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).

$A$ sphere of surface area $4 \ m^2$ at temperature $400 \ K$ and having emissivity $0.5$ is located in an environment of temperature $200 \ K$. The net rate of energy exchange of the sphere is (Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$) (in $W$)

What will be the ratio of the rate of radiation of a metal sphere at two different temperatures $T_1 = 527^\circ C$ and $T_2 = 127^\circ C$ (in $:$)?

If the temperature of the $Sun = 6000 \, K$,the radius of the Sun is $7.2 \times 10^{5} \, km$,the radius of the Earth is $6000 \, km$,and the distance between the Earth and the Sun is $15 \times 10^{7} \, km$,find the intensity of light on Earth.

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

Two spherical black bodies of radii $r_1$ and $r_2$ and with surface temperatures $T_1$ and $T_2$ respectively radiate the same power. Then the ratio of $r_1$ and $r_2$ will be: