The earth receives 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 xx 10^(11)` m and the radius of the sun is `7.0 xx 10^(8)` m. Treating sun as a black body, it follows from the above data that its surface temeperature is

Explanation

The energy received per second per unit area from sun at a distance of `1.5xx10^(11)m` is `1400J//sm^(2)` . The total energy released by sun per second
`=1400xx4pixx(1.5xx10^(11))^(2)`
Therefore, the total energy released per second per unit surface area of the sun
`(1400xx4pixx(1.5xx10^(11))^(2))/(4pixx(7xx10^(8))^(2))`
This energy `E` is also equal to `E=sigmaT^(4)`
`implies T=[(1400xx4pixx(1.5xx10^(11))^(2))/(4pixx(7xx10^(8))^(2)xx5.67xx10^(-8))]^(1//4)=5803K`