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

Answer

D

Explanation

According to Stefan.s law, `Q = sigma AT^(4)` or `T= ((Q)/(sigma A))^(1//4) = ((Q)/(sigma 4pi R^(2)))^(1//4)`