Name:__________________________________
17 December 2003
ENVR 116
Introduction to Aerosol Science
December 17, 2003
FINAL EXAMINATION
By signing my name at the top of this page, I pledge to comply with the UNC honor code as I
take this examination.
Note: The first three questions of this exam comprise a test that covers material since the
last test. Results of this test will be graded separately, and count 25% toward your grade
for the course. The last three questions of this exam comprise the comprehensive final
exam. These results will also be graded separately and count 15% toward your grade for
the course. You have three hours to complete the entire final exam, and you can use this
time however you wish to complete all six questions.
TEST #3
1. (30 points) A negatively charged rain droplet 1000 µm (1 mm) in diameter carries about
4 x 108 electronic charges in a thunderstorm.
a. (15 points) What percentage of its maximum possible charge does the raindrop carry?
In this context, compute maximum charge as though the raindrop were a solid particle.
b. (15 points) The raindrop evaporates as it falls until it becomes so small that
electrostatic repulsion forces overcome surface tension forces and the droplet explodes.
What diameter will the droplet have just before it explodes?
EL = 9 x 108 V/m for electrons
EL = 2.1 x 1010 V/m for positive ions
KE = 9.0 x 109 N m2/C2
e = 1.6 x 10-19 C
γ = 0.072 N/m
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Name:__________________________________
17 December 2003
2. (30 points) At charge equilibrium, theory suggests that 24.1 % of particles 0.1 µm in
diameter will carry one negative charge. An aerosol with equilibrium charge distribution flows
between two flat plates that are 1 cm apart and 10 cm long as shown in the diagram below. The
velocity of the aerosol as it flows between the plates is 10 cm/s.
1 cm
+
10 cm
a. (14 points) What is the minimum voltage difference between the upper and lower
plates that should be applied to collect singly charged particles that are 0.1 µm in
diameter?
b. (8 points) Determine whether all singly charged particles larger than 0.1 µm in
diameter will also be collected at this voltage.
c. (8 points) The plates are 5 cm wide. A total of 1 m3 of aerosol that contains these
particles flows between the plates, and the lower plate collects 10 particles/cm2 of surface
area. What was the concentration of 0.1 µm particles in the 1 m3 of original aerosol?
Express your answer as number of particles/m3 of aerosol.
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Name:__________________________________
17 December 2003
3. (15 points)
Circle the best answer for each set of statements below:
1. After 10 minutes of coagulation the number concentration of a monodisperse aerosol has
decreased by a factor of 30. During this time the average particle size:
a) doubles.
b) triples.
c) remains constant.
d) cannot be determined from the information given.
2. The geometric standard deviation of a highly polydisperse aerosol (GSD0 = 2.5) will
_________ as a result of coagulation.
a) increase.
b) decrease.
c) remain constant.
d) all of the above are possible.
3. Simple monodisperse coagulation is limited to:
a) liquid aerosols.
b) particles where dp > λp.
c) particles suspended in air only.
d) conditions where Cc > 1.
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Name:__________________________________
17 December 2003
COMPREHENSIVE FINAL EXAM
1. (30 points) Particles in an aerosol are comprised of particles that are 0.3 µm, 0.6 µm, and
1.2 µm in diameter. The number concentration for particles of each size is 1 x 108/m3, so that the
total number concentration is 3 x 108/m3. Particle density is 1500 kg/m3.
a. (15 points) What is the mass concentration of the total aerosol? Express your answer
in µg/m3.
b. (15 points) Assume the particles are water droplets, with refractive index of 1.33.
What fraction of light with wavelength of 0.52 µm will pass through 1000 m of this
aerosol?
Note – Values of extinction efficiency are given in the figure on the next page.
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Name:__________________________________
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17 December 2003
Name:__________________________________
17 December 2003
2. (40 points) Explain in one or two sentences whether you agree or disagree with each
statement below. Support your position with equations or calculations when appropriate. Each
statement is worth 4 points.
a. The slip correction factor becomes more important as gas pressure decreases.
b. Particles collect more efficiently by impaction on larger diameter targets.
c. An Aerosizer measures the size distribution of an aerosol quickly, easily, and
accurately.
d. If you can see an aerosol, then breathing it is probably harmful to your health.
e. Diffusion is more important than gravitational settling for particles that are very small.
f. A solid particle will diffuse faster than a liquid particle because liquid droplets can
absorb gas molecules when they impact.
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Name:__________________________________
17 December 2003
g. Brownian deposition in a tube is independent of the particle diameter.
h. Homogenous particle nucleation always occurs when S > 1.
i. Increasing the average molecular speed of gas molecules will increase the evaporation
rate of a droplet.
j. Pollen particles are best modeled by a lognormal size distribution.
k. (extra credit) A cow eats hay corn, and field grass. Therefore, eating meat (steak in
this case) is an efficient way to deliver vegetables to your body.
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Name:__________________________________
17 December 2003
3. (30 points)
Calculate the CMD, MMD, and GSD from the following aerosol data:
Lower
Bound
(µm)
0.1
0.2
0.37
0.62
1.8
3
Upper
Bound
(µm)
0.2
0.37
0.62
1.8
3
4.5
Particle
Counts
5
65
230
620
70
10
CMD: __________
MMD:__________
GSD:___________
These data were collected using a cascade impactor in air at standard conditions. Particles on
each plate were counted rather than weighed. State whether the measured MMD of the aerosol
will increase, decrease, or stay the same if:
(3 points each)
a) the gas viscosity during collection was reduced by 50%.
b) the air was sampled at super-isokinetic conditions.
c) the aerosol was charged with a Boltzmann charge distribution.
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