10 April, 2014
The Sun
Blackbody radiation and
the greenhouse effect
Keywords
1. Radiation: Law of Stefan-Boltzmann
2. Radiation and the Earth atmosphere
3. Greenhouse effect (simple models)
Ronald Griessen 2008
Vrije Universiteit, Amsterdam
1
2
What heats the
564 million tons of hydrogen
are converted into 560 million
tons of helium per second
(0.42 MeV)
E=mc2
3.8 x 1026 W
1 MeV=1.6 x 10-13 J
63 MW/m2
3
1. Measuring the Sun’s temperature
564 million tons of hydrogen
are converted into 560 million
tons of helium per second
3.8 x 1026 W
Planck’s Law
30000
Spectral Irradiance (W/m /eV))
E=mc2
4
2
But how do we know this?
dE 2 2
h
 2 h
d
c e k BT  1
25000
63 MW/m2
20000
5800 K
15000
10000
T = 5800 K
5000
0
0
2
4
6
8
Photon energy [eV]
5
6
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10 April, 2014
2. Calculating the total power
World Total Primary Energy Supply 2005
3.8 x 1026 W
3.8 x 1026 W
T = 5800 K
Stefan–Boltzmann law
 = 5.67x10-8Wm-2K-4
17.2 TW
8
7
http://www.iea.org/textbase/nppdf/free/2007/Key_Stats_2007.pdf
IEA: KeyWorld2013.pdf
Solar area Sahara
1368 W/m2
1.5 x 1011 m
Future world power consumption
1010 persons  5 kW/person = 50 TW




148 m2/person
R2
63 MW/m2
Solar constant: 1350 W/m2
50% reaches the Earth’s surface
25% due to R2/4R2
Efficiency of photovoltaics: 20%.
1.48  106 km2
R2
7 x 108 m
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9
50 TW
Heat transfer through radiation
1200 x 1200 km2
1200 x 1200 km2
63 MW/m2
63 MW/m2
0.8 km2 gives 50 TW
0.8 km2 gives 50 TW
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10 April, 2014
Summary heat transfer by radiation
You are radiating, too
Stefan–Boltzmann law
Spectral energy density dE/df
S = 5.67 x 10-8 T4 [W/m2]
Planck’s Law
1.5
dE   2 2
h
 2 h
d
c e k BT  1
1.0
300 K
600 K
900 K
1200 K
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Photon energy [eV]
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Some constants
Planck's constant: h
6.626 0693(11)×10-34 Js =
4.135 667 43(35)×10-15 eVs
Wien's displacement
constant
b = 2.897 7685(51)×10–3 mK
 max  Tb
1.380 6505(24)×10−23 J/K =
8.617 343(15)×10−5 eV/K
Boltzmann constant: kB
Stefan–Boltzmann
constant: 
5.670 400(40)×10−8 Wm-2K-4
Speed of light: c
299 792 458 m/s
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Spectral irradiance on Earth
dE   2 2
h
 2 h
d
c e k BT  1
15
16
Incoming and reflected solar energy
70% absorbed
100 %
The Greenhouse effect
Atmosphere:
6%
Clouds: 20 %
Earth’s surface: 4 %
17
18
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10 April, 2014
Without atmosphere
5600 K
Absorption by the atmosphere
260 K
5600 K
260 K
19
Why water and CO2 ?
20
Earth without an atmosphere
equilibrium:
O
H
O
+
ASSun
_
_
H
+
SSun
C
O
 R 2 S Sun 1  A   4 R 2 S Earth
4
1  A S Sun  4S Earth  4 TEarth
1 − 0. 31366 W m−2  4  5. 67  10 −8 W m−2 K −4  T 4
T Earth  255 K
SE
_
(1-A)SSun
_
+
_
+
e.m. wave
e.m. wave
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Earth with totally absorbing atmosphere:
Greenhouse effect
Sa
ASSun
SSun
T Earth  −18 o C
2 Sa  S Earth
 R 2 S Sun 1  A   4 R 2 Sa  4 R 2 S Earth
SE
(1-A)SSun
Sa
S Sun 1  A   4S a  4S Earth
4
S Sun 1  A   2S Earth  2 TEarth
T Earth  303 K
T Earth  30 o23C
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Direct Global Warming Potentials (mass basis)
relative to carbon dioxide
GAS
Pre-1750 Current
concentra tropospheric
-tion
concentration
GWP *)
(100-year
time horizon)
Atmospheric
lifetime
(years)
variable
Carbon dioxide (CO2)
280 ppm
377.3 ppm
1
Methane (CH4)
730 ppb
1847 ppb
23
12
Nitrous oxide (N2O)
270 ppb
319 ppb
296
114
Tropospheric ozone (O3)
25 ppb
34 ppb
n.a.
hours-days
CFC-11 (CCl3F)
zero
253 ppt
4600
45
HFC-23 (CHF3)
zero
14 ppt
12000
260
Perfluoroethane (C2F6)
zero
3 ppt
11900
10000
*) Global Warming Potential
GWP 
T
 0 Igas Mgas dt
T
 0 ICO 2 MCO 2 dt
I = radiative forcing
M = amount of gas at time t
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10 April, 2014
Radiative forcing
Radiative forcing
conc ppmv warming
effect (oC)
H2O vapour
5000
20.6
CO2
360
7.2
O3
0.03
2.4
N2O
0.3
0.8
CH4
1.7
0.8
TOTAL
sun spots
33.0
without atmosphere
25
warmer  more H2O
feedback !
in reality
T Earth  288 K (15 o C)
T Earth  255 K
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Effect of change in solar “constant”
axial tilt (nutation): 41 ky
Stefan–Boltzmann law 
P  T4
excentricity: 95,125,400 ky
longitude of perihelion
precession: 19,22,24 ky
P  T 4
dP
dT
20% variation!
insolation
 4T 3
dP
P

