AOSC 620
PHYSICS AND CHEMISTRY
OF THE ATMOSPHERE, I
Professor Russell Dickerson
Room 2413, Computer & Space Sciences Building
Phone(301) 405-5364
russ@atmos.umd.edu
web site www.meto.umd.edu/~russ
Copyright © R. R. Dickerson & Z.Q. Li
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"You are here to learn the subtle science and exact art of
potion making. As there is little foolish wand-waving here,
many of you will hardly believe this is magic. I don't expect
you will really understand the beauty of the softly simmering
cauldron with its shimmering fumes, the delicate power of
liquids that creep through human veins, bewitching the
mind, ensnaring the senses... I can teach you how to bottle
fame, brew glory, even stopper death -- if you aren't as big a
bunch of dunderheads as I usually have to teach."
Copyright © 2013 R. R. Dickerson
& Z.Q. Li
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Professor Severus Snape
(Thanks to J. K. Rowling)
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"You are here to learn the subtle science and exact art of
atmospheric chemistry and physics. As there is little foolish
dynamical wand-waving here, many of you will hardly
believe this is science. I don't expect (at first) you will really
understand the beauty of the softly simmering sunrise with
its shimmering photochemical fumes, the delicate power of
liquids that creep through the air catalyzing multiphase
reactions, bewitching the mind, ensnaring the senses... I can
teach you how to bottle clouds, predict the future (of a
chemical reaction), brew smog, or prevent it, even stopper
death -- if you pay attention and do your homework."
Copyright © 2013 R. R. Dickerson
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Logistics
Office Hours: Tuesdays 3:30 – 4:30 pm
Wednesdays 1:00 – 2:00 pm
Worst time is 1- 2 pm Tues or Thrs.
Exam Dates: October 14, November 25, 2014
Final Examination: Thursday, Dec. 18, 2014
10:30am-12:30pm
www/atmos.umd.edu/~russ/syllabus620.html
Copyright © R. R. Dickerson & Z.Q. Li
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Changes to Syllabus, 2013/4
Warm precipitation processes and the theory of
radar will be taught in AOSC 621.
This class will cover spectroscopy, stratospheric
ozone and measurements of photolysis rates; theory
to be covered in 621.
Copyright © R. R. Dickerson & Z.Q. Li
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Experiment: Room temperature
Measure, or estimate if you have no thermometer, the
current room temperature.
Do not discuss your results with your colleagues.
Write the temperature on a piece of paper and hand it in.
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& Z.Q. Li
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Homework #1
HW problems 1.1, 1.2, 1.3, 1.6, from Rogers and
Yao; repeat 1.1 for the atmosphere of another
planet or moon.
Copyright © 2013 R. R. Dickerson
& Z.Q. Li
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Lecture 1. Thermodynamics of Dry Air.
Objective: To find some useful relationships among
air temperature (T), volume (V), and pressure (P),
and to apply these relationships to a parcel of air.
Ideal Gas Law: PV = nRT
Where: n is the number of moles of an ideal gas.
m = molecular weight (g/mole)
M = mass of gas (g)
R = Universal gas constant
= 8.314 J K-1 mole-1
= 0.08206 L atm K-1 mole-1
= 287 J K-1 kg-1 (for air)
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Dalton’s law of partial pressures
P = Si pi
PV = Si piRT = RT Si pi
The mixing ratios of the major constituents
of dry air do not change in the troposphere
and stratosphere.
Copyright © R. R. Dickerson & Z.Q. Li
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Definition of Specific Volume
 = V/m = 1/r
PV/M = nRT/m
P = R’T
Where R’ = R/m
Specific volume, , is the volume occupied by 1.0 g
(sometimes 1 kg) of air.
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& Z.Q. Li
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Definition of gas constant for dry air
p = R’T
Upper case refers to absolute pressure or volume while lower
case refers to specific volume or pressure of a unit (g)
mass.
p = RdT
Where Rd = R/md and md = 28.9 g/mole.
Rd = 287 J kg-1 K-1
(For convenience we usually drop the subscript)
Copyright © 2013 R. R. Dickerson
& Z.Q. Li
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First Law of Thermodynamics
The sum of heat and work in a system is constant, or
heat is a form of energy (Joules Law).
1.0 calorie = 4.1868 J
Q = DU + DW
Where Q is the heat flow into the system, DU is the
change in internal energy, and W is the work
done.
In general, for a unit mass:
đq = du + đw
Note đq and đw are not exact differential, as they are
not the functions of state variables.
Copyright © 2013 R. R. Dickerson
& Z.Q. Li
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Work done by an ideal gas.
Consider a volume of air with a surface area A.
Let the gas expand by a uniform distance of dl.
