Math 105e — Hypothetical "Project Section" as Homework: Annual Tons of CO2.

Directions: This homework assignment is in the form of a portion of an imagined end of semester project report. Carry out the steps and reasoning, justification, units, etc, to create a complete "section II of our project". This is not exactly what a section of your project should look like (in some cases for example, when finding new, better data, you'd "erase" -- not include in the project -- the earlier calculation) and you can bring a draft for me to look at. It's also not what your project is required to look like -- there are other types of analyses that would be appropriate. However it steps you through the one kind of analysis that is likely to be helpful, for at least some parts, of many of your end of semester projects.

As such, it is a stepping-stone to your gaining more mathematical ability, skills, confidence, and sophistication, towards being able to create such analyses on your own -- there won't be a fill-in the blank and you'll be creating your own projects, working in groups, from scratch -- at the end of the semester.

DIRECTIONS: You must work in groups of size 3 or 4 (the only exceptions are if you request (and receive) an ok for group of size 2 no later than the next class we meet).

"...For part II of our project, our project group decided to carry out a from-the-bottom-up calculation (based on data from several sources) of (e-1) total CO2 emissions in the U.S. as well as (e-2) total CO2 emissions from cars in the U.S., and to compare our results with statistics given by other sources. We found the following quote from National Georgraphic's website, "The Green Guide" –

How do Americans generate so much CO2? Nearly a third of the carbon dioxide emissions generated in the U.S. come from transportation, and of those emissions nearly two-thirds come from personal automobiles. When combusted, each gallon of gas creates about 25.3 big balloons -- or pounds -- pounds of carbon dioxide.
Here's how it breaks down. A gallon weighs a little over 6 pounds, 85 percent of which is carbon, giving 5.25 pounds of carbon per gallon. Each carbon atom combines with two oxygen atoms from the atmosphere when it burns, adding 14 pounds per gallon, for a total emission of 5.25 + 14 = 19.25 pounds of CO2. Just to produce gasoline from oil creates an additional 6.05 pounds of carbon dioxide, giving 25.3 [pounds] of CO2 for every gallon. (Source: National Geographic's website, "TheGreenGuide")

Using the above estimates, we were able to find out, roughly what percentage of Americans' CO2 emissions come from personal automobiles. Below we show all steps and reasoning in our calculation, including showing clearly all conversions between fractions and percents:

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About 1/3 of CO2 is from transportation and (almost) 2/3 of that is from personal automobiles; thus, if US CO2 emissions is (e-1) and (e-2) stands for total emissions of CO2 from cars, and if we let T stand for US CO2 emissions from transportation, then T ≈ (1/3)·(e-1) and

cars CO2 = (e-2) ≈(2/3)·T ≈(2/3)·(1/3)·(e-1)So we get see that (1/3)(2/3) or 2/9, is our estimate for what portion of all US emissions come from cars. This is 0.222....(etc) or about 22.2 percent.

This approximate percentage should let us carry out rough conversions between the two statistics (e-1 and e-2) cited above. [For future reference, we also note how only 6 pounds of gasoline become, after combustion, over 19 pounds of CO2 and contribute the release of some 25 pounds of CO2. The Site CarbonFund.org uses somewhat less clear terminology by stating that unleaded gas "has" 19 pounds of CO2 without explaining the derivation]

The CarbonFund site was useful in other ways however, citing the U.S. National Highway Traffic Safety Administration states that average fuel economy for cars sold in 2005 was about 25.2. mpg, and, citing the Federal Highway Administration, mentions that in 2001 the average distance driven by U.S. drivers was 13,785 mi/yr. One problem is that the two years (2001 and 2005) are not identical. Another issue is that the average fuel efficiency of all cars on the road at any given point in time (which includes new and old and some very old cars) is not the same as the average fuel efficiency of all cars sold that year. Citing EPA which cites a Dept. of Transportations model, the figure of 20.3 mpg is given for the average of the entire car fleet on the road. Putting aside the issue of 2001 versus 2005 for the time being (and choosing not to use the earlier "25.2" figure), we were able to estimate roughly how many gallons of gas Americans used up per year, for a year during the 2001-2005 period. Below, we show all our steps and explain all our reasoning:

The average U.S. driver used up ≈_____ gallons per year.

Justification: ___________________________________________________________________________

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Average driver: 13785mi/20.3mpg = (13785 mi)÷(20.3 mi/gal) ≈ 679 gallons (One issue: Does "13,785" mean "per car" or "per person"? But we may reasonably assume these are "close enough" for our purposes here)

From this, we were able to estimate that a total of roughly _____________ gallons were used for driving by all Americans combined, per single year during that 2001-2005 period.

Note:For our justification below, the urls of the data we cite are as follows. At http://www.researchandmarkets.com/reports/c7353 we found that "The number of vehicles on the roads of the N American region as of 1st January 2003, is estimated at 257.8 million units"
In addition, http://answers.google.com/answers/threadview?id=761538 states that according to "The Transportation Energy Data Book: Edition 25 -- 2006" there were as of that time about 226,000,000 cars and trucks (combined) in the US..but also cited for "total vehicles in use" a figure of just over 238,000,000."
This is why our group chose, in our justification below, to use the average of these three figures, namely the average of 258 million, 226 million and 238 million is (258+226+238)/3 = 240 and 2/3 million which we rounded up to 241 million -- hence that is the figure we used below.

