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

Options

A. 5801K
B. `10^6K`
C. `50.1K`
D. `5801^@C`

Answer

A

Explanation

According to Stefan's law
`R=sigmaT^4`
Total surface area of the sun`=4piR_S^2`.
There, the total energy radiated per second by the sun per unit solid angle
`=-(sigmaT^4xx4piR_S^2)/(4pi)=sigmaT^4R_S^2`
Let `R_(es)` be the distance of earth from the sun. Hence intensity of radiation of earth
`l=(sigmaT^4R_S^2)/(R_(es)^2)`
`:. 1400=(5.6xx10^-8)T^4[(7.0xx10^8)/(1.5xx10^11)]`
`T=5801K`