If the temperature of a black body increases from $7\,^{\circ}C$ to $287\,^{\circ}C$,then the rate of energy radiation increases by

$A$ spherical black body with a radius of $12 \ cm$ radiates $450 \ W$ power at $500 \ K$. If the radius were halved and the temperature doubled,the power radiated in watt would be

An electric heater kept in a vacuum is heated continuously by passing an electric current. Its temperature:

Two spherical black bodies have radii $r_1$ and $r_2$. Their surface temperatures are $T_1$ and $T_2$. If they radiate the same power,then $\frac{r_2}{r_1}$ is:

$A$ tungsten body of diameter $2.3 \ cm$ is at $2000 \ ^oC$. It radiates $30 \%$ of the energy radiated by a black body of the same radius and temperature. Find the radius of a black body which will radiate energy at the same rate at the same temperature (in $cm$).

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 $K$).