The gas exerts a force on its surroundings F, where:
F = pA (pressure is force per unit area)
W = force x distance
= F x dl
= pA x dl = pdV
For a unit mass đw = pd
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Expanding gas parcel.
dl
A
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& Z.Q. Li
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In general the specific work done
by the expansion of an ideal gas
from state a to b is W = ∫ab pdα
a
b
p↑
α1
α→
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& Z.Q. Li
α2
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W = ∮ pdα
a
b
p↑
α1
α→
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& Z.Q. Li
α2
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Definition Heat Capacity
• Internal energy change, du, is usually seen as a
change in temperature.
• The temperature change is proportional to the
amount of heat added.
dT = đq/c
Where c is the specific heat capacity.
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& Z.Q. Li
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If no work is done, and for a constant specific
volume:
đq = cvdT = du or
cv = du/dT = Δu/ΔT for an ideal gas
At a constant pressure:
đq = cpdT = du + pdα
= cvdT + pdα or
cp = cv + p dα/dT
But pα = R’T and
p dα/dT = R’ thus
cp = cv + R’
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& Z.Q. Li
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pα = R’T
Differentiating
d(pα) = pdα + αdp = R’dT or
pdα = R’dT − αdp
From the First Law of Thermo for an ideal gas:
đq = cvdT + pdα = cvdT + R’dT − αdp
But cp = cv + R’
đq = cpdT − αdp
This turns out to be a powerful relation for ideal
gases.
Copyright © 2013 R. R. Dickerson
& Z.Q. Li
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Let us consider four special cases.
1. If a process is conducted at constant pressure
(lab bench) then dp = 0.
For an isobaric process:
đq = cpdT − αdp becomes
đq = cpdT
2. If the temperature is held constant, dT = 0.
For an isothermal process:
đq = cpdT − αdp becomes
đq = − αdp = pdα = đw
Copyright © 2013 R. R. Dickerson
& Z.Q. Li
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Next two special cases.
3. If a process is conducted at constant density then
dρ = dα = 0.
For an isosteric process:
đq = cvdT = du
4. If the process proceeds without exchange of heat
with the surroundings dq = 0.
For an adiabatic process:
cvdT = − pdα and cpdT = αdp
Copyright © 2013 R. R. Dickerson
& Z.Q. Li
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The adiabatic case is powerful.
Most atmospheric temperature changes, esp. those
associated with rising or sinking motions are
adiabatic (or pseudoadiabatic, defined later).
For an adiabatic process:
cvdT = − pdα and cpdT = αdp
du is the same as đw
Remember α = R’T/p thus
đq = cpdT = R’T/p dp
Separating the variables and integrating
cp/R’ ∫dT/T = ∫dp/p
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& Z.Q. Li
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cp/R’ ∫dT/T = ∫dp/p
(T/T0) = (p/p0)K
Where K = R’/cp = 0.286
• This allows you to calculate, for an
adiabatic process, the temperature change
for a given pressure change. The sub zeros
usually refer to the 1000 hPa level in
meteorology.
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& Z.Q. Li
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If we define a reference pressure of 1000 hPa (mb)
then:
(T/θ) = (p/1000)K
Where θ is defined as the potential temperature, or
the temperature a parcel would have if moved to
the 1000 hPa level in a dry adiabatic process.
θ = T (1000/p)K
• Potential temperature, θ, is a conserved quantity in
an adiabatic process.
Copyright © 2013 R. R. Dickerson
& Z.Q. Li
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Weather Symbols
http://www.ametsoc.org/amsedu/dstreme/
extras/wxsym2.html
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& Z.Q. Li
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The Second Law of Thermodynamics
dφ ≡ đq/T
Where φ is defined as entropy.
dφ = cvdT/T + pdα/T
= cvdT/T + R’/α dα
∫dφ = ∫đq/T = ∫cv/TdT + ∫R’/α dα
For a cyclic process
∮ đq/T = ∮ cv/TdT + ∮R’/α dα
Copyright © 2014 R. R. Dickerson
& Z.Q. Li
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∮ đq/T = ∮ cv/TdT + ∮R’/α dα
But ∮ cv/T dT = 0 and ∮R’/α dα = 0
because T and α are state variables; thus
∮ đq/T = 0
∮ dφ = 0
Entropy is a state variable.
Copyright © 2013 R. R. Dickerson
& Z.Q. Li
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Remember
Remember
therefore
đq = cpdT − αdp
đq/T = cp/T dT − α/T dp
dφ = cp/T dT − α/T dp
α/T = R’/p
dφ = cp/T dT − R’/p dp
= cp/θ dθ
Δφ = cpln(θ/θ0)
In a dry, adiabatic process potential temperature
doesn’t change thus entropy is conserved.
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& Z.Q. Li
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7am
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& Z.Q. Li
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10 am
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& Z.Q. Li
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