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Lecture 5 --Blackbody Radiation/
Planetary Energy Balance
Abiol 574
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Electromagnetic Spectrum
(m)
1000 100 10 1 0.1 0.01
visible
light
0.7 to 0.4 m
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Electromagnetic Spectrum
(m)
1000 100 10 1 0.1 0.01
ultraviolet
visible
light
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Electromagnetic Spectrum
(m)
1000 100 10 1 0.1 0.01
ultraviolet
visible
lightinfrared
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Electromagnetic Spectrum
(m)
1000 100 10 1 0.1 0.01
ultraviolet
visible
lightinfraredmicrowaves x-rays
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Electromagnetic Spectrum
(m)
1000 100 10 1 0.1 0.01
ultraviolet
visible
lightinfraredmicrowaves x-rays
High
Energy
Low
Energy
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Blackbody Radiation
Blackbody radiationradiation emitted by a body that
emits (or absorbs) equally well at all wavelengths
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The Planck Function
Blackbody radiation follows the Planck function
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Basic Laws of Radiation
1) All objects emit radiant energy.
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Basic Laws of Radiation
1) All objects emit radiant energy.
2) Hotter objects emit more energy than colder
objects.
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Basic Laws of Radiation
1) All objects emit radiant energy.
2) Hotter objects emit more energy than colder
objects. The amount of energy radiated is
proportional to the temperature of the object.
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Basic Laws of Radiation
1) All objects emit radiant energy.
2) Hotter objects emit more energy than colder
objects. The amount of energy radiated is
proportional to the temperature of the object
raised to the fourth power.
This is the Stefan Boltzmann Law
F = T4F = flux of energy (W/m2)
T = temperature (K)
= 5.67 x 10-8 W/m2K4 (a constant)
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Basic Laws of Radiation
1) All objects emit radiant energy.
2) Hotter objects emit more energy than colder
objects (per unit area). The amount of energy
radiated is proportional to the temperature of
the object.
3) The hotter the object, the shorter the
wavelength () of emitted energy.
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Basic Laws of Radiation
1) All objects emit radiant energy.
2) Hotter objects emit more energy than colder
objects (per unit area). The amount of energy
radiated is proportional to the temperature of
the object.
3) The hotter the object, the shorter the
wavelength () of emitted energy.
This isWiens Law
max 3000 mT(K)
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Stefan Boltzmann Law.
F = T4F = flux of energy (W/m2)
T = temperature (K)
= 5.67 x 10
-8
W/m
2
K
4
(a constant)
Wiens Law
max 3000 mT(K)
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We can use these equations to calculate properties
of energy radiating from the Sun and the Earth.
6,000 K 300 K
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T(K)
max(m)
region inspectrum F
(W/m2)
Sun 6000
Earth 300
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T(K)
max(m)
region inspectrum F
(W/m2)
Sun 6000 0.5
Earth 300 10
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Electromagnetic Spectrum
(m)
1000 100 10 1 0.1 0.01
ultraviolet
visible
lightinfraredmicrowaves x-rays
High
Energy
Low
Energy
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T(K)
max(m)
region inspectrum F
(W/m2)
Sun 6000 0.5 Visible
(yellow?)
Earth 300 10 infrared
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Blue light from the Sun is removed from the beam
by Rayleigh scattering, so the Sun appears yellow
when viewed from Earths surface even though its
radiation peaks in the green
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T(K)
max(m)
region inspectrum F
(W/m2)
Sun 6000 0.5 Visible
(green)
Earth 300 10 infrared
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Stefan Boltzman Law.
F = T4F = flux of energy (W/m
2
)T = temperature (K)
= 5.67 x 10-8 W/m2K4 (a constant)
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T(K)
max(m)
region inspectrum F
(W/m2)
Sun 6000 0.5 Visible
(green)
7 x 107
Earth 300 10 infrared 460
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Solar Radiation and Earths Energy Balance
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Planetary Energy Balance
We can use the concepts learned so far
to calculate the radiation balance of the
Earth
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Some Basic Information:
Area of a circle = r2Area of a sphere = 4 r2
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Energy Balance:
The amount of energy delivered to the Earth is
equal to the energy lost from the Earth.
Otherwise, the Earths temperature would
continually rise (or fall).
E B l
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Energy Balance:
Incoming energy = outgoing energy
Ein = Eout
Ein
Eout
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(The rest of this derivation will be done on the
board. However, I will leave these slides in here
in case anyone wants to look at them.)
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How much solar energy reaches the Earth?
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How much solar energy reaches the Earth?
As energy moves away from the sun, it is
spread over a greater and greater area.
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How much solar energy reaches the Earth?
As energy moves away from the sun, it is
spread over a greater and greater area.
This is the Inverse Square Law
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So = L / area of sphere
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So = L / (4 rs-e2
) = 3.9 x 1026 W = 1370 W/m2
4 x x (1.5 x 1011m)2
So is the solar constant for Earth
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So = L / (4 rs-e2
) = 3.9 x 1026 W = 1370 W/m2
4 x x (1.5 x 1011m)2
So is the solar constant for Earth
It is determined by the distance between Earth (rs-e)
and the Sun and the Sun luminosity.
E h l t h it l t t
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Each planet has its own solar constant
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How much solar energy reaches the Earth?
Assuming solar radiation covers the area of a circledefined by the radius of the Earth (re)
Ein re
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How much solar energy reaches the Earth?
Assuming solar radiation covers the area of a circledefined by the radius of the Earth (re)
Ein = So (W/m2) x re2 (m2)
Ein re
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How much energy does the Earth emit?
