$A$ black sphere has radius $R$ whose rate of radiation is $E$ at temperature $T$. If the radius is made $\frac{R}{3}$ and the temperature is made $3T$,the rate of radiation will be:

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

Two spheres $S_1$ and $S_2$ have same radii but temperatures $T_1$ and $T_2$ respectively. Their emissive power is same and emissivity in the ratio $1:4$. Then the ratio $T_1: T_2$ is

Two spherical black bodies of radii $r_1$ and $r_2$ at temperatures $T_1$ and $T_2$ respectively radiate power in the ratio $1:2$. Then $r_1:r_2$ is:

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 $b = 2898 \ \mu m \ K$).

$A$ black body is at a temperature of $500 \; K$. It emits energy at a rate which is proportional to: