Q. A spherical black body with a radius of $12\ cm$ radiates $440\ W$ power at $500K$. If the radius were halved and the temperature doubled, the power radiated in watt would be
A) 225
B) 450
C) 900
D) 1800
Explanation
(d) Radiated power by blackbody $P = \frac{Q}{t} = A\sigma T^{4}$
$\Rightarrow P \propto AT^{4} \propto r^{2}T^{4} \Rightarrow \frac{P_{1}}{P_{2}} = \left( \frac{r_{1}}{r_{2}} \right)^{2}\left( \frac{T_{1}}{T_{2}} \right)^{4}$
$\Rightarrow \frac{440}{P_{2}} = \left( \frac{12}{6} \right)^{2}\left( \frac{500}{1000} \right)^{4} \Rightarrow P_{2} = 1760\ W \approx 1800\ W$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.