A) \[{{T}_{0}}\propto {{d}^{2}}\]
B) \[{{T}_{0}}\propto {{d}^{-2}}\]
C) \[{{T}_{0}}\propto {{d}^{1/2}}\]
D) \[{{T}_{0}}\propto {{d}^{-1/2}}\]
Correct Answer: D
Solution :
Energy received per second by the planet \[=\frac{P}{4\pi {{d}^{2}}}(\pi {{R}^{2}})\] where, P is power radiated by the sun and R is the radius of the planet. Further, energy radiated per second by the planet according to Stefans law is \[\sigma (4\pi {{R}^{2}})T_{0}^{4}\]. For thermal equilibrium to exist, we get \[\frac{P}{4\pi {{d}^{2}}}(\pi {{R}^{2}})=\sigma (4\pi {{R}^{2}})T_{0}^{4}\] \[\Rightarrow \] \[{{T}_{0}}^{4}\propto {{d}^{-2}}\] \[\Rightarrow \] \[{{T}_{0}}\propto {{d}^{-1/2}}\]
You need to login to perform this action.
You will be redirected in
3 sec
