The $SI$ unit and dimension of Stefan's constant $\sigma$ in the case of Stefan's law of radiation are

$A$ black body radiates $20\,W$ at temperature $227^{\circ}C$. If the temperature of the black body is changed to $727^{\circ}C$,then its radiating power will be ..... $W$.

If the ratio of the radii of two spheres of the same material and at the same temperature is $1:2$,find the ratio of their emissive power.

$A$ black body of mass $34.38 \ g$ and surface area $19.2 \ cm^2$ is at an initial temperature of $400 \ K$. It is allowed to cool inside an evacuated enclosure kept at a constant temperature of $300 \ K$. The rate of cooling is $0.04 \ ^{\circ}C/s$. The specific heat of the body in $J \ kg^{-1} \ K^{-1}$ is (Stefan's constant $\sigma = 5.73 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$)

At what temperature $T$ (in $K$) will a perfectly black body radiate energy at the rate of $5.67 \, W \, cm^{-2}$ (in $, K$)? Given Stefan's constant $\sigma = 5.67 \times 10^{-8} \, W \, m^{-2} K^{-4}$.

$A$ rectangular surface of a black body at $127^{\circ}C$ with dimensions $8 \ cm \times 4 \ cm$ emits energy at a rate of $E$. If the length and width are halved and the temperature is increased to $327^{\circ}C$,find the new rate of energy emission.