Assuming the sun to be a spherical body of radius R at a temperature of T K , evaluate the total radiant power, incident on earth, at a distance r from the sun. ( r 0 is the radius of the earth and σ is Stefan's constant)

Step-by-step solution

From Stefan's law, the rate at which energy is radiated by sun at its surface is P = σ × 4 π R 2 T 4 [Sun is a perfect black body as it emits radiations of all wavelengths and so for it e =1] The intensity of this power at earth's surface is I = P 4 π r 2 = σ × 4 π R 2 T 4 4 π r 2 = σ R 2 T 4 r 2 The area of earth which receives this energy is only one-half of total surface area of earth, whose projection would be π r 0 2 . ∴ Total radiant power as received by earth = π r 0 2 × I = π r 0 2 × σ R 2 T 4 r 2 = π r 0 2