Q. The radiant energy from the sun incident normally at the surface of earth is $20\ kcal/m^{2}\min$. What would have been the radiant energy incident normally on the earth, if the sun had a temperature twice of the present one
A) $160\ kcal/m^{2}\ min$
B) $40\ kcal/m^{2}\ min$
C) $320\ kcal/m^{2}\ min$
D) $80\ kcal/m^{2}\ min$
Explanation
(c) $\frac{E_{2}}{E_{1}} = \left( \frac{T_{2}}{T_{1}} \right)^{4} \Rightarrow \frac{E_{2}}{20} = \left( \frac{2T}{T} \right)^{4} = 16 \Rightarrow E_{2} = 320\ kcal/m^{2}\min$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.