Question

A spherical ball A of surface area 20 cm² is kept at the centre of a hollow spherical shell B of area 80 cm². The surface of A and the inner surface of B emit as blackbodies. Both A and B are at 300 K. (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 = 20 cm² = 20$\times$10^$-$4 m²
Surface area of the spherical shell, S_B = 80 cm² = 80$\times$10^$-$4 m²
Temperature of the spherical ball, T_A = 300 K
Temperature of the spherical shell, T_B = 300 K

Radiation energy emitted per second by the spherical ball A is given by
$$\begin{gathered} E_A=\sigma S_A{T_A}^4 \\ \Rightarrow E_A=6.0\times {10}^{-8}\times 20\times {10}^{-4}\times {\left(300\right)}^4 \\ \Rightarrow E_A=0.97\mathrm{J} \end{gathered}$$

Radiation energy emitted per second by the inner surface of the spherical shell B is given by
$$\begin{gathered} E_B=\sigma S_B{T_B}^4 \\ \Rightarrow E_B=6.0\times {10}^{-8}\times 80\times {10}^{-4}\times {\left(300\right)}^4 \\ \Rightarrow E_B=3.76\mathrm{J}\approx 3.8\mathrm{J} \end{gathered}$$

Energy emitted by the inner surface of B that falls back on its surface is given by

$$\begin{gathered} E=E_B-E_A=3.76-0.94 \\ \Rightarrow E=2.82\mathrm{J} \end{gathered}$$