AOSC 620 PHYSICS AND CHEMISTRY OF THE ATMOSPHERE, I

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AOSC 620PHYSICS AND CHEMISTRYOF THE ATMOSPHERE,
I
Professor Russell Dickerson Room 2413, Computer
Space Sciences Building Phone(301)
405-5364 russ_at_atmos.umd.edu web site
www.meto.umd.edu/russ
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Professor Severus Snape (Thanks to J. K. Rowling)
"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."
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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."
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Logistics

• Office Hours Tuesdays 330 430 pm
• Wednesdays 100 200 pm
• Worst time is 1-2pm Tues or Thrs.
• Exam Dates Oct. 13 Dec.3, 2009.
• Final Examination Thursday, December 17, 2009
  1030am -1230 p.m.
• www/atmos.umd.edu/russ/syllabus620.html

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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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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.
• Due 9/15/09

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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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Daltons 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.
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Definition of Specific Volume

• V/m 1/r
• PV/M nRT/m
• Pa RT
• Where R R/m
• Specific volume, a, is the volume occupied by 1.0
  g (sometimes 1 kg) of air.

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Definition of gas constant for dry air

• pa RT
• Upper case refers to absolute pressure or volume
  while lower case refers to specific volume or
  pressure of a unit (g) mass.
• pa 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)

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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
• dq du dw
• Note dq and dw are not exact differential, as
  they are not the functions of state variables.

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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 dw pda

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Expanding gas parcel.
dl
A
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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 pda
a
b
p?
a1
a2
a?
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W ? pda
a
b
p?
a1
a2
a?
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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 dq/c
• Where c is the specific heat capacity.

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• If no work is done, and for a constant specific
  volume
• dq cvdT du or
• cv du/dT ?u/?T for an ideal gas
• At a constant pressure
• dq cpdT du pda
• cvdT pda or
• cp cv p da/dT
• But pa RT and
• p da/dT R thus
• cp cv R

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• pa RT
• Differentiating
• d(pa) pda adp RdT or
• pda RdT - adp
• From the First Law of Thermo for an ideal gas
• dq cvdT pda cvdT RdT - adp
• But cp cv R
• dq cpdT - adp
• This turns out to be a powerful relation for
  ideal gases.

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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
• dq cpdT - adp becomes
• dq cpdT
• 2. If the temperature is held constant, dT 0.
• For an isothermal process
• dq cpdT - adp becomes
• dq - adp pda dw

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• Next two special cases.
• 3. If a process is conducted at constant density
  then d? da 0.
• For an isosteric process
• dq cvdT du
• 4. If the process proceeds without exchange of
  heat with the surroundings dq 0.
• For an adiabatic process
• cvdT - pda and cpdT adp

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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 - pda and cpdT adp
• du dw
• Remember a RT/p thus
• dq cpdT RT/p dp
• Separating the variables and integrating
• cp/R ?dT/T ?dp/p

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• cp/R ?dT/T ?dp/p
• (T/T0) (p/p0)K
• Where K R/cp 287/1005 0.286 (unitless)
• 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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• If we define a reference pressure of 1000 hPa
  (mb) then
• (T/?) (p/1000)K
• Where ? 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.
• ? T (1000/p)K
• Potential temperature, ?, is a conserved quantity
  in an adiabatic process.

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Weather Symbols
http//www.ametsoc.org/amsedu/dstreme/ extras/wxsy
m2.html
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The Second Law of Thermodynamics

• df dq/T
• Where f is defined as entropy.
• df cvdT/T pda/T
• cvdT/T R/a da
• ? dq/T ? cv/TdT ?R/a da

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• ? dq/T ? cv/TdT ?R/a da
• But ? cv/T dT 0 and ?R/a da 0
• because T and a are state variables thus
• ? dq/T 0
• ? df 0
• Entropy is a state variable.

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• Remember
• dq cpdT - adp
• dq/T cp/T dT - a/T dp
• df cp/T dT - a/T dp
• Remember a/T R/p
• therefore
• df cp/T dT - R/p dp
• cp/? d?
• ?f cpln(?/?0)
• In a dry, adiabatic process potential temperature
  doesnt change thus entropy is conserved.

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7am
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10 am