The Sun, the Earth, and the Evolution of the Earth’s Atmosphere - Air Pollution and Global Warming: History, Science, and Solutions - page 33

1.2 10 4

10 4

Sun

Far
UV

Near
UV

1 10 4

10 2

8 10 3

Visible

10 0

6 10 3

Ultraviolet Infrared

4 10 3

10 -2

Earth

Visible

2 10 3

10 -4

0.01 0.1 1 10 100

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Wavelength ( µ m)

Wavelength (µm)

Figure 2.4. Radiation spectrum as a function of
wavelength for the sun's photosphere and the Earth
when both are considered blackbodies. The sun's
spectrum is received at the top of the Earth's
atmosphere.

Figure 2.5. UV and visible portions of the solar
spectrum. This spectrum is received at the top of the
Earth's atmosphere.

Boltzmann (1844-1906). The law states
F b = ε B T 4 (2.2)
where F b is the radiation intensity (W m − 2 ), summed
overall wavelengths, emitted by a body at temperature
T ,

(0.01 to0.38 m), and longer infrared (IR) wave-

lengths (0.75 to 1,000

m) are also emitted. At 300 K,
infrared wavelengths are the wavelengths emitted with
greatest intensity.
Figure 2.4 focuses on the 6,000 K and 300 K spectra
in Figure 2.3. These are the radiation spectra of the sun's
photosphere and of the Earth, respectively. The solar
spectrum can be divided into the UV, visible, and IR
spectra. The UV spectrum can be further divided into
the far UV (0.01 to 0.25

10 − 8
Wm − 2 K − 4 is the Stefan-Boltzmann constant. The
emissivity ,which ranges from 0 to 1, is the efficiency
at which a body emits radiation in comparison with the
emissivity of a blackbody, which is unity. Soil has an
emissivity of 0.9 to 0.98, and water has an emissivity of
0.92 to 0.97. All the curves in Figures 2.3 to 2.5 show
emission spectra for blackbodies (

ε is the emissivity of the body, and B = 5.67 ×

m) and near UV (0.25 to

ε = 1).

0.38 m) spectra (Figure 2.5). The near UV spectrum

is subdivided into UV-A (0.32 to0.38

m), UV-B (0.29

Example 2.2
How does doubling the Kelvin temperature of a
blackbody change the intensity of radiative emis-
sion of the body? What is the ratio of intensity
of the sun's radiation compared with that of the
Earth's?

to 0.32 m) wavelength

regions. The visible spectrum contains the colors of the
rainbow. For simplicity, visible light is categorized as
blue (0.38 to 0.5

m), and UV-C (0.25 to0.29

m), green (0.5 to 0.6 m), or red

(0.6 to 0.75 m). Infrared wavelengths are partitioned

into solar-IR (near-IR) (0.75 to 4 m) and thermal-IR

(far-IR) ( 4to1,000 m) wavelengths. The intensity of

the sun's emission is strongest in the visible spectrum,
weaker in the the solar-IR and UV spectra, and weakest
in the thermal-IR spectrum. That of the Earth's emission
is strongest in the thermal-IR spectrum.
Figures 2.3 to 2.5 provide wavelength dependencies
of the intensity of radiation emissions of a body at a
given temperature. Integrating intensity over all wave-
lengths (summing the area under any of the curves)
gives the total intensity of emission of a body at a given
temperature. This intensity is proportional to the fourth
power of the object's kelvin temperature ( T ) and is given
by the Stefan-Boltzmann law , derived empirically in
1879 by Austrian physicist Josef Stefan (1835-1893)
and theoretically in 1889 by Austrian physicist Ludwig

Solution
From Equation 2.2, the doubling of the Kelvin
temperature of a body increases its intensity of
radiative emission by a factor of 16. The temper-
ature of the sun's photosphere (5,785 K) is about
twenty times that of the Earth (288 K). Assuming
both are blackbodies (

1), the intensity of the
sun's radiation (63.5 million W m −2 )is163,000
times that of the Earth's (390 W m −2 ).

ε =

2.3. Primordial Evolution of the Earth
and Its Atmosphere
Earth formed when rock-forming elements (identified
in Table 2.1), present as gases at high temperatures