A spherical ball A having a surface area of 20 cm ^2 is positioned at the centre of a hollow spherical shell B of area 80 cm ^2 . The surface of A and the inner surface of B both emit as blackbodies. A and B are both maintained at a temperature of 300 K . How much of the energy emitted per second by the inner surface of B falls back onto this surface itself?

Step-by-step solution

Let F_ AB be the fraction of energy emitted by sphere A that falls on sphere B . Since A is completely enclosed by B , all radiation emitted by A falls on B , giving F_ AB = 1 . Using the reciprocity theorem for thermal radiation: A_A F_ AB = A_B F_ BA F_ BA = A_A A_B F_ AB = 20 80 1 = 0.25 The fraction of energy emitted by B that falls back onto its own inner surface is: F_ BB = 1 - F_ BA = 1 - 0.25 = 0.75 The total energy emitted per second by the inner surface of B (acting as a blackbody) is given by Stefan-Bolt