If the temperature of a perfectly black body is reduced from $T$ to $T/2$,find the percentage decrease in the rate of emission.

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 original temperature of a black body is $727^{\circ}C$. The temperature at which this black body must be raised so as to double the total radiant energy is ....... $K$.

$A$ body of area $1\, cm^2$ is heated to a temperature $1000\, K$. The amount of energy radiated by the body in $1\, second$ is .......... $Joule$ (Stefan's constant $\sigma = 5.67 \times 10^{-8}\, W\, m^{-2}K^{-4}$)

$A$ 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.)

Two bodies $A$ and $B$ at temperatures $T_1 \ K$ and $T_2 \ K$ respectively have the same dimensions. Their emissivities are in the ratio $16:1$. At $T_1 = x T_2$,they radiate the same amount of heat per unit area per unit time. The value of $x$ is