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Climate Sciences: Atmospheric Thermodynamics

Instructor: Lynn Russell, NH343 http://aerosol.ucsd.edu/courses.html

Text: Curry & Webster

Atmospheric Thermodynamics

Ch1 Composition

Ch2 Laws

Ch3 Transfers Ch12

EnergyBalance

Ch4 Water

Ch5 Nucleation

Ch6 Processes

Ch7 Stability

Ch8 Clouds

Ch12 EnergyBalance

Ch13 Feedbacks

Climate Sciences: Atmospheric Thermodynamics

Instructor: Lynn Russell, NH343 http://aerosol.ucsd.edu/courses.html

Text: Curry & Webster

Course Principles

Green classroom Minimal handouts, optional paper text, etc.

Respect for learning On time, on schedule: quizzes No chatting (in class), no cheating

Focused exams Core principles not algebra

Office hours help on homework, projects Team learning by projects

Bring different backgrounds to common topics

Homework Schedule Email Single PDF to lmrussell@ucsd.edu

Due Oct. 14 (Monday, 12 noon) Ch. 1, Problem 11 Ch. 2, Problem 2

Due Oct. 23 (Wednesday, 12 noon) Ch. 3, Problem 1, 2 (typo in answer key), 3

Due Oct. 30 (Wednesday, 12 noon) Ch. 4, Problem 4, 5

Midterm Nov. 6 (Wednesday, in class) Due Nov. 13 (Wednesday, 12 noon)

Ch. 5, Problem 3, 7 (erratum in 7d) Ch. 6, Problem 4, 6

Due Nov. 18 (Monday, 12 noon) Ch. 7, Problem 3 (not graded, outline approach only, discuss)

What do we learn in Ch. 1? What P, T, U are for a fluid What an ideal gas is How P, T, v relate for an ideal gas (and we

call this relationship an equation of state) What chemical components constitute the

atmosphere (for homosphere

2

The Greenhouse Effect Solar radiation

Long-wave radiation

IPCC 2013

Review Topics in Ch. 1

Thermodynamic quantities Composition Pressure Density Temperature Kinetic Theory of Gases

Curry and Webster, pp. 1-17 Feynman, Book I, ch. 39

Thermal Structure of the Atmosphere

3

Thermodynamic Quantities Classical vs. Statistical thermodynamics Open/closed systems Equation of state f(P,V,T)=0 Extensive/intensive properties Thermal, engine, heat/work cycles

Intensive quantities: P, T, v, n Extensive quantities: V, N

Concentration: n=N/V Volume: v=V/N

System Environment

Composition Structure

Comparison to other planets N2, O2, Ar, CO2, H2O: 110 km constitute 99% Water, hydrometeors, aerosol

Pressure Force per unit area 1 bar = 105 Pa; 1 mb = 1 hPa; 1 atm = 1.013 bar Atmosphere vs. Ocean

Atmosphere

Ocean

4

Pressure Force per unit area

1 bar = 105 Pa; 1 mb = 1 hPa; 1 atm = 1.013 bar

Density Specific volume: v=V/m

0.78 m3 kg-1 for air Density: =m/V

1.29 kg m-3 for air

Temperature Zeroeth Law of Thermodynamics

Equilibrium of two bodies with third Allows universal temperature scale

Temperature scale Two fixed points: Kelvin, Celsius Thermometer

Lapse Rate = -T/z Change in temperature with altitude Typically =6.5 K/km

Temperature inversion

5

ICAO Standard Atmosphere Hydrostatic Balance

Applicable to most atmospheric situations (except fast accelerations in thunderstorms)

Why? This is just a force balance on an air parcel.

g = 1pz

p = pgRdT

z

Curry and Webster, Ch. 1

gm = Ap then use m = v = Az

g = A pAz( )

= pz

Homogeneous Atmosphere

Density is constant Surface pressure is finite Scale height H gives where pressure=0

p0 = gH

H = pg

=RdT0g

g = 1pz

dp = gdz

dpp0

0 = gdz0

H

0 p0 = gH 0( )

Curry and Webster, Ch. 1

Hydrostatic + Ideal Gas + Homogeneous

Evaluate lapse rate by differentiating ideal gas law

p = RdTpz

= RdTz

1pz

= Rd

Tz

g = 1pz

= Tz

=gRd

= 34.1oC/km

Density constant

Ideal gas

Hydrostatic

Curry and Webster, Ch. 1

Lapse Rate

= -dT/dz Change in

temperature with height

Defined to be positive in troposphere

Troposphere: dT = 70 C dz = 10 km

So, = 7 C/km

Hydrostatic Equation (1)

Hydrostatic Balance (1.33)

Geopotential Height (1.36a)

Homogeneous atmosphere (1.38)

g = 1pz

Z = 1g0

gdz0

z

p0 = gHN.B. constant[ ]

H = RdT0g

= 8 km

pz

= RdTz

N.B. ideal gas[ ]

= Tz

=gRd

= 34.1C km-1

6

Hydrostatic Equation (2)

Isothermal Atmosphere (1.42)

Constant Lapse Rate (1.48)

p = pgRdT

z

N.B. T = constant[ ]

p = p0 exp z H( ) for H = RT g

dpp

= gRd

dzT0 z

N.B. = constant[ ]

p = p0TT0

gRd

Kinetic Theory of Gases What is the pressure of a gas? What is the temperature of a gas? Pressure-volume-temperature relationship(s)

How does pressure (and volume) relate to energy?

Kinetic energy Internal energy

The fine print

Initial Momentum: mvx

Final Momentum: -mvx

If all atoms had same x-velocity vx: Momentum Change for one Atom-Collision: [Initial]-[Final] = mvx-(-mvx) = 2mvx Number of Atom-Collisions-Per-Time: [Concentration]*[Volume] = [n]*[vxA] Force = [Number]*[Momentum Change] = [nvxA]*[2mvx] = 2nmAvx2 Pressure = [Force]/[Area] = 2nmvx2

For atoms with average velocity-squared of : Pressure = [Force]/[Area] = nm

Force: F Area: A

Collision Distance-Per-Time: vxt/t=vx

Individual collisions Perfect reflection Ideal gas Monatomic gas

Population-averaged Velocity: =[vi2 + vii2 + viii2 ++ vn2]/n Scalar multipliers: =[mvi2 + mvii2 + mviii2 ++ mvn2]/2n

How many will hit right wall? n/2

vii

viii

vi

3D velocity: =++ Random motion (no preferred direction): ==

= /3

v

vx vz

vy

P = nm =[2/2]*[nm]*[/3] =[2/3]n* =[2/3]n*[kinetic energy of molecule]

PV =[2/3]*[N*] =[2/3]*U =[2/3]*Ek

Concentration: n=N/V Total internal energy: U Kinetic energy of gas

7

PV =[2/3]*Ek Ek =[3/2]* PV

Define T = f(Ek) For scale choose T=(2/3Nk)*Ek Ek =(3/2)*NkT

Then PV = NkT = nR*T

Kinetic energy of gas RHS is independent of gas --> so scale can be universal

Mean k.e.: Ek/N=(3/2)kT k=1.38x10-23 J/K

R*=N0k=8.314 J/mole/K

Temperature is defined to be

proportional to the average kinetic energy of the molecules.