The earth receives on its surface radiation from the sun at the rate of 1400 W m - 2 . The distance of the centre of the sun from the surface of the earth is 1 . 5 × 10 11 m and the radius of the sun is 7 . 0 × 10 8 m . Treating sun as a block body, it follows from the above data that its surface temperature is

Step-by-step solution

According to Stefan's law, d Q d T = σ T 4 The total surface area of the sun = 4 π R s 2 Therefore, the total energy radiated per second by the sun per unit solid angle = - σ T 4 × 4 π R s 2 4 π = σ T 4 R s 2 Let R es be the distance of the earth from the sun. Hence, the intensity of radiation of the earth l ⁡ = σ T 4 R s 2 / R es 2 ∴    1 4 0 0 = 5.6 × 1 0 - 8 T 4 7.0 × 1 0 8 1.5 × 1 0 1 1 2 T   =   5801   K