10 April, 2017
564 million tons of hydrogen
are converted into 560 million
tons of helium per second
of thisoftalk
HeatPurpose
balance
Earth
ASSun
SSun
E=mc2
SE
(1-A)SSun
3.8 x 1026 W
Rinke Wijngaarden
63 MW/m2
1
What heats the
2
564 million tons of hydrogen
are converted into 560 million
tons of helium per second
(0.42 MeV)
E=mc2
1 MeV=1.6 x 10-13 J
3.8 x 1026 W
But how do we know this?
63 MW/m2
4
3
1. Measuring the Sun’s temperature
2. Calculating the total power
3.8 x 1026 W
Planck’s Law
25000
2
Spectral Irradiance (W/m /eV))
30000
20000
5800 K
15000
dE 2 2
h
 2 h
d
c e k BT  1
T = 5800 K
T = 5800 K
 = 5.67x10-8Wm-2K-4
10000
5000
0
0
2
4
6
Stefan–Boltzmann law
8
Photon energy [eV]
5
6
1
10 April, 2017
World Total Primary Energy Supply 2014
1368 W/m2
sun: 3.8 x 1026 W
1.5 x 1011 m
R2
63 MW/m2
17.6 TW
7 x 108 m
7
http://www.iea.org/textbase/nppdf/free/2007/Key_Stats_2007.pdf
IEA: KeyWorld2016.pdf
8
Solar area Sahara
50 TW
Future world power consumption
1010 persons  5 kW/person = 50 TW
1200 x 1200 km2
W/m2
Solar constant: 1350
50% reaches the Earth’s surface
25% due to R2/4R2
Efficiency of photovoltaics: 20%.
148 m2/person
63 MW/m2
1.48  106 km2
0.8 km2 gives 50 TW
9
10
Summary heat transfer by radiation
Heat transfer through radiation
Stefan–Boltzmann law
S = 5.67 x 10-8 T4 [W/m2]
Spectral energy density dE/df




R2
1200 x 1200 km2
63 MW/m2
0.8 km2 gives 50 TW
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
11
Planck’s Law
1.5
0.5
1.0
1.5
2.0
Photon energy [eV]
2.5
3.0
12
2
10 April, 2017
Some constants
Spectral irradiance on Earth
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
dE   2 2
h
 2 h
d
c e k BT  1
14
15
Incoming and reflected solar energy
70% absorbed
100 %
Albedo = 0.3
The Greenhouse effect
Atmosphere:
6%
Clouds: 20 %
Earth’s surface: 4 %
16
Without atmosphere
5600 K
17
Absorption by the atmosphere
260 K
5600 K
18
260 K
19
3
10 April, 2017
Why water and CO2 ?
Earth without an atmosphere
O
H
_
equilibrium:
ASSun
H
1 − 0. 31366 W m−2  4  5. 67  10 −8 W m−2 K −4  T 4
C
+
 R 2 S Sun 1  A   4 R 2 S Earth
4
1  A S Sun  4S Earth  4 TEarth
_
O
+
SSun
T Earth  255 K
O
SEarth
_
(1-A)SSun
_
+
T Earth  −18 o C
_
+
e.m. wave
e.m. wave
20
Earth with totally absorbing atmosphere:
Greenhouse effect
SSun
Sa
ASSun
2 Sa  S Earth
21
Earth with totally absorbing atmosphere:
Greenhouse effect
SSun
Sa
ASSun
2 Sa  S Earth
 R 2 S Sun 1  A   4 R 2 Sa  4 R 2 S Earth
SE
Sa
SE
(1-A)SSun
(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
 R 2 S Sun 1  A   4 R 2 Sa  4 R 2 S Earth22
Radiative forcing
without atmosphere
T Earth  255 K
T Earth  30 o23C
Radiative forcing
in reality
T Earth  288 K (15 o C)
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
warmer  more H2O
feedback !
sun spots
33.0
Mount Chimaera / Yanartaş
25
4
10 April, 2017
Direct Global Warming Potentials (mass basis)
relative to carbon dioxide
GWP *)
axial tilt (nutation): 41 ky
Pre-1750 Current
concentra tropospheric
-tion
concentration
(100-year
time horizon)
Atmospheric
lifetime
(years)
Carbon dioxide (CO2)
280 ppm
377.3 ppm
1
variable
Methane (CH4)
730 ppb
1847 ppb
23
12
114
GAS
Nitrous oxide (N2O)
270 ppb
319 ppb
296
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
excentricity: 95,125,400 ky
longitude of perihelion
precession: 19,22,24 ky
20% variation!
insolation
Will the temperature
also change by 20%?
T
 0 Igas Mgas dt
GWP 
T
 0 ICO 2 MCO 2 dt
I = radiative forcing
M = amount of gas at time t
26
27
Effect of change in solar “constant”
Radiative forcing
We consider heat emitted/received by Earth
The geometry is constant.
We consider the flux per m2 for simplicity
Stefan–Boltzmann law 
CO2 increase 280386 ppm gives S = 1.66 W/m2
Clouds increase greenhouse effect by S = 30 W/m2
P  T 4
dP
dT
Clouds reduce solar absorption by S = 48 W/m2
 4T 3
dP
P

4T 3 dT
T 4
dT
T

1 dP
4 P

4dT
T
Total atmospheric greenhouse effect is S = 140 W/m2
dP  4T 3 dT
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 smaller.

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
28
Non-linear relation: warming vs conc.
140
1
1366
4
1.66
1
1366
4
289  29. 619 K
289  0. 351 2 K
29
Sunspots and solar input to Earth
100%
ΔF CO2  lnC/C0  with   5. 3
30
solar irradiance (Wm-2)
0%
More Sun spots: (1) More irradiance (2) More ozone  More greenhouse 31
5
10 April, 2017
Sunspots and temperature
Conclusions
CO2 and Temperature
CO2
CO2 (ppm) [75 years smoothed]
400
350
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 is rising
32
Introduction of new energy vectors, CO2 regulations etc.  YOU
33
What can we do?
Find sources of energy that do not produce CO2
• 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
heat
flow/fluid dynamics
semiconductor
What will we do?
How does it work? How much energy can we get from it?
34
6