If the radius of a star is `R` and it acts as a black body, what would b the temperature of the star, in which the rate of energy production is `Q`?

Options

A. `Q/4piR^(2)sigma`
B. `(Q/4piR^(2)sigma)^(-1/2)`
C. `(4piR^(2)Q//sigma)^(1/4`
D. `(Q//4piR^(2)sigma)^(1/4)`

Answer

D

Explanation

From stefan's law, `E=sigmaT^(4)`
So, the rate of energy populatioin, `Q = E xx A rArrQ=sigmaT^(4)xx4piR^(2)`
Temperature of star, `T=(Q/(4piR^(2)sigma))^(1//4)`