A spherical black body with a radius of $$12\,cm$$  radiates $$450\,watt$$   power at $$500\,K.$$  If the radius were halved and the temperature doubled, the power radiated in watt would be

Solution :
Radiated power of a black body,
$$P = \sigma A{T^4}$$
where, $$A =$$  surface area of the body
$$T =$$  temperature of the body
and $$\sigma =$$  Stefan's constant
When radius of the sphere is halved, new area,
$$A' = \frac{A}{4}$$
∴ Power radiated,
$$\eqalign{ & P' = \sigma \left( {\frac{A}{4}} \right){\left( {2T} \right)^4} = \frac{{16}}{4} \cdot \left( {\sigma A{T^4}} \right) \cr & = 4P = 4 \times 450 = 1800\,watts \cr} $$