The ratio of radiant energies radiated per unit surface area by two bodies is $16 : 1$. The temperature of the hotter body is $1000 \ K$. Then,the temperature of the colder body will be ....... $K$.

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

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:

Two black spheres $P$ and $Q$ have radii in the ratio $4:3$. The wavelengths of maximum intensity of radiation are in the ratio $4:5$ respectively. The ratio of radiated power by $P$ to $Q$ is

The energy spectrum of a black body exhibits a maximum around a wavelength $\lambda_o$. The temperature of the black body is now changed such that the energy is maximum around a wavelength $\frac{3\lambda_o}{4}$. The power radiated by the black body will now increase by a factor of

$A$ hot metallic sphere of radius $r$ radiates heat. Its rate of cooling is