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