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ER 102
Solutions to the 2007 Midterm Examination
J. Harte
Spring 2007
1.
a.
A micron is 10
-4
cm, and water has a density of 1 g/cm
3
and thus a cubic micron has a mass
of approximately
10
-12
grams.
b.
Taking a typical person to have a mass of 5 x 10
4
g, we get
metabolic rate of bacterium = 100 Watts(10
-12
/5 x 10
4
)
3/4
= 0.3 x 10
-10
Watts.
c.
Assuming 75 Gt(C)/y for annual NPP, and using 1 Gt = 10
15
g, we get a total annual energy
release of
40 kJ/g(C) x 75 x 10
15
g(C)/y = 3 x 10
21
J/y ~ 10
14
Watts
.
Dividing by the wattage of a bacterium, we get a total population size of
10
14
/ (0.3 x 10
-10
) ~
3 x 10
24
bacteria
.
d. Total bacteria mass: total bacteria (part c) x mass per bacteria (part a)
= (3 x 10
24
bacteria)(10
-12
g/bacteria)
=
3 x 10
12
grams of bacteria
Total human mass: total humans (6.9 x 10
9
humans) x mass per human (5 x 10
4
g/human)
=
3 x 10
14
grams of humans
The mass of all bacteria is about one hundred times smaller as the mass of all living humans
today.
e.

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