Two spheres of radii $4 \, m$ and $1 \, m$ have temperatures $2000 \, K$ and $4000 \, K$ respectively. Find the ratio of their emitted energy.

The 'Kangri' is an earthen pot used to stay warm in Kashmir during the winter months. Assume that the 'Kangri' is spherical and of surface area $7 \times 10^{-2} \,m^{2}$. It contains $300 \,g$ of a mixture of coal,wood,and leaves with a calorific value of $30 \,kJ/g$ (and provides heat with $10 \%$ efficiency). The surface temperature of the 'Kangri' is $60^{\circ}C$ and the room temperature is $0^{\circ}C$. Then,a reasonable estimate for the duration $t$ (in $h$) that the 'Kangri' heat will last is (take the 'Kangri' to be a black body).

$A$ black body is heated from $7\,^oC$ to $287\,^oC$. The ratio of radiation emitted is

If the temperature of the sun (black body) is doubled,the rate of energy received on earth will be increased by a factor of

$A$ spherical black body of radius $12 \, cm$ radiates $450 \, W$ of power at $500 \, K$. If the radius is halved and the temperature is doubled,the power radiated will be ..... $W$.

Find the emissive power from the $0.3 \, cm^2$ surface of a tungsten filament bulb at $3000 \, K$ temperature. Take emissivity $e = 0.4$ for the tungsten bulb. (in $, W$)