The distance between the Sun and the Earth is $2 \times 10^{8} \ km$, the temperature of the Sun is $6000 \ K$, and the radius of the Sun is $7 \times 10^{5} \ km$. If the emissivity of the Earth is $0.6$, find the temperature of the Earth in thermal equilibrium (in $K$).

$A$ black rectangular surface of area $A$ emits energy $E$ per second at $27^{\circ}C$. If the length and breadth are reduced to half of their initial values and the temperature is raised to $327^{\circ}C$, then the energy emitted per second becomes: (in $E$)

$A$ sphere and a cube,both made of copper,have equal volumes and are black. They are allowed to cool at the same temperature and in the same atmosphere. The ratio of their rate of loss of heat is:

The rate of emission of radiation of a black body at $273^{\circ} C$ is $E$. What will be the rate of emission of radiation of this body at $0^{\circ} C$?

$A$ 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 $\sigma = 5.67 \times 10^{-8} \ W m^{-2} K^{-4}$):

$A$ black body is at $727^\circ C$. It emits energy at a rate which is proportional to