An object is at a temperature of $400^{\circ}C$. At what temperature would it radiate energy twice as fast? The temperature of the surroundings may be assumed to be negligible.

The amount of heat energy radiated by a metal at temperature $T$ is $E$. When the temperature is increased to $3T$,the energy radiated is: (in $E$)

$A$ black body radiates at the rate of $W$ watts at a temperature $T$. If the temperature of the body is reduced to $T/3$,it will radiate at the rate of (in Watts):

$A$ black body at a temperature of $127^{\circ}C$ radiates heat at the rate of $1 \ cal/cm^2 \cdot s$. At a temperature of $527^{\circ}C$,the rate of heat radiation from the body in $cal/cm^2 \cdot s$ will be:

$A$ 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.)

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. Find the value of $\frac {A_2}{A_1}$.