300 K
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How much energy does the Earth emit?
Eout = F x (area of the Earth)
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How much energy does the Earth emit?
Eout = F x (area of the Earth)
F = T4
Area = 4 re2
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How much energy does the Earth emit?
Eout = F x (area of the Earth)
F = T4
Area = 4 re2
Eout = ( T4) x (4 re2)
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(m)
1000 100 10 1 0.1 0.01
Earth Sun
Hotter objects emit
more energy thancolder objects
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(m)
1000 100 10 1 0.1 0.01
Earth Sun
Hotter objects emit
more energy thancolder objects
F = T4
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(m)
1000 100 10 1 0.1 0.01
Earth Sun
Hotter objects emit at
shorter wavelengths.
max = 3000/T
Hotter objects emit
more energy thancolder objects
F = T4
H h d th E th it?
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How much energy does the Earth emit?
Eout = F x (area of the Earth)
Eout
H h d th E th it?
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How much energy does the Earth emit?
Eout = F x (area of the Earth)
F = T4
Area = 4 re2
Eout = ( T4) x (4 re2)Eout
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How much solar energy reaches the Earth?
Ein
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How much solar energy reaches the Earth?
We can assume solar radiation covers the area of acircle defined by the radius of the Earth (re).
Einre
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How much solar energy reaches the Earth?
We can assume solar radiation covers the area of acircle defined by the radius of the Earth (re).
Ein = So x (area of circle)
Einre
R b
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So = L / (4 rs-e2
) = 3.9 x 1026
W = 1370 W/m2
4 x x (1.5 x 1011m)2
So is the solar constant for Earth
It is determined by the distance between Earth (rs-e)
and the Sun and the Suns luminosity.
Remember
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How much solar energy reaches the Earth?
We can assume solar radiation covers the area of acircle defined by the radius of the Earth (re).
Ein = So x (area of circle)
Ein = So (W/m2) x re2 (m2)
Einre
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How much solar energy reaches the Earth?
Ein = So re2
BUT THIS IS NOT QUITE CORRECT!
**Some energy is reflected away**
Einre
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How much solar energy reaches the Earth?
Albedo (A) = % energy reflected away
Ein = So re2 (1-A)
Einre
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How much solar energy reaches the Earth?
Albedo (A) = % energy reflected away
A= 0.3 today
Ein = So re2 (1-A)Ein = So re2 (0.7)
reEin
Energy Balance:
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gy
Incoming energy = outgoing energy
Ein = Eout
Eout
Ein
Energy Balance:
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gy
Ein = Eout
Ein = So re2 (1-A)
Eout
Ein
Energy Balance:
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gy
Ein = Eout
Ein = So re2 (1-A)Eout = T4(4 re2)
Eout
Ein
Energy Balance:
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gy
Ein = Eout
So re2 (1-A) = T4 (4 re2)
Eout
Ein
Energy Balance:
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Ein = Eout
So re2 (1-A) = T4 (4 re2)
Eout
Ein
Energy Balance:
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Ein = Eout
So (1-A) = T4 (4)
Eout
Ein
Energy Balance:
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Ein = Eout
So (1-A) = T4 (4)T4 = So(1-A)
4Eout
Ein
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T4 = So(1-A)
4If we know So and A, we can calculate the
temperature of the Earth. We call this theexpected temperature (Texp). It is the
temperature we would expect if Earth behaves
like a blackbody.
This calculation can be done for any planet,provided we know its solar constant and albedo.
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T4 = So(1-A)
4For Earth:
So = 1370 W/m2A = 0.3
= 5.67 x 10-8 W/m2K4
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T4 = So(1-A)
4For Earth:
So = 1370 W/m2A = 0.3
= 5.67 x 10-8
T4
= (1370 W/m2
)(1-0.3)4 (5.67 x 10-8 W/m2K4)
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T4 = So(1-A)
4For Earth:
So = 1370 W/m2
A = 0.3 = 5.67 x 10-8
T4 = (1370 W/m2)(1-0.3)
4 (5.67 x 10-8
W/m2
K4
)
T4 = 4.23 x 109 (K4)
T = 255 K
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Expected Temperature:
Texp = 255 K
(oC) = (K) - 273
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Expected Temperature:
Texp = 255 K
(oC) = (K) - 273
So.
Texp= (255 - 273) = -18oC
(which is about 0oF)
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Is the Earths surface really -18 oC?
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Is the Earths surface really -18 oC?
NO. The actual temperature is warmer!
The observed temperature (Tobs) is 15oC, or
about 59 oF.
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Is the Earths surface really -18 oC?
NO. The actual temperature is warmer!
The observed temperature (Tobs) is 15oC, or
about 59 oF.
The difference between observed andexpected temperatures (T):
T = Tobs - Texp
T = 15 - (-18)
T = + 33 oC
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T = + 33 oCIn other words, the Earth is 33 oC warmer thanexpected based on black body calculations
and the known input of solar energy.
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T = + 33 oCIn other words, the Earth is 33 oC warmer thanexpected based on black body calculations
and the known input of solar energy.
This extra warmth is what we call theGREENHOUSE EFFECT.
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T = + 33 oC
In other words, the Earth is 33 oC warmer thanexpected based on black body calculations
and the known input of solar energy.
This extra warmth is what we call theGREENHOUSE EFFECT.
It is a result of warming of the Earths surface
by the absorption of radiation by molecules in
the atmosphere.
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The greenhouse effect:
Heat is absorbed or trappedby gases in the atmosphere.
Earth naturally has a
greenhouse effect of +33o
C.
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The concern is that the amount of greenhouse warming
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