## The Spectral Distribution of the Sun as a Radiation Source

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In this chapter we briefly describe the solar spectral distribution, or distribution of energy with respect to wavelength, over the region of the electromagnetic spectrum of use to renewable energy systems. The sun radiates energy at wavelengths ranging from the X-ray and gamma ray spectral region out into the very long wavelength radio spectral region. We will restrict our discussion, for the most part, to solar energy in the wavelength region between the ultraviolet (UV) of wavelength 250 nanometers (nm) and the near infrared (NIR) with wavelength of 4000 nm or 4.0 micrometers.

The Planck theory of blackbody radiation provides a first approximation to the spectral distribution, or intensity as a function of wavelength, for the sun. The black-body theory is based upon a "perfect" radiator with a uniform composition, and states that the spectral distribution of energy is a strong function of wavelength and is proportional to the temperature (in units of absolute temperature, or Kelvin), and several fundamental constants. Spectral radiant exitance (radiant flux per unit area) is defined as:

where A is wavelength (in meters), h is Planck's constant = 6.626196x10-34 Joule seconds (J s), c is the velocity of light in vacuum = 2.9979250x108 meter per second (ms-1), k is Boltzman's constant = 1.3806x10-23 Joule per Kelvin (J K-1), and T is absolute temperature in Kelvins.

The sun is not a "perfect" radiator, nor does it have uniform composition. The sun is composed of about 92% hydrogen, 7.8% helium. The remaining 0.2% of the sun is made up of about 60 other elements, mainly metals such as iron, magnesium, and chromium. Carbon, silicon, and most other elements are present as well.1 The interaction of the atoms and ions of these elements with the radiation created by the annihilation of matter deep within the sun modifies and adds structure to the solar spectral distribution of energy. Astrophysicists such as Kurucz have used quantum calculations and the relative abundance of elements in the sun to compute the theoretical spectral distribution from first principles.5 Figure 1 shows a plot of the Kurucz computed spectral distribution at very high resolution (0.005 nanometer at UV) as well as an inset showing much lower resolution (0.5 nanometer in UV to 5 nm in IR) plot.

Figure 2 is a plot of the low resolution ETR spectrum compared with the Planck function for a blackbody with a temperature of 6000 Kelvin. The differences in the infrared, beyond 1000 nanometers are small. The larger differences in the shortwave-length region are due to the absorption of radiation by the constituents of the solar composition, resulting in the "lines" observed by Fraunhofer and named after him.

250 1000 1750 2500 3250 4000

Wavelength (nanometers)

Fig. 1. The theoretical extraterrestrial solar spectral distribution (at the top of the Earth's atmosphere at the mean Earth-Sun distance of one astronomical unit) of Kurucz at high and low spectral resolution.

Fig. 1. The theoretical extraterrestrial solar spectral distribution (at the top of the Earth's atmosphere at the mean Earth-Sun distance of one astronomical unit) of Kurucz at high and low spectral resolution.

500 1000 1500 2000 2500 3000 3500 4000 Wavelength (nm)

Fig. 2. The low-resolution ETR spectral distribution (gray jagged curve) and the 6000-Kelvin blackbody spectral distribution.

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