The Physics of Energy sources
Greenhouse effect
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Ref 1: Boyle, Everett and Ramage, Energy Systems and Sustainability (2003)
1
Starting with the Blackbody emission
!   A body at a given temperature will have a thermal emission
!   Planck s law
2hν 3
I (ν , T ) =
in W .m − 2 .Hz −1.sr −1
⎛ hν ⎞
⎛
⎞
⎜
⎟
2 ⎜ ⎝ kT ⎠
c e
− 1⎟
⎜
⎟
⎝
⎠
h : Planck constant k : Boltzmann constant
ν : Frequency T : temperature of Blackbody
More generally, an object is associated to a grey body
Emission of grey body = ε (ν ).I (ν , T )
ε (ν ) is the emissivity of the object (depends on material)
For a good mirror, ε (ν ) < 0.01
So, for a blackbody emissivity=1
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Planck, Wien and Rayleigh-Jeans
Planck Law
Rayleigh-Jeans
Approx.
2kTν 2
R − J (ν , T ) =
c2
I (ν , T ) =
2hν 3
⎛
c 2 ⎜ e
⎜
⎝
⎛ hν ⎞
⎜
⎟
⎝ kT ⎠
⎞
− 1⎟
⎟
⎠
in W .m − 2 .Hz −1.sr −1
Wien
Approx.
⎛ hν ⎞
2hν 3 −⎜⎝ kT ⎟⎠
Wien(ν , T ) = 2 e
c
T=300K
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Frequency (Hz)
3
I (ν , T ) =
2hν 3
⎛ ⎛⎜ hkTν ⎞⎟ ⎞
c ⎜ e ⎝ ⎠ − 1⎟
⎜
⎟
⎝
⎠
2
in W .m − 2 .Hz −1.sr −1
Example of Blackbody emission
(frequency, Temperature)
T=400K
T=300K
One of the most famous:
Cosmic Microwave Background
T=200K
Frequency (Hz)
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COBE Satellite
(1992)
4
Blackbody emission 2 (Wavelength, Temperature)
1 .10
11
1 .10
12
λ=
− 11
10
1 .10
300K
c
⇒
ν
I (λ , T ) =
13
77K
1 .10
14
2hc 2
⎛ hc ⎞
⎛
⎞
⎜
⎟
5 ⎜ ⎝ λkT ⎠
λ e
− 1⎟
⎜
⎟
⎝
⎠
in W .m − 2 .m −1.sr −1
B(ν i , 300K)
B(ν i , 77K)
1 .10
15
1 .10
16
1 .10
17
20K
B(ν i , 20K)
B(ν i , 4.2K)
B(ν i , 1.5K)
4.2K
1 .10
18
1 .10
19
− 20
10 1 .10
λ in microns
log – log scale
1.5K
20
10
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10
3
1 .10
100
6
λi⋅ 10
4
1 .10
3
5× 10
5
How does a greenhouse work?
Analogy between the glass of a greenhouse and the atmosphere of
the Earth: they have the same role for the greenhouse effect.
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The Sun
Star emission= Blackbody with T= star surface temperature
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The atmosphere
Transmission
absorption
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Greenhouse effect
Figures from Global warming art
http://www.globalwarmingart.com/wiki/Image:Greenhouse_Effect_png
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A more accurate thermal balance
Figure from Adam Frederick – Severewx.com
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Summary: What did we see?
!   Blackbody emission: Planck function
!   Could you explain briefly the concept?
!   Would you be able to plot it (shape) vs frequency or wavelength?
!   Would you be able to tell in which part of the EM spectrum the Sun is
radiating most of its power?
!   Greenhouse effect
!   Would you be able to explain it in a few sentences?
!   Would you be able to explain the interaction of the radiation within the
atmosphere?
!   Do you know which gases cause the greenhouse effect?
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