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ATMO 336

Weather, Climate and SocietyHeat Transfer

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What is Heat?

Heat-Energy in the process of being transferred from a warmer object to a cooler object

Consider a pot of water on a hot burner.

Consider the following questions:

Williams, p. 19

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Heat Transfer Questions

What causes the…

Pan bottom and handle to get warmer?

Top of the water to become warmer?

Water temperature to not exceed 100oC? √

Region away from side of pan to feel warm?

Williams, p. 19

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Conduction

Heat transfer due to collision of molecules.Conduction warms the bottom of the pan!Conductivity - rate of heat transfer across a 1 cm thick

slab of material if one side is kept 1oC warmer than the other

Do a Cheap Experiment: Touch metal on your chair!

1 cmMetal Water AirHeat

Transfer

1oC

0oC

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Heat Conductivity

Material Heat Conductivity (Cal s-1 cm-1 oC-1)

Still Air 6.1 x 10 -5

Dry Soil 6.0 x 10 -4

Still Water 1.4 x 10 -3

Wet Soil 5.0 x 10 -2

Granite (Rock) 6.5 x 10 -2

Iron (Metal) 0.16

Silver (Metal) 1.01

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Specific Heat Capacity

Heat required to raise temperature of 1 gm of substance 1oC.

Metal has lower heat capacity than water!

Material Specific Heat Capacity (Cal gm -1 oC-1)

Still Water 1.0

Granite (Rock) 0.19

Iron (Metal) 0.11

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Convection

Heat transfer due to vertical exchange of mass

Occurs in fluids (liquids, gases) because of gravity

Warm, buoyant air rises - Cool, dense air sinks

Convection warms top of liquid!

Warm

Cool Warm

Cool

Warm

Cool

heat below - convection heat side - convection heat top - no convection

gravitygravity

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Convection Movies

2D Convection Tank Animation 2D Convection Model Ra=10**6

2D Convection Model Ra=10**7 IC12D Convection Model Ra=10**7 IC2

3D Rayleigh-Benard Convection Model

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Modes of Heat Transfer

Williams, p. 19

Latent Heat

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Take Home Points

• Heat-Energy transfer due to temperature differencesThree modes of heat transferConduction – molecule to moleculeConvection – transport of fluidRadiation – electromagnetic waves

(On Deck)• Latent Heat – energy of phase changes

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Modes of Heat Transfer

Conduction Convection Radiation

Williams, p. 19

Latent Heat

Remember this thought experiment and

the incandescent light bulb demo

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Latent Heat Take 2

Williams, p 63

Ice Liquid Vapor

Takes energy from environment

Vapor Liquid Ice

Emits energy to environment

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Radiation

• Any object that has a temperature greater than 0 K, emits radiation.

• This radiation is in the form of electromagnetic waves, produced by the acceleration of electric charges.

• These waves don’t need matter in order to propagate; they move at the “speed of light” (3x105 km/sec) in a vacuum.

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Electromagnetic Waves

• Two important aspects of waves are:– What kind: Wavelength or distance between

peaks.– How much: Amplitude or distance between

peaks and valleys.

Wavelength

Amplitude Frequency

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Why Electromagnetic Waves?

• Radiation has an Electric Field Component and a Magnetic Field Component– Electric Field is Perpendicular to Magnetic Field

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Photons

• NOT TO CONFUSE YOU, but…• Can also think of radiation as individual

packets of energy or PHOTONS.• In simplistic terms, radiation with shorter

wavelengths corresponds to photons with more energy (i.e. more BB’s per second) and with higher wave amplitude (i.e. bigger BB’s)

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Emitted Spectrum

White Light from Flash Light

Purple GreenRed

•Emitted radiation has many wavelengths.

Prism

(Danielson, Fig. 3.14)

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Electromagnetic Spectrum

WAVELENGTH

Danielson, Fig. 3.18

Wavelengths of Meteorological Significance

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Radiation Effects on Humans

Danielson, Fig. 3.18

http://hyperphysics.phy-astr.gsu.edu/hbase/mod4.html#c1

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Plank’s Law: Emitted SpectrumEnergy from Sun is spread unevenly over all wavelengths.

Wavelength

En

erg

y E

mit

ted

Emission spectrum of Sun

Ahrens, Fig. 2.7

Planck’s Law

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Planck’s Law and Wien’s Law

The hotter the object, the shorter the brightest wavelength.

Danielson, Fig. 3.19

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Wien’s Law

Relates the wavelength of maximum emission to the temperature of mass

MAX= (0.29x104 m K) x T-1

Warmer Objects => Shorter Wavelengths• Sun-visible light

MAX= (0.29x104 m K) x (5800 K)-1 = 0.5 m

• Earth-infrared radiation

MAX= (0.29x104 m K) x (290 K)-1 = 10 m

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Wien’s Law

What is the radiative temperature of an incandescent bulb whose wavelength of maximum emission is near 1.0 m ?

• Apply Wien’s Law:

MAX= (0.29 x 104 m K) x T-1

• Temperature of glowing tungsten filament

T= (0.29 x 104 m K) x ( MAX)-1

T= (0.29 x 104 m K) x (1.0 m)-1 = 2900K

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What is Radiative Temperature of Sun if Max Emission Occurs at 0.5 m?

