$A$ body of area $1\, cm^2$ is heated to a temperature $1000\, K$. The amount of energy radiated by the body in $1\, second$ is .......... $Joule$ (Stefan's constant $\sigma = 5.67 \times 10^{-8}\, W\, m^{-2}K^{-4}$)

Two spheres of the same material have radii $r_1$ and $r_2$ and surface temperatures $T_1$ and $T_2$ respectively. If their emissive power (total power radiated) is the same,find the ratio of their radii $r_1/r_2$.

Two bodies $A$ and $B$ at temperatures $T_1 \ K$ and $T_2 \ K$ respectively have the same dimensions. Their emissivities are in the ratio $16:1$. At $T_1 = x T_2$,they radiate the same amount of heat per unit area per unit time. The value of $x$ is

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 $K$).

Compare the rate of loss of heat from a metal sphere at $627^{\circ} C$ with the rate of loss of heat from the same sphere at $327^{\circ} C$,if the temperature of the surrounding is $27^{\circ} C$. (nearly)

The original temperature of a black body is $727^{\circ}C$. The temperature at which this black body must be raised so as to double the total radiant energy is ....... $K$.