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

Rate of energy production `(Q)= sigma epsilon AT^4`
`implies T=[(Q)/(sigma(4piR^2))]^(1//4)`, `epsilon = 1 & A=4 pi R^2`