The luminousity of a star is 10000 times that of the sun. if the surface temperature of the sun is 6000 K, then the surface temperature of the star is

Options

A. 8446 K
B. 84860 K
C. 848600 K
D. 60,000 K

Answer

D

Explanation

`P_(1)=I_(1)A_(1) and P_(2)=I_(2)A_(2)`
But `P_(1)=sigmaA_(1)T_(1)^(4) and P_(2)=sigmaA_(1)T_(1)^(4)`
`therefore sigmaT_(1)^(4)A_(1)=I_(1)A_(1)`
`sigmaT_(2)^(4)A_(2)=I_(2)A_(2)`
`((T_(2))/(T_(1)))^(4)=(I_(2))/(I_(1))`
`(T_(2))/(T_(1))=((I_(2))/(I_(1)))^(1//4)=(10^(4))^(1//4)=10`
`T_(2)=T_(1)xx10=6000K`