The diameter of the sun is 1.39*109 m. Estimate the percentage of the total radiation emitted by the sun, which approximates a blackbody at 5760 K, that is actually intercepted by the Earth. Of the total radiation falling on the Earth, about 70% falls on the ocean. Estimate the amount of radiation from the sun that falls on land, and then estimate the ratio of energy currently used worldwide and the amount of terrestrial solar energy that is available. Discuss why all of the energy cannot be harnessed.
GIVEN
• Diameter of sun (Ds)= 1.39*109 m
• Sun is approximate black body at temperature (Ts) =5760 K
• 70% of radiation falls on the ocean.
• Diameter of the earth (De)= 1.27*107 m
• Distance between sun and earth (Rse )=1.53*1011 m
FIND
• Amount of radiation from sun that falls on land
• Ratio of energy currently used worldwide and the amount of terrestrial solar energy that is available.
• Discuss why all energy cannot be harnessed.
ASSUMPTIONS
• The sun’s radiation is assumed as ideal black body radiation.
The total radiation from sun is given by
The amount of radiation reaching the earth is obtained by using energy balance equation
Total radiation intercepted by earth is the circle side facing the sun. Thus
Thus the percentage of solar radiation intercepted by earth is
The amount of energy that falls on land
Total energy currently used worldwide(Tw) 12.3 TW
The ratio of energy totally used and solar energy that is available
The reasons why all the energy cannot be harnessed is
• Solar energy spreads all over the surface of earth and it is not possible to harness energy from surfaces everywhere.
• The efficiency of energy that can be converted to solar energy is low.
• Land, gases and atmosphere absorb the solar energy that is incident on earth and cannot be recovered.
• Part of energy incident on earth is reflected which cannot be harnessed.
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