It contains a brief description of the Stefan-Boltzmann law, used in the class of Hydrology at the University of Trento

1. Riccardo Rigon
IlSole,F.Lelong,2008,ValdiSella
Solar Radiation
The Stefan-Boltzmann law

2. R. Rigon
Radiation
emitted
emissivity
Stefan-Boltzmann constant
absolute temperatureR = ✏ T4
Every body with a temperature different than T=0 K emits radiation as a function
of its temperature according to the Stefan-Boltzmann law
The Stefan-Boltzmann law
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2
The Sun

3. R. Rigon
RSun = ✏ T4
= 1 ⇤ 5.67 ⇤ 10 8
⇤ 60004
⇡ 25.12 ⇤ 109
J m 2
s 1
The physics of Radiation
On the basis of the temperature of the Sun photosphere (~6000 K), and the
Stephan-Boltzmann law, the total energy emitted by the Sun is
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3
The Sun

4. R. Rigon
The Sun is practically a blackbody. The difference between a true blackbody
and the Sun is due to the fact that the corona and the chromosphere
selectively absorb certain wavelengths.
The Sun is nearly a “blackbody”!
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4
The Sun

5. R. Rigon
The area below the curves is given by the Stefan-Boltzmann law. The curves
themselves are given by Planck’s law.
The Sun is nearly a “blackbody”!
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5
The Sun

6. R. Rigon
The complete electromagnetic spectrum
The spectrum of solar radiation stretches far beyond the visible band where,
however, nearly half the available energy is concentrated
Figure2.9
C.B.Agee
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6
The Sun

7. R. Rigon
Planck’s Law
•Planck’s law is the general law for electromagnetic emission from the
surface of a blackbody*:
W =
2⇡c2
h 5
e
ch
KT 1
[Wm 2
µm 1
]
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7
The Sun
* Stefan-Boltzmann law is just the integration of Plank’s law over wavelengths