in science is this ability to
test the hypothesis and see if the model gives accurate predictions. If the model
consistently gives accurate predictions, then the hypothesis, laws, and theories that went
into making the model are given support (you may remember that you can never prove a
theory correct, only prove it wrong or support it.) On the other hand, if the model gives
inaccurate predictions, then likely there is a problem in the model (and thus the
hypothesis, theory or law the model is based on) and the model will need to be revised
and tested again.
Judging the quality of a model:
If I were to ask you whether one model was better than another, how would you
tell? Perhaps one globe, in addition to having the rivers and countries has bumps to
represent the mountains and show elevations in three dimensions (or otherwise provide
more detail). Perhaps one set of atomic models is bigger and easier to see, made of better
materials or is more expensive. Or maybe one atomic model shows something (like
double bonding P-orbitals) that another model does not show.
Scientists would judge the quality of models a little differently. In addition to
merely “showing” or otherwise communicating an idea, models are used to pose
questions and make predictions. Does the model make accurate predictions? Does it
help a scientist answer the question that (s)he is trying to answer? A more detailed model
is not always preferable. Think about globes or maps for instance. If you want to use a
map to figure out how to drive from Minneapolis to New Orleans, you would want a map
with roads marked. However, if you were using the map to study the climate, biome
type, terrain, elevation, or looking at a river trip down the Mississippi instead of a road
trip, you would want other information than roads on your map/model. No one map is
absolutely better than another map, each map (or model) is suited for a particular job.
Likewise, a map that had all of this information (roads, rivers, biomes, elevation, etc.) at
the same time would be too cluttered to do a good job at any one task, so more detail is
not always better. In fact, all models are approximations that try to clear away (omit)
some of the unimportant (or at least less important) details in exchange for making some
parts much clearer.
A carbon footprint model:
Wikipedia defines carbon footprint as “a measure of the amount of carbon dioxide
(CO2) emitted through the combustion of fossil fuels … in the case of an individual or
household, as part of their daily lives.” This fossil fuel use could include both direct and
indirect use. For instance, an electric car is advertised as having “zero emissions”,
because it does not burn fossil fuels and does not have an exhaust pipe. On the other
hand, where does this electricity come from? If this car was used in North Dakota, over
90% of electricity is generated by burning coal. Thus, since fossil fuels were likely
burned in generating the electricity used to recharge the car, from a carbon footprint
standpoint, this car is not “zero emissions”. On the other hand, Vermont generates about
80% of its electricity from nuclear and most of the rest from hydroelectric, neither of
which emit CO2.
Task 1. (15-30 minutes)
Brainstorm a list for what factors (variables) would contribute to your carbon
footprint, directly or indirectly. What activities that you do (ignoring breathing) increase
the amount of CO2 in the air? How much do they increase the amount of CO2? For now,
just put a box around each variable, the darker the box, the bigger effect you anticipate
this variable having. A number of resources will be provided later to help you figure out
an exact number, just brainstorm for now.
Also brainstorm if there are variables that might moderate some of the above
carbon footprint. For instance, it takes about 0.35 kilowatt-hours of electricity (with
subsequent CO2 production depending on state) to make an aluminum can. However, if
this can is recycled, approximately 95% of this energy (and the CO2 that goes with it) is
saved the next time around. What other variables can you identify that might lesson
some of the impacts listed above?
Once you have finished brainstorming alone, discuss your lists with several other
students. If you get additional variables from them, please identify them in a different
color, again indicating the strength of this variable in influencing your carbon footprint
by making the box heavier for those variables with a larger influence. Also share ideas
about what factors may decrease (or at least moderate) your carbon footprint.
Task 2. Gather background data (allow students adequate time to collect this
information, so perhaps a week between task 1 and task 3 would be appropriate)
NOTE: Prior to completing this activity, it is necessary to collect the following
information (from your family), and the tables below will help you to organize it:
How many miles you drive in a week/month/ or year for each vehicle.
What is the average mileage, year, make, and model for each vehicle?
What is the average (or total) amount of energy and amount of money spent in
your house for a month or year (this can be found on a utility bill). Please write down all
sources, for instance, if you heat with LP gas and wood, how many cords of wood did
you burn last year and how many gallons of LP gas did you use? For those of you living
in apartments – you may NOT have access to this information because it is all wrapped
up in your rent. Contact me and we will consider other options like working with a
partner from a house.
How many plane trips did you take? To where?
Year
Make
Amount
Used Per
Month
Amount
Used Per
Year
Model
Miles Per
Miles
Gallon
Driven
(city/highway)
Vehicle 1
Vehicle 2
Vehicle 3
Vehicle 4
Dollars
spent per
month
Dollars
spent per
year
“green”
source?
