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ENERGY AND RESOURCES 102
QUANTITATIVE ASPECTS OF GLOBAL ENVIRONMENTAL PROBLEMS
Professor John Harte
with TAs Doug Bushey, Matthias Fripp, Eric Hallstein
FINAL EXAMINATION
May 15, 2007
This is a closed book, closed notes, exam.
You may use two 2-sided sheets filled with any
materials you wish; calculators are also permitted.
Each problem is worth the number of points
indicated.
There are a total of 180 points, which is also the number of minutes you have for the
entire exam.
So allocate your time wisely.
The problems are not tricky; don’t make them harder than necessary;
look for the
simplest possible way to answer them.
Always show your work so that credit can be given for valiant attempts.
If you write neatly,
the grader won’t get angry reading your paper and will be more likely to be generous!
If you
need a number and can’t find it, please guess the value and state clearly what your guess is.
Even if the guess is wrong, you can get a lot of partial credit for working consistently with a
guessed value.
Of course a good guess will get more credit than a bad one.
Have a good summer!
1.
Consider a 4-year undergraduate program in which 4000 new students enter the freshman
class each year.
The students can be divided into 3 groups: 1000 flunk out at the end of the first
year, 1000 more flunk out at the end of the second year, and the remaining 2000 go on to
graduate at the end of year 4.
a.
At steady state, what is the stock of students in the school? (3 pts.)
b.
What is the average residence time of the students.
(3 pts.)
c. What are the partial residence times associated with exit by each of the three modes (flunk out
at end of first year, flunk out at end of 2
nd
year, graduate after 4 years) (3 pts.)
d.
Verify that the sum of the inverse partial residence times is the inverse of the average
residence time.
(3 pts.)
2.
Based on what you have learned about global warming, explain why you might expect to see
future atmospheric circulation weaken in the equator-to-pole direction and strengthen in the
vertical direction.
(8 pts.)
3. No direct pH measurement was made on a rain sample, but on the basis of the following
measured results, estimate what its pH must have been, and justify any approximations you
make.
(10 pts.)
[SO
4
-2
] = 10
-5
[NO
3
-1
] = 10
-5
[Ca
+2
] = 0.6 x 10
-5

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*Sign up* 4.
Suppose that next year 5 MT(N)/y from anthropogenic N emissions fertilizes vegetation
around the earth, with that N incorporated into additional plant growth and resulting in increased
leaf biomass on the planet.
a. Using a reasonable value for the C:N ratio of newly photosynthesized leaves, estimate how big

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