The earth receives solar radiation at a rate of 8.2 ~J ~cm ⁻² ~min ⁻¹ . If the sun radiates as the black bodies, the temperature at the surface of the sun will be (the angle subtended by sun on the earth in suppose 0.53^ and Stefan constant is =5.67 10⁻⁸ Wm ⁻² ~K ^4 )

Step-by-step solution

Let diameter of the sun is d while radius of the earth is r then aligned D 2 & 0.53 180 & =9.25 10⁻³ aligned The radiation emitted per unit area of the sun is 4 ( d 2 )^2 T^A= D^2 T^A The radiation received at the earths surface per unit time per unit area is d T^4 4 r^2 = T^4 4 ( d R )^2 array rlrl & & T^4 4 ( D R )^2 & =82 Jcm ⁻² ~min ⁻¹ & or & 1 4 5.67 10⁻⁸ T^4 (9.25 10⁻³ )^2 & = & 8.2 10⁻⁴ 60 Wm ⁻² & & T & =5794 ~K 5800 ~K array