Two parallel plates in vacuum, separated by a distance which is small compared with their linear dimensions, are at temperatures $T_1$ and $T_2$ respectively $\left(T_1>T_2\right)$.
(a) If the plates are non-transparent to radiation and have emission powers $e_1$ and $e_2$ respectively, show that the net energy $W$ transferred per unit area per second is
$$
W=\frac{E_1-E_2}{\frac{E_1}{e_1}+\frac{E_2}{e_2}-1} .
$$
where $E_1$ and $E_2$ are the emission powers of black bodies at temperatures $T_1$ and $T_2$ respectively.
(b) Hence, what is $W$ if $T_1$ is 300 K and $T_2$ is 4.2 K , and the plates are black bodies?
(c) What will $W$ be if $n$ identical black body plates are interspersed between the two plates in (b)?
$$
\left(\sigma=5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}^4\right)
$$