$A$ container has a small hole. At what temperature (in $K$) should it be maintained so that it emits $1 \ cal$ of energy per second per $m^2$?

Two bodies $P$ and $Q$ have thermal emissivities of $\varepsilon_P$ and $\varepsilon_Q$ respectively. Surface areas of these bodies are same and the total radiant power emitted is also at the same rate. If the temperature of $P$ is $\theta_P$ Kelvin,then the temperature of $Q$ i.e.,$\theta_Q$ 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).

Suppose the Sun is a spherical body of radius $r$ with a surface temperature of $t \, ^\circ C$. It radiates energy like a black body. The power received per unit area at a distance $R$ from the center of the Sun will be: ($\sigma$ is the Stefan-Boltzmann constant)

$A$ black body at a high temperature $T \ K$ radiates energy at the rate $E \ W/m^2$. When the temperature falls to $(T/2) \ K$,the radiated energy will be:

Two identical metal balls at temperatures $200^{\circ}C$ and $400^{\circ}C$ are kept in air at $27^{\circ}C$. The ratio of net heat loss by these bodies is: