Calculate the surface temperature of the planet,if the energy radiated by unit area in unit time is $5.67 \times 10^4 \, W$. (Assume the planet to be a black body).

$A$ black metal foil is warmed by radiation from a small sphere at temperature $T$ and at a distance $d$. It is found that the power received by the foil is $P$. If both the temperature and distance are doubled,the power received by the foil will be:

The ratio of the radii of two spheres made of the same material is $1:4$ and the ratio of their temperatures is $2:3$. The ratio of the energy emitted by the spheres per second will be:

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 $K$).

$A$ hot metallic sphere of radius $r$ radiates heat. Its rate of cooling is

Three very large plates of the same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2T$ and $3T$ respectively. The temperature of the middle (i.e.,second) plate under steady-state condition is