$8.$ A thin, gray, diffuse$-$emitting plate with dimensions of $0\mathrm{.}5$ m x $0\mathrm{.}5$ m x $0\mathrm{.}01$ m is exposed to radiation from a blackbody at $800$ K$.$ The emissivity of the plate is $0\mathrm{.}4,$ and the plate is maintained at a temperature of $400$ K$.$ Determine the net radiation heat transfer rate from the plate.