Question

A spherical black body of radius 12 cm radiates 450 W power at 500 K. If the radius were halved and the temperature doubled, the power radiated would be

• A. 225 W
• B. 450 W
• C. 900 W
• D. 1800 W

Answer 1

Power radiated, $P=4\pi r^2\sigma T^4\Rightarrow P\propto r^2{T}^4$
$\therefore \frac{P_2}{P_1}={\left(\frac{R_2}{R_1}\right)}^2{\left(\frac{T_2}{T_1}\right)}^4={\left(\frac{1}{2}\right)}^2\times {\left(\frac{2}{1}\right)}^4=4\Rightarrow P_2=4P_1=4\times 450=1800W$