$A$ black body at $227^{\circ}C$ radiates heat at the rate of $20 \, cal \, m^{-2} \, s^{-1}$. When its temperature is raised to $727^{\circ}C$,the rate of heat radiation will be $x \, cal \, m^{-2} \, s^{-1}$. Find $x$.

The spectrum of a black body at two temperatures $27\,^oC$ and $327\,^oC$ is shown in the figure. Let $A_1$ and $A_2$ be the areas under the two curves respectively. The value of $\frac{A_2}{A_1}$ is

The adjoining diagram shows the spectral energy density distribution $E_\lambda$ of a black body at two different temperatures. If the areas under the curves are in the ratio $16 : 1$,the value of temperature $T$ is ......... $K$. (in $,000$)

$A$ wire of length $L$ and diameter $d$ is used in a bulb. The temperature of the wire is $T$ and the power radiated by the wire is $P$. Its emissivity is $e$ ($\sigma$ = Stefan's constant). (Assume that the emissivity of the wire material is the same at all wavelengths).

When the temperature of a black body increases, it is observed that the wavelength corresponding to maximum energy changes from $0.26 \mu m$ to $0.13 \mu m$. The ratio of the emissive powers of the body at the respective temperatures is

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