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 $\frac {A_2}{A_1}$.

Assume that the solar constant is $1.4 \, kW/m^2$,the radius of the sun is $7 \times 10^5 \, km$,and the distance of the earth from the center of the sun is $1.5 \times 10^8 \, km$. Given Stefan's constant is $\sigma = 5.67 \times 10^{-8} \, W m^{-2} K^{-4}$,find the approximate temperature of the sun in $K$.

$A$ 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 ..... $W$.

Two spheres of the same material have radii $1 \ m$ and $4 \ m$ and temperatures $4000 \ K$ and $2000 \ K$ respectively. The ratio of the energy radiated by them is .....

$A$ black sphere of radius $R$ radiates power $P$ at a certain temperature $T$. If the temperature is doubled and the radius is also doubled,the new power radiated will be: (in $P$)

The wavelength of maximum intensity of radiation emitted by a star is $289.8 \ nm$. The radiation intensity of the star is (Stefan's constant $= 5.67 \times 10^{-8} \ W m^{-2} K^{-4}$, Wien's constant $b = 2898 \ \mu m \ K$).