$A$ black body is at a temperature of $500 \; K$. It emits energy at a rate which is proportional to:

The total energy of a black body radiation source is collected for five minutes and used to heat water. The temperature of the water increases from $10.0^{\circ} C$ to $11.0^{\circ} C$. The absolute temperature of the black body is doubled and its surface area halved and the experiment repeated for the same time. Which of the following statements would be most nearly correct?

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).

If the temperature of a black body increases from $7^oC$ to $287^oC$,then the rate of energy radiation increases by a factor of:

The actual temperature of a black body is $727^{\circ}C$. At what temperature in $K$ will the black body emit twice the radiation?

If the temperature of a perfectly black body is increased by $50\%$,find the percentage increase in the amount of radiation emitted from its surface.