Spectral Distribution of Blackbody Radiation
159
intercept of In@,. The necessary computations are in the table. A graph
of the data is shown in the accompanying figure.
Zenith angle 9 Airmass rn Q,
In Q,
30
1.15
871 6.770
45
1.41
785 6.666
60
2.00
620 6.430
The slope is -0.4 so k = 0.4 per airmass. The intercept is 7.23 so
@, = exp(7.23) = 1380 w/m2; this value is near the solar constant of
about 1360 w/m2.
10.6 Spectral Distribution of Blackbody
Radiation
One of the major breakthroughs of modern physics was the discovery
of a correct model for the spectral distribution of blackbody radiation.
Classical approaches predicted that the amount of energy emitted by a
surface would increase without bound as the wavelength of the radiation
decreased. This implied that all of the energy in the universe would ultimately be funneled to short wavelengths and emitted; a situation referred
to as the "ultraviolet catastrophe." The catastrophe was the fault of the
model, of course, not of nature. This was all solved by Planck's quantum
hypothesis, that energy is emitted in discrete packages, or quanta, whose
energy and wavelength are related by Eq. (10.1). Planck's model for the
radiant spectral flux density from a blackbody radiator is
Here Eb(h, T) (W/m
3 ) is the radiant spectral flux density or spectral
emittance, T is the kelvin temperature, h is Planck's constant, and k is the
Boltzmann constant (1.38 x
JK). Blackbody spectra are plotted
in Fig. 10.4 for sources at 6000 K and 288 K, corresponding roughly to
sun and earth emittance spectra. Note that we have used a logarithmic
scale for wavelength so that both spectra can be shown in the same graph.
The two spectra overlap slightly between 3 and 4 pm, but the amount of
energy in the overlap is negligible. We therefore specify 4 p m as the top
end of the solar spectrum and the bottom end of the terrestrial thermal
spectrum. The scale for the sun emittance is lo6 larger than for the earth.
Essentially all of the energy emitted by the earth comes from the sun, but
the earth intercepts only a very small fraction of the energy the sun emits.
The wavelength of peak spectral emittance is a function of temperature
of the emitting surface, as can be seen from Fig. 10.4. The wavelength
at peak emittance (on a wavelength basis) is found by differentiating
159
intercept of In@,. The necessary computations are in the table. A graph
of the data is shown in the accompanying figure.
Zenith angle 9 Airmass rn Q,
In Q,
30
1.15
871 6.770
45
1.41
785 6.666
60
2.00
620 6.430
The slope is -0.4 so k = 0.4 per airmass. The intercept is 7.23 so
@, = exp(7.23) = 1380 w/m2; this value is near the solar constant of
about 1360 w/m2.
10.6 Spectral Distribution of Blackbody
Radiation
One of the major breakthroughs of modern physics was the discovery
of a correct model for the spectral distribution of blackbody radiation.
Classical approaches predicted that the amount of energy emitted by a
surface would increase without bound as the wavelength of the radiation
decreased. This implied that all of the energy in the universe would ultimately be funneled to short wavelengths and emitted; a situation referred
to as the "ultraviolet catastrophe." The catastrophe was the fault of the
model, of course, not of nature. This was all solved by Planck's quantum
hypothesis, that energy is emitted in discrete packages, or quanta, whose
energy and wavelength are related by Eq. (10.1). Planck's model for the
radiant spectral flux density from a blackbody radiator is
Here Eb(h, T) (W/m
3 ) is the radiant spectral flux density or spectral
emittance, T is the kelvin temperature, h is Planck's constant, and k is the
Boltzmann constant (1.38 x
JK). Blackbody spectra are plotted
in Fig. 10.4 for sources at 6000 K and 288 K, corresponding roughly to
sun and earth emittance spectra. Note that we have used a logarithmic
scale for wavelength so that both spectra can be shown in the same graph.
The two spectra overlap slightly between 3 and 4 pm, but the amount of
energy in the overlap is negligible. We therefore specify 4 p m as the top
end of the solar spectrum and the bottom end of the terrestrial thermal
spectrum. The scale for the sun emittance is lo6 larger than for the earth.
Essentially all of the energy emitted by the earth comes from the sun, but
the earth intercepts only a very small fraction of the energy the sun emits.
The wavelength of peak spectral emittance is a function of temperature
of the emitting surface, as can be seen from Fig. 10.4. The wavelength
at peak emittance (on a wavelength basis) is found by differentiating