Copyright © R. R. Dickerson & Z.Q. Li11 Professor Russell Dickerson Room 2413, Computer & Space...

Copyright © R. R. Dickerson & Z.Q. Li 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

Copyright © 2013 R. R. Dickerson & Z.Q. Li

22

"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."

3

Professor Severus Snape

(Thanks to J. K. Rowling)

Copyright © 2013 R. R. Dickerson 44

"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."


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


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.


77

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.


88

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.


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)


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.


1111

Definition of Specific Volume

= V/m = 1/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.


1212

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)


1313

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 + đw

Note đq and đw are not exact differential, as they are not the functions of state variables.


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


1515

Expanding gas parcel.

A

dl


1616

In general the specific work done by the expansion of an ideal gas

from state a to b is W = ∫ab pdα

p↑

α→

ab

α1 α2


1717

W = ∮ pdα

p↑

α→

ab

α1 α2


1818

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.


1919

If no work is done, and for a constant specific volume:

đq = cvdT = du or

cv = du/dT = Δu/ΔT for an ideal gasAt a constant pressure:

đq = cpdT = du + pdα

= cvdT + pdα or

cp = cv + p dα/dTBut pα = R’T and p dα/dT = R’ thus

cp = cv + R’


2020

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.


2121

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 becomesđq = − αdp = pdα = đw


2222

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


2323

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 dpSeparating the variables and integrating

cp/R’ ∫dT/T = ∫dp/p


2424

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.


2525

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.


2626

Weather Symbolshttp://www.ametsoc.org/amsedu/

dstreme/extras/wxsym2.html


2727

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


2828

∮ 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.


2929

Remember

đq = cpdT − αdp

đq/T = cp/T dT − α/T dp

dφ = cp/T dT − α/T dpRemember α/T = R’/p therefore

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.


3030

7am


3131

10 am

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