A planet is at an average distance d from the sun and its average surface temeperature is T. Assume that the planet receives energy only from the sun and loses energy only through radiation from the surface. Neglect atmospheric effects. If `Tpropd^(-n)`, the value of n is

Options

A. 2
B. 1
C. `(1)/(2)`
D. `(1)/(4)`

Answer

C

Explanation

Let P be the power raditated by the sun and R be the radius of planet.
Energy received by planet `=(P)/(4pi d^(2)) xx pi R^(2)`
Energy radiated by planet `= sigma (4pi R^(2))T^(4)`
For thermal equilibrium, `(P)/(4pi d^(2)) xx pi R^(2) = sigma 4pi R^(2)T^(4)`
or `T^(4) prop (1)/(d^(2)) or T prop (1)/(d^(1//2)) or T prop d^(-1//2) :. n= (1)/(2)`