$A$ black body radiates energy at the rate of $E \text{ W/m}^2$ at a high temperature $T \text{ K}$. When the temperature is reduced to $\left(\frac{T}{2}\right) \text{ K}$, the radiant energy is

The 'Kangri' is an earthen pot used to stay warm in Kashmir during the winter months. Assume that the 'Kangri' is spherical and of surface area $7 \times 10^{-2} \,m^{2}$. It contains $300 \,g$ of a mixture of coal,wood,and leaves with a calorific value of $30 \,kJ/g$ (and provides heat with $10 \%$ efficiency). The surface temperature of the 'Kangri' is $60^{\circ}C$ and the room temperature is $0^{\circ}C$. Then,a reasonable estimate for the duration $t$ (in $h$) that the 'Kangri' heat will last is (take the 'Kangri' to be a black body).

$A$ sphere is at temperature $600 \text{ K}$. In an external environment of $200 \text{ K}$, its cooling rate is $R$. When the temperature of the sphere falls to $400 \text{ K}$, then the cooling rate $R'$ will become:

The wavelength of maximum intensity of radiation emitted by a star is $289.8 \ nm$. The radiation intensity of the star is (Stefan's constant $= 5.67 \times 10^{-8} \ W m^{-2} K^{-4}$, Wien's constant $b = 2898 \ \mu m \ K$).

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 $K$)

The surface of a black body is at a temperature $727^{\circ} C$ and its cross-section is $1 \,m^2$. Heat radiated from this surface in one minute in joules is (Stefan's constant $=5.7 \times 10^{-8} \,W / m^2 / K^4$ )