The radiant energy from the sun incident normally at the surface of the earth is $20 \, kcal/(m^2 \cdot min)$. What would have been the radiant energy incident normally on the earth,if the sun had a temperature twice of the present one? (in $kcal/(m^2 \cdot min)$)

$A$ metal ball of surface area $200 \; cm^2$ and temperature $527^{\circ}C$ is surrounded by a vessel at $27^{\circ}C$. If the emissivity of the metal is $0.4$,then the rate of loss of heat from the ball is approximately .......... $J/s$. $(\sigma = 5.67 \times 10^{-8} \; J/(m^2 \cdot s \cdot K^4))$

If the temperature of a perfectly black body is increased by $10\%$,the intensity of radiation emitted by its surface will increase by ......$\%$.

The radiation emitted by a star $A$ is $10000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $6000 \ K$ and $2000 \ K$ respectively, the ratio of the radii of the star $A$ and the sun is: (in $: 1$)

$A$ sphere and a cube,both made of copper,have equal volumes and are black. They are allowed to cool at the same temperature and in the same atmosphere. The ratio of their rate of loss of heat is:

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 $\sigma = 5.67 \times 10^{-8} \, W \, m^{-2} K^{-4}$.