A perfectly black body in the shape of a solid sphere of radius R has an internal source of power  $P$ producing heat. In equilibrium, the surface temperature of the sphere is T. When it is covered by a thin shell of emissivity $e=1$  concentrically, the surface temperature of the solid sphere increases to $T^{\text{'}}$and the power radiated by it becomes $P^{\text{'}}$. The radius of the shell is slightly greater than R.