• Apply Wien’s Displacement Law

max=2900mK

T

T=2900mKmax

T=2900mK0.5m

T=5800K

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Stefan-Boltzmann’s (SB) Law

• The hotter the object, the more radiation emitted.

• Double the temperature Total emitted radiation increases by a factor of 16!

• Stefan-Boltzmann’s Law

E= (5.67x10-8 Wm-2K-4 ) x T4

E=2x2x2x2=16

4 times

Sun Temp: 6000K

Earth Temp: 300K

Aguado, Fig. 2-7

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How Much More Energy is Emitted by the Sun per m2 Than the Earth?

• Apply Stefan-Boltzman Law

• The Sun is 160,000 Times More Energetic per m2 Than the Earth, Plus Its Area is Mucho Bigger!

-2 -2 -4

-2

-2

48

8 4

48

4 544

(W m ) W m K

W mW m

(5.67 10 )

(5.67 10 ) (5800 )5.67 ( )( 10 ) 290

(5800 ) 1.6 1020(290 )

Sun

Earth

E T

E KKE

KK

−

−

−

= ×

×=×

= = ×=

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How Much More Energy is Emitted by the Sun than the Earth?

• Apply Stefan-Boltzman Law

2

2

-2 -2 -4

-2 -4

-2 -4

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8 4 4 54448

25 43

(W m ) W m K

W m K KW m K K

(5.67 10 )

(5.67 10 ) (5800 ) 5800 1.6 10202905.67 ( )( 10 ) 290

4 7.0 10 1.2 10 (12,000 )4 6.4 10

Sun

Earth

Sun Sun

Earth Earth

Sun

E T

EE

A r times largerA r

A

ππ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

−

−

−

= ×

× = ×= ==×

×= ×≈ ≈×

92.0 10 (2 )Sun

EarthEarth

E billion times moreenergeticA E

×≈

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Radiative Equilibrium

• Radiation absorbed by an object increases the energy of the object.– Increased energy causes temperature to

increase (warming).

• Radiation emitted by an object decreases the energy of the object.– Decreased energy causes temperature to

decrease (cooling).

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Radiative Equilibrium (cont.)

• When the energy absorbed equals energy emitted, this is called Radiative Equilibrium.

• The corresponding temperature is the Radiative Equilibrium Temperature.

• Concept is analogous to a bathtub with the faucet running and the drain unplugged. If water in exceeds water out, level rises. If water in is less than water out, level falls.If water in equals water out, level is constant or at an equilibrium level.

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Modes of Heat Transfer

Williams, p. 19

Latent Heat

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General Laws of Radiation

• All objects above 0 K emit radiant energy• Hotter objects radiate more energy per unit

area than colder objects, result of Stefan-Boltzman Law

• The hotter the radiating body, the shorter the wavelength of maximum radiation, result of

Wien’s Displacement Law• Final point: objects that are good absorbers of

radiation are also good emitters!

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Why Selective, Discrete Absorption/Emission?

Life as we perceive it: A continuous world!

Atomic perspective: A quantum world!

Gedzelman 1980, p 103

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Energy States for AtomsElectrons can orbit in

only permitted states

A state corresponds to specific energy level

Only quantum jumps between states can occur

Intervals correspond to specific wavelengths of radiation

Hydrogen Applet Probability States

Gedzelman 1980, p 104

Hydrogen Atom

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Energy States for Molecules

Molecules can also rotate, vibrate, librate

But only at specific energy levels or frequencies

Quantum intervals between modes correspond to specific wavelengths

Gedzelman 1980, p 105

H2O molecule H2O Bands H2O Bands

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Selective Absorption

The Bottom Line

Each molecule has a unique distribution of quantum states!

Each molecule has a unique spectrum of absorption and emission frequencies of radiation!

H2O molecule

Williams, p 63

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Humans are Selective Absorbers

Danielson, Fig. 3.18

http://hyperphysics.phy-astr.gsu.edu/hbase/mod4.html#c1

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Ahrens, Fig. 2.9

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Absorption Visible (0.4-0.7 m) is

absorbed very littleO2 an O3 absorb UV

(shorter than 0.3 m) Infrared (5-20 m) is

selectively absorbedH2O & CO2 are strong

absorbers of IRLittle absorption of IR

around 10 m – atmospheric window

MODTRAN3 (D. Archer)

Full Spectrum (D. Archer)

Visible

IR

Ahrens, Fig. 2.9

UV

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Total Atmospheric Absorption

Visible radiation (0.4-0.7 m) is not absorbedInfrared radiation (5-20 m) is selectively absorbed,

but there is an emission window at 10 m

Ahrens, Fig. 2.9

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Key Points

• Radiation is emitted from all objects that have temperatures warmer than absolute zero (0 K).

• Wien’s Law: wavelength of maximum emissionMAX= (0.29x104 m K) x T-1

• Stefan-Boltzmann Law: total energy emissionE= (5.67x10-8 W/m2 ) x T4

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Key Points

• Radiative equilibrium and temperatureEnergy In = Energy Out (Eq. Temp.)

• Each molecule has a Unique distribution of permitted, quantum energy statesUnique spectrum of absorption and emission frequencies of radiation

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Key Points

• Three modes of heat transferConduction: molecule-to-molecule

Convection: fluid motion

Radiation: electromagnetic waves

• Heat transfer works to equilibrate temperature differences