Parallel rays of light of intensity $I = 912 \ W m^{-2}$ are incident on a spherical black body kept in surroundings of temperature $T_0 = 300 \ K$. Take Stefan-Boltzmann constant $\sigma = 5.7 \times 10^{-8} \ W m^{-2} K^{-4}$ and assume that the energy exchange with the surroundings is only through radiation. The final steady state temperature of the black body is close to: (in $K$)

$A$ sphere,a cube,and a thin circular plate,all made of the same material,same mass,and same surface finish,are heated to a temperature of $200^{\circ} C$. Which of these objects will cool slowest when left in air at room temperature?

$A$ black coloured solid sphere of radius $R$ and mass $M$ is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature $T_0$. The initial temperature of the sphere is $3T_0$. If the specific heat of the material of the sphere varies as $\alpha T^3$ per unit mass with the temperature $T$ of the sphere,where $\alpha$ is a constant,then the time taken for the sphere to cool down to temperature $2T_0$ will be ($\sigma$ is Stefan-Boltzmann constant).

Find the radiant energy emitted per second in $Js^{-1}$ by a lamp filament at $2000 K$. The surface area is $5.0 \times 10^{-5} m^{2}$,the relative emissivity is $0.85$,and $\sigma = 5.7 \times 10^{-8} W m^{-2} K^{-4}$.

Compare the rate of loss of heat from a metal sphere at $627^{\circ} C$ with the rate of loss of heat from the same sphere at $327^{\circ} C$,if the temperature of the surrounding is $27^{\circ} C$. (nearly)

If the radiation emitted by a perfect radiator has maximum intensity at a wavelength of $2900 Å$,the intensity of radiation emitted by it is (Stefan-Boltzmann's constant $= 5.67 \times 10^{-8} W m^{-2} K^{-4}$ and Wien's constant $= 2.9 \times 10^{-3} m K$).