Q: A spherical black body with a radius of 12 cm radiates 450 W power at 500 K. If the radius were halved and the temperature double, the power radiated in watt would be
(a) 225
(b) 450
(c) 900
(d) 1800
Ans: (d)
Sol: $\large E = e \sigma A T^4 $
$\large E = e \sigma (4\pi r^2) T^4 $
$\large E \propto r^2 T^4 $
$\large \frac{E}{E’} = \frac{r^2}{(r/2)^2} (\frac{T}{2T})^2 $
$\large \frac{E}{E’} = \frac{1}{4} $
$\large \frac{450}{E’} = \frac{1}{4} $
E’ = 1800 W