Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K respectively. The energy radiated per second by the first sphere is

The energy radiated per second E, by a body of surface area A, at temperature T K is given by
$\mathrm{E}={\mathrm{k\sigma AT}}^4$  (Stefan's law)
where   k = relative emissivity

 E₁ = energy radiated per second by first sphere 
$\begin{array}{l}=\mathrm{k\sigma }\left\{4\mathrm{\pi }(1{)}^2\right\}(4000{)}^4\\ =\mathrm{k\sigma \pi }\left(1024\times {10}^{12}\right)\text{ joule }\end{array}$
Similarly,
$\begin{array}{l}{\mathrm{E}}_2=\mathrm{k\sigma }\left\{4\mathrm{\pi }(4{)}^2\right\}(2000{)}^4\\ =\mathrm{k\sigma \pi }\left(1024\times {10}^{12}\right)\text{ joule }\end{array}$
$\therefore {\mathrm{E}}_1={\mathrm{E}}_2$