4T 3 dT
T 4
dT
T

1 dP
4 P

4dT
T
dP  4T 3 dT
Will the temperature
also change by 20%?
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Radiative forcing
dP
P
 20% 
dT
T
 5%  ΔT  15 K
Real past variability is < 15 K.
The 20% in dP/P is for 65oN, average over earth is much smaller.
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Non-linear relation: warming vs conc.
100%
CO2 increase 280386 ppm gives S = 1.66
0%
W/m2
Clouds increase greenhouse effect by S = 30 W/m2
Clouds reduce solar absorption by S = 48 W/m2
Total atmospheric greenhouse effect is S = 140 W/m2

1 dP
4 P
total greenhouse
dT 
1 dP
4 P
T
1
4
CO2 increase
dT 
1 dP
4 P
T
1
4
dT
T
140
1
1366
4
1.66
1
1366
4
289  29. 619 K
ΔF CO2  lnC/C0  with   5. 3
289  0. 351 2 K
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10 April, 2014
Sunspots and temperature
More Sun spots: (1) More irradiance (2) More ozone  More greenhouse 31
Conclusions
32
What can we do?
CO2 and Temperature
CO2
Find sources of energy that do not produce CO2
400
CO2 (ppm) [75 years smoothed]
350
• geothermal heat
• chemical
(CO2)
• gravitational (tides) flow
• nuclear
we don’t do this
• solar
solar heat heat
photovoltaics semiconductor
bioenergy
we don’t do this
hydropower flow
wavepower flow
Law Dome Ice Core
Mauna Loa
300
250
1000
1200
1400
1600
Date
1800
2000
http://cdiac.ornl.gov/ftp/trends/co2/lawdome.combined.dat
CO2 is certainly rising fast
It is 40% higher now that it was during the past 106 y
politics
The temperature seems to be rising
heat
flow/fluid dynamics
semiconductor
What will we do?
Introduction of new energy vectors, CO2 regulations etc.  YOU
33
How does it work? How much energy can we get from it?
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Leerdoelen
Isolatie
woning isolatie
Pipelines
Bulk
Straling: satelliet (microgolf
Elektisch
Chemisch: Energieopslag Energietransport
Chemisch ‐ fuelcells
Warmte – phase change
Electrisch: batterij, condens
Mechanisch: vliegwiel, wate
Windmolens
Fotovoltaisch
Fotolytisch
Solarthermal
Solar ponds
Solar chimney
Warmtepomp
Getijden, golfkracht
Waterkracht
OTEC
Geothermal
Omgekeerde osmose / blue
Paleotemperatuur + oorzak
Wat doet CO2, wat is het gr
Klimaat aarde en IPCC Energieopwekking
Warmte balans aarde
Klimaatmodellen
solar irradiance (Wm-2)
Sunspots and solar input to Earth
Thermodynamica
Temperatuur (TiplerMosca p 564)
x
Ideale gaswet (TiplerMosca p 569) – nodig voor
Maxwell-Boltzman distributie (TiplerMosca p 582
Thermal energy + Carnot – gasturbine voor elektr
Warmtepomp
Latent heat (TiplerMosca p 594) – warmte opslag
Heat capacity (TiplerMosca p 606, 611)
Straling
x
Geleiding
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Gibbs Free energy, (Electro+)Chemical potential
Equipartitie en kinetische gastheorie (TiplerMosca
Wet van Wien
x
x
x
x
x
x
x
x
x x x x
Stromingsleer
Continuiteitsvergelijking (AndrewsJelly 54)
x
Diffusie van warmte en atomen
x
Bernouilli - windmolen
Pitot/Venturi (TiplerMosca p 443) Lift (AndrewsJ
Magnus effect (AndrewsJelly 64)
Betz (windmolens) Turninevergelijking (AndrewsJ
Snelheisprofiel in buizen - waterkrachtopslag bijv.
Poiseuille
Wet van Archimedes - getijdekracht boeien
Stability of ships (Stephenson) - getijdekracht boe
The force on a water dam (TiplerMosca p 427)
Drukverdeling in de atmosfeer (TiplerMosca p 43
Viscositeit (TiplerMosca p 446)
x x
x x
x
x
x
x
x
x
x
x
x
x
x
x
x
x x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x x
Vaste Stof
Bandstructuur
PN – junctie met/zonder licht
Basic electrochemistry
Nernst equation (for Erwin)
x
x
de tol
x
x
x
Mechanica
x
x
x
x
x
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