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Copyright © R. R. Dickerson & Z.Q. Li33 Logistics Office Hours: Tuesdays 3:30 – 4:30 pm (except today) Wednesdays 1:00 – 2:00 pm Worst time is 1- 2 pm Tues or Thrs. Exam Dates: October 13, November 24, 2015 Final Examination: Thursday, Dec. 17, :30am- 12:30pm www/atmos.umd.edu/~russ/SYLLABUS_620_2015.html
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Copyright © R. R. Dickerson 2015 11
Professor Russell Dickerson Room 2413, Computer & Space Sciences Building Phone(301) [email protected] web site www.meto.umd.edu/~russ
AOSC 620PHYSICS AND CHEMISTRY
OF THE ATMOSPHERE, I
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Objectives of AOSC 620 & 621• Present the basics of atmospheric chemistry and
physics.• Teach you experimental and theoretical methods.• Show you tools that will help you solve
problems that have never been solved before.• Prepare you for a career that pushes back the
frontiers of atmospheric or oceanic science.
Copyright © R. R. Dickerson & Z.Q. Li 33
Logistics
Office Hours: Tuesdays 3:30 – 4:30 pm(except today)Wednesdays 1:00 – 2:00 pmWorst time is 1- 2 pm Tues or Thrs.Exam Dates: October 13, November 24, 2015Final Examination: Thursday, Dec. 17, 2015 10:30am-12:30pmwww/atmos.umd.edu/~russ/SYLLABUS_620_2015.html
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Changes to Syllabus, 2015/16
Basically all of atmospheric chemistry will be taught in AOSC 620.
The remainder of cloud physics and radiation will be taught in AOSC 621.
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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.
Copyright © R. R. Dickerson 77
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 See R&Y Chapter 1Salby Chapter 1.2 and 2.2-2.3W&H Chapter 3.
Copyright © R. R. Dickerson & Z.Q. Li 88
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)
Copyright © R. R. Dickerson & Z.Q. Li 99
Dalton’s law of partial pressures
P = i pi
PV = i piRT = RT i 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/PV/M = nRT/m
P = R’TWhere R’ = R/m
Specific volume, is the volume occupied by 1.0 g (sometimes 1 kg) of air.
Copyright © 2015 R. R. Dickerson & Z.Q. Li
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Definition of gas constant for dry air
p = R’TUpper 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 © 2015 R. R. Dickerson & Z.Q. Li
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First Law of ThermodynamicsThe 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 = U + WWhere Q is the heat flow into the system, U is the
change in internal energy, and W is the work done.In general, for a unit mass:
đq = du + đwNote đq and đw are not exact differential, as they are
not the functions of state variables.
Copyright © R. R. Dickerson & Z.Q. Li 1313
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.
A
dl
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In general the specific work done by the expansion of an ideal gas from state a to b is W = ∫a
b pdα
p↑
α→
ab
α1 α2
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W = ∮ pdα
p↑
α→
ab
α1 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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If no work is done, and for a constant specific volume:
đq = cvdT = du orcv = du/dT = Δu/ΔT for an ideal gas
At a constant pressure:đq = cpdT = du + pdα
= cvdT + pdα orcp = cv + p dα/dT
But pα = R’T and p dα/dT = R’ thus
cp = cv + R’
Copyright © 2015 R. R. Dickerson & Z.Q. Li
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pα = R’TDifferentiating
d(pα) = pdα + αdp = R’dT orpdα = 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 © 2015 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 becomesđq = cpdT
2. If the temperature is held constant, dT = 0.For an isothermal process:
đq = cpdT − αdp becomesđq = − αdp = pdα = đw
Copyright © 2015 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 © 2015 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 đwRemember α = R’T/p thus
đq = cpdT = R’T/p dpSeparating 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 = 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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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.
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Weather Symbolshttp://www.ametsoc.org/amsedu/
dstreme/extras/wxsym2.html
Copyright © 2014 R. R. Dickerson & 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
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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 = 0Entropy is a state variable.
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Rememberđq = cpdT − αdp
đq/T = cp/T dT − α/T dpdφ = cp/T dT − α/T dp
Remember α/T = R’/p Therefore
In a dry, adiabatic process potential temperature doesn’t change thus entropy is conserved.
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