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.

At $127^{\circ}C$,the radiated energy is $2.7 \times 10^{-3} \text{ J/s}$. At what temperature in $K$ is the radiated energy $4.32 \times 10^{6} \text{ J/s}$?

$A$ star $(P)$ behaves like a perfectly black body emitting radiant energy at temperature $T$. Another star $(Q)$ also behaves like a perfectly black body emitting radiant energy at temperature $T/4$ and has a radius eight times the radius of star $(P)$. The ratio of radiant energy emitted by $(P)$ to that by $(Q)$ is

If the temperature of the sun is doubled,the rate of energy received by the earth will be increased by a factor of:

$A$ solid copper sphere (density $\rho$ and specific heat capacity $c$) of radius $r$ at an initial temperature $200 \, K$ is suspended inside a chamber whose walls are at almost $0 \, K$. The time required (in $\mu s$) for the temperature of the sphere to drop to $100 \, K$ is:

The distance between the Sun and the Earth is $2 \times 10^{8} \ km$, the temperature of the Sun is $6000 \ K$, and the radius of the Sun is $7 \times 10^{5} \ km$. If the emissivity of the Earth is $0.6$, find the temperature of the Earth in thermal equilibrium (in $K$).