Electric
(kWh)
Natural gas
(therms)
LP (gallons)
Fuel Oil
(gallons)
Wood
(chords)
Coal
Other?
Other factors that some models think are important:
 What foods do you commonly eat? (fruit/vegetables/starches, dairy, meat). On
average, are you vegan, vegetarian, or do you eat meat?


How much garbage do you produce per week (lbs)? work?
home?
figure about a pound per gallon? So if you fill a 20 gallon kitchen bag a week, 20
lbs. If it’s one of those new 60 gallon cans for the garbage truck with the
automated arm, then 60 lbs. If you know you pack it tighter, up it a little.
How much waste do you recycle per week? It takes about a 24-pack of aluminum
cans to make a pound. A week’s worth of regional newspapers (Fargo Forum)
might be 3 lbs. Star Tribune probably closer to 7 lbs per week. Think about it
and give your best estimate.
Task 3. Examine the models (requires access to computers and the internet. Most of
my students finished 50 minutes or less.)
Now examine several (at least 3) of the model below that claim to calculate your
carbon footprint. No two models will ask you the same questions or calculate your
carbon footprint the same way. Most of these websites will provide an explanation of the
model (formula and reasoning) that they used to calculate your carbon footprint. The
EPA site (#7) does a great job of that, as do 1, 2, 4, and 6. These are worth a read.
In my unique case, I found all models lacking. Write down the following:
a) Your carbon footprint from each site
b) What unique questions this site asked you (or included in their model) that you
should add to your brainstorming list (Task 1)?
c) Which of the factors that you felt was very important (from Task 1) that this
model did seem to incorporate?
d) Finally, were their any factors that this website lumped together or used an
average for? Why would they use an average?
e) After analyzing your sites, compare and contrast. Could you say which is
“better”? Which site would you use? Would it depend? On what? Why?
Sites:
1. http://www.climatecrisis.net/takeaction/carboncalculator/
2. http://www.begreennow.com/users/calculator
3. http://www.carbonfootprint.com/USA/calculator.html
4. http://www.safeclimate.net/calculator/
5. http://web.conservation.org/xp/CIWEB/programs/climatechange/carboncalculator.xml
6. http://www.nature.org/initiatives/climatechange/calculator/
7. Environmental Protection Agency
http://www.epa.gov/climatechange/emissions/ind_calculator.html
8. British Petroleum – a “Big Oil” company
http://www.bp.com/extendedsectiongenericarticle.do?categoryId=9015627&contentId=7
029058
Which 3 sites you choose to compare are up to you, although here are my suggestions:
 7 and 8 are sponsored by different types of groups than 1-6. Does either give a
different result than those from more “green” sites?
 #6 is calculated in a very different way than any of the others, and gave me a very
different number. Interesting from a comparison standpoint?


#1, #4, #5 seemed fairly similar to me, probably not worth doing more than one
from that group.
#3 has some unique features, (because it is from overseas?)
Several of these sites also allow you to click on a link to see how they did their
calculations. The EPA site does a great job of that, as do 1, 2, 4, and 6. Please visit at
least 2 of these calculations pages (preferably the EPA site).
Task 4 (Extension).
You have been provided with a variety of data, including chemical formula,
balanced equations, heats of combustion/heat values, and densities for common fuels.
Likewise, the efficiencies of typical power plants for each type of fuel are also provided.
Based on this information create your own model in Excel for calculating a carbon
footprint.
a) First you will need to determine a formula for each variable. For instance, wood
is composed of carbon, hydrogen and oxygen, primarily polymers of sugar
(C6H12O6). When burned C6H12O6 + 6 O2  6CO2 + 6H2O. With a molecular
weight of 180g/mole, or just over 5 moles per Kg, and considering a cord of wood
is approximately 1500 to 2000kg,
1 cord x 1750 kg x 5.6 mole sugar x 6 moles CO2 x 0.044kg = 2587 kg CO2
1 cord
1 kg sugar
1 mole sugar
1 mole CO2 1 cord
So, my Spreadsheet would have column A (cords of wood burned) and B (CO2 from
wood). In B, the formula B3=A3*2587 would convert whatever cords were put in A2
into kg of CO2 in B3.
1
2
3
A
cords
3
B
CO2
=A2*2587
C
D
E …
Z (total CO2)
= B2+D2+...
b) if no formula is available, then try to look for an appropriate approximation. For
instance, in the above example, if the best information you can find is that
10,000,000 cords of wood was burned last year/300,000,000 people in the USA,
gives an average of 86 kg of CO2 per person in the U.S. from firewood. You
could do these averages on a statewide or countrywide basis.