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//4 pi R^(2) sigma`
B. `(Q//4 pi R^(2) sigma)^(-1//2)`
C. `(4 pi R^(2) Q// sigma)^(1//4)`
D. `(Q // 4 pi R^(2) sigma)^(1//4)`

Answer

D

Explanation

(4) `Q = sigma A T^(4) = sigma 4 pi R^(2) T^(4)`
`T = (Q // 4 pi R^(2) sigma)^(1//4)`