Justification: ___________________________________________________________________________

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679 gallons per car times 241 million cars gives (679*241) million, which is 163,639 million, which is about 163.6 billion gallons of gas used up (this being our rough estimate) by all US drivers, per year, during the period in question.

We later found that the same url at answers.google.com states "Vehicle miles traveled, 2003 (million miles) 2,890,893" Initially we were confused and thought the figure was only about 2.89 million miles but then realized this can't be true for all of driving for all Americans; the units are "millions of miles" so the correct figure is 2,890,893,000,000 miles were driven.

From this we found another way to calculate the total number of gallons of gas used up per year by all US drivers, using the 20.3 mpg figure. Here is a careful calculation (with units) of our result:

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"2 890 893 000 000 / ( 20.3) = 142.408522 billion" (via google calculator) thus with units we can state: (2,890,893,000,000 mi/yr) / ( 20.3 mi/gal) is about 142.4 billion gal/yr.

Had our two numbers been very far apart, we would have re-checked both (i) the numbers in the data we were using and (ii) our calculations. However the two numbers came out close, so this gives us some measure of confidence that we have a decent estimate of the total number of gallons of gas used for driving, in the U.S. per year during 2001-2005. We decided to stick with the latter number for number of gallons used per year from driving, from here on.

Now, by using the figure of 19.5 pounds of CO2 (which is the quantity of CO2 directly released by burning up a gallon of gas) then we arrive at the following estimate of how many pounds of CO2 are produced per year by all of US driving:

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Using google calculator we converted this into tons of CO2:

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Google Calculator: "19.5 * 142.4 = 2 776.8" means that (19.5 pounds of CO2/gallon burned)*(142.4 billion gallons) = 2,776.8 billion pounds of CO2, or about 2,777 billion pounds of CO2. And, with 2,000 pounds in one ton, this would be about 1.389 billion tons of CO2. Justification with units: ......

We then used google calculator to convert this (English tons where one English ton is 2000 pounds) into metric tons (where a metric ton is 1,000 kg) since some websites gave their numbers in metric tons. We found:

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Google Calculator: "2000 pounds in metric tons" returns "2000 pounds = 0.90718 metric tons" so one gets about (0.90718)*(1.389) billion metric tons, or 1.26 billion metric tons.

Finally using our very first number in this section, where we gave an estimate of the percentage of all US CO2 emissions which is represented by emissions from driving, we can use our estimate for the total number of metric tons of CO2 from US driving per year, to estimate the total amount of CO2 emission per year, from all sources, for the US:

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If this were 22% of the total the total would be 1.26/.22 ≈ 5.7 billion metric tons from all sources

What if we used the fuller accounting figure of 25.3 pounds? Then our estimate of the total number of metric tons of CO2 per year in the US would be higher. First, we'd need to recalculate the amount of CO2 from cars. We carry out these two recalculations below:

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We would get 3,610 (instead of 2,777) billion pounds of CO2. To save a few steps, lets use the ratio (25.3)/(19.5) ≈ 1.30 or so, to multiply the 1.26 billion metric tons: in that case the total (counting also CO2 released when gasoline is produced) would be 1.30 * 1.26 = 1.638 billion metric tons of CO2.

If this were 22% of the total, the total would be 7.445 billion metric tons, or 7,445 million metric tons of CO2 from all sources. Our justification with units: [...]

We were pleased when we compared this last estimate with the following reference: our estimate comes very close to the figure given in the CarbonFund.org page cited earlier, which states:

"Total US emissions were 7,122 million metric tons CO2-equivalent in 2004" (Source: Energy Information Agency of the U.S.)"

(We could have gotten a bit closer to "7,122" by being less accurate (rounding to less accuracy) earlier but of course it would be cheating to do that on purpose to retroactively try to make this 'more accurate' - using more accuracy will give us a more honest assessment of how close our model/modeling steps above are to this other estimate cited on the other website..)

We should be careful however: we should not assume that the cited 7,122 million metric tons of CO2 equivalent necessarily used the figure of 25.3 pounds of CO2 per gallon of gasoline burned. It probably reached this figure in other ways. The fact we are close (even the earlier figure of just under 6 billion metric tons is "close" for a rough calculation such as this -- as opposed to a full research project with original data) gives us a measure of confidence, however, in our calculations above being in the right ballpark.

http://www.carbonfund.org/site/pages/carbon_calculators/category/Assumptions/

For part III. of our project (see the Introduction section where we gave a short 1 or 2 sentence summary of each part) we note that Americans use energy for many for purposes besides driving of course:

Another big chunk of CO2 comes from making the electricity that lights our homes and runs air conditioners, refrigerators and other appliances...The pounds of CO2 emitted per kilowatt-hour (one hour's use of one kilowatt of energy) vary depending on the type of fuel your utility uses. Coal-fired power plants emit up to 2.49 lbs/kWh while wind and other renewable energy sources release none. The national average, combining all energy generation methods, is about 1.34 lbs/kWh. A single 75 watt bulb burning for two hours a day generates an average of six pounds, or six big balloons, of carbon dioxide a month.

We can now begin our analysis of electricity usage in US households, clean sources of electricity, and the effects of using more efficient lighting, heating, and cooling.

[...etc...]