Question

A spherical ball A of surface area $20c{m}^2$ is kept at the center of a hallow spherical shell B of area $80c{m}^2$ the surface of A and the inner surface of B emit as blackbodies. Both A and B are at 300K (a) how much is the radiation energy emitted per second by the ball A? (b) How much is the radiation energy emitted per second by the inner surface of B ? (c) How much of the energy emitted by the inner surface of B falls back on this surface itself ?

Answer 1

Given:

Surface area of the spherical ball,

$S_A=20c{m}^2=20\times {10}^{-4}{m}^2$

Surface area of the spherical shell,

$S_B=80cm²=80\times {10}^{-4}m²$

Temperature of the spherical ball, $T_A=300K$

Temperature of the spherical shell, $T_3=300K$

• (A) Radiation energy emitted per second by spherical ball A is given by,

$E_A=\sigma S_A{T}_A^4$

$\to E_A=6\times {10}^{-8}\times 20\times {10}^{-4}\times 300⁴$

$\to E_A=0.97J$

• (B). Radiation energy emitted per second by inner surface of spherical shell B is given by,

$E_B=\sigma S_B{T}_B^4$

$\to E_A=6\times {10}^{-8}\times 80\times {10}^{-4}\times 300⁴$

$\to E_A=3.8J$

• Energy emitted by inner surface B of that fall back on its surface is given by,

$E=E_B-E_A$

$\to E=2.82J$