If the temperature of a perfectly black body is increased by $10\%$,the intensity of radiation emitted by its surface will increase by ......$\%$.

Radiation from a black body at the thermodynamic temperature $T_1$ is measured by a small detector at distance $d_1$ from it. When the temperature is increased to $T_2$ and the distance to $d_2$,the power received by the detector is unchanged. What is the ratio $d_2/d_1$?

If the temperature of the $Sun = 6000 \, K$,the radius of the Sun is $7.2 \times 10^{5} \, km$,the radius of the Earth is $6000 \, km$,and the distance between the Earth and the Sun is $15 \times 10^{7} \, km$,find the intensity of light on Earth.

For two identical cylindrical emitters,the ratio of their radii is $1:4$ and the ratio of their temperatures is $2:1$. The ratio of the amount of heat emitted by them is ....... (Assume length is proportional to radius for the cylinders).

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

$A$ very small hole in an electric furnace is used for heating metals. The hole nearly acts as a black body. The area of the hole is $200 \ mm^2$. To keep a metal at $727^{\circ} C$,the heat energy flowing through this hole per second,in joules,is (given $\sigma = 5.67 \times 10^{-8} \ W m^{-2} K^{-4}$):