Q. The ratio of radiant energies radiated per unit surface area by two bodies is 16 : 1, the temperature of hotter body is $1000K$, then the temperature of colder body will be
A) $250\ K$
B) $500\ K$
C) $1000\ K$
D) $62.5\ K$
Explanation
(b) $Q \propto T^{4} \Rightarrow \frac{Q_{1}}{Q_{2}} = \frac{T_{1}^{4}}{T_{2}^{4}} \Rightarrow T_{2}^{4} = \left( \frac{E_{2}}{E_{1}} \right)T_{1}^{4}$
$\Rightarrow T_{2}^{4} = \frac{1}{16} \times (1000)^{4} = \left( \frac{1000}{2} \right)^{4}$
$\Rightarrow T_{2} = 500K$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.