Lecture 5 -- Blackbody Radiation/ Planetary Energy Balance

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Lecture 5 -- Blackbody Radiation/Planetary
Energy Balance

• Abiol 574

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Electromagnetic Spectrum
visible light
0.7 to 0.4 ?m
? (?m)
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Electromagnetic Spectrum
visible light
ultraviolet
? (?m)
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Electromagnetic Spectrum
visible light
ultraviolet
infrared
? (?m)
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Electromagnetic Spectrum
visible light
ultraviolet
infrared
x-rays
microwaves
? (?m)
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Electromagnetic Spectrum
visible light
ultraviolet
infrared
x-rays
microwaves
High Energy
Low Energy
? (?m)
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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
• All objects emit radiant energy.

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• Basic Laws of Radiation
• All objects emit radiant energy.
• Hotter objects emit more energy than colder
  objects.

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• Basic Laws of Radiation
• All objects emit radiant energy.
• 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
• All objects emit radiant energy.
• 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 ? T4
• F 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
• All objects emit radiant energy.
• Hotter objects emit more energy than colder
  objects (per unit area). The amount of energy
  radiated is proportional to the temperature of
  the object.
• The hotter the object, the shorter the wavelength
  (?) of emitted energy.

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• Basic Laws of Radiation
• All objects emit radiant energy.
• Hotter objects emit more energy than colder
  objects (per unit area). The amount of energy
  radiated is proportional to the temperature of
  the object.
• The hotter the object, the shorter the wavelength
  (?) of emitted energy.
• ?This is Wiens Law
• ?max ? 3000 ?m
• T(K)

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? Stefan Boltzmann Law. F ? T4 F flux
of energy (W/m2) T temperature (K) ? 5.67
x 10-8 W/m2K4 (a constant) ? Wiens Law
?max ? 3000 ?m T(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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Electromagnetic Spectrum
visible light
ultraviolet
infrared
x-rays
microwaves
High Energy
Low Energy
? (?m)
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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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? Stefan Boltzman Law. F ? T4 F flux
of energy (W/m2) T temperature (K) ? 5.67
x 10-8 W/m2K4 (a constant)
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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 ?
r2 Area 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).
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Energy Balance Incoming energy outgoing
energy Ein Eout
Eout
Ein
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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.
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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 circle defined 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 circle defined 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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Sun
Earth
Hotter objects emit more energy than colder
objects
? (?m)
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Sun
Earth
Hotter objects emit more energy than colder
objects F ? T4
? (?m)
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Hotter objects emit at shorter wavelengths. ?max
3000/T
Sun
Earth
Hotter objects emit more energy than colder
objects F ? T4
? (?m)
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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
Eout (? T4) x (4 ? re2)
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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 a
circle defined by the radius of the Earth (re).
Ein
re
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How much solar energy reaches the Earth? We can
assume solar radiation covers the area of a
circle defined by the radius of the Earth
(re). Ein So x (area of circle)
Ein
re
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Remember
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.
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How much solar energy reaches the Earth? We can
assume solar radiation covers the area of a
circle defined by the radius of the Earth
(re). Ein So x (area of circle) Ein So
(W/m2) x ? re2 (m2)
Ein
re
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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
Ein
re
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How much solar energy reaches the Earth? Albedo
(A) energy reflected away Ein So ? re2
(1-A)
Ein
re
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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)
re
Ein
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Energy Balance Incoming energy outgoing
energy Ein Eout
Eout
Ein
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Energy Balance Ein Eout Ein So ? re2 (1-A)
Ein
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Energy Balance Ein Eout Ein So ? re2
(1-A) Eout ? T4(4 ? re2)
Ein
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Energy Balance Ein Eout So ? re2 (1-A) ?
T4 (4 ? re2)
Ein
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Energy Balance Ein Eout So ? re2 (1-A) ?
T4 (4 ? re2)
Ein
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Energy Balance Ein Eout So (1-A) ? T4 (4)
Ein
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Energy Balance Ein Eout So (1-A) ? T4
(4) T4 So(1-A) 4?
Ein
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T4 So(1-A) 4?
If we know So and A, we can calculate the
temperature of the Earth. We call this the
expected 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) 4?
For Earth So 1370 W/m2 A 0.3 ? 5.67 x
10-8 W/m2K4
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T4 So(1-A) 4?
For 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/m2K4)
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T4 So(1-A) 4?
For 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/m2K4) 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) -18 oC (which is
about 0 oF)
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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 15 oC, 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 15 oC, or about 59 oF. The
difference between observed and expected
temperatures (?T) ?T Tobs - Texp ?T 15 -
(-18) ?T 33 oC
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?T 33 oC In other words, the Earth is 33 oC
warmer than expected based on black body
calculations and the known input of solar energy.
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?T 33 oC In other words, the Earth is 33 oC
warmer than expected based on black body
calculations and the known input of solar
energy. This extra warmth is what we call the
GREENHOUSE EFFECT.
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?T 33 oC In other words, the Earth is 33 oC
warmer than expected based on black body
calculations and the known input of solar
energy. This extra warmth is what we call the
GREENHOUSE 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
trapped by gases in the atmosphere. Earth
naturally has a greenhouse effect of 33 oC.
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The concern is that the amount of greenhouse
warming will increase with the rise of CO2 due to
human activity.