$A$ black body,at a temperature of $227\,^{\circ}C$,radiates heat at a rate of $7\, cal\, cm^{-2} \,s^{-1}$. At a temperature of $727\,^{\circ}C$,the rate of heat radiated in the same units will be ..... units.

Two spherical bodies of radii $r_1$ and $r_2$ have surface temperatures $T_1$ and $T_2$ respectively. They radiate the same power. The ratio $r_1/r_2$ 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 $0^{\circ} C$?

$A$ black body radiates energy at the rate of $E \text{ W/m}^2$ at a high temperature $T \text{ K}$. When the temperature is reduced to $\left(\frac{T}{2}\right) \text{ K}$, the radiant energy is

$A$ wire of length $10 \ cm$ and diameter $0.5 \ mm$ is used in a bulb. The temperature of the wire is $1727^{\circ} C$ and power radiated by the wire is $94.2 \ W$. Its emissivity is $\frac{x}{8}$ where $x=$ . . . . . . (Given $\sigma=6.0 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$,$\pi=3.14$ and assume that the emissivity of wire material is same at all wavelengths.)

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