(Furnace aperture) A small circular hole of area in the wall of a furnace behaves…

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

(Furnace aperture) A small circular hole of area

2.0\,\text{cm}^2

in the wall of a furnace behaves like an ideal blackbody aperture. The furnace is initially in thermal equilibrium at

1200\,\text{K}

. Take

\sigma = 5.67\times10^{-8}\,\text{W m}^{-2}\text{K}^{-4}

. Answer the following. (i) Derive an expression for the ratio of the radiated power per unit area at

1500\,\text{K}

to that at

1200\,\text{K}

. (ii) Hence calculate the power (in watts) leaving the aperture after the temperature is raised to

1500\,\text{K}

. Assume the emissivity remains unity throughout.