[UPSC CSE 2017] Black Body Radiation (Q450, 15M)

Write down Stefan-Boltzmann law of radiation and derive it from Planck's law of radiation. An aluminium foil of relative emittance 0.1 is placed between two concentric spheres (assumed perfectly black) at temperatures 300\,\mathrm{K} and 200\,\mathrm{K} respectively. Find the temperature of the foil once the steady state is reached.