$8\mathrm{.}26$ Two circular discs of the same radius are held parallel and close

together. They are maintained at temperatures $T_1$ and $T_2$ and their

surfaces have emissivities ${}_1$ and ${}_2.$ Show that the net flow of energy

between the discs by radiation is equivalent to having black surfaces

with an effective radiation constant given by

$\frac{{}_{\text{e}\text{f}\text{f}}}{}={}_1\frac{{}_2}{{}_1+{}_2-{}_1{}_2}$

where $$ is the Stefan$-$Boltzmann constant.