Blackbody radiation — UPSC Physics Optional CSE 2003 Paper I

Earth receives 1.3\text{KW/m}^2 of radiant energy from the Sun. Assuming Sun to be a spherical black body of radius 7 \times 10^8\text{m} and Earth-sun distance to be 1.5 \times 10^{11}\text{m}, Calculate the surface temperature of Sun. (Stefan-Boltzmenn constant \sigma = 5.67 \times 10^{-8}\text{ Wm}^{-2}\text{K}^{-4}).