Two black spheres $P$ and $Q$ have radii in the ratio $4:3$. The wavelengths of maximum intensity of radiation are in the ratio $4:5$ respectively. The ratio of radiated power by $P$ to $Q$ is

$A$ star emits radiation with maximum intensity at a wavelength of $289.9 \, nm$. What is the intensity of the radiation emitted by the star? (Given: Stefan's constant $\sigma = 5.67 \times 10^{-8} \, W/m^2K^4$,Wien's constant $b = 2898 \, \mu m \cdot K$)

The ratio of radiant energies radiated per unit surface area by two bodies is $16 : 1$. The temperature of the hotter body is $1000 \ K$. Then,the temperature of the colder body will be ....... $K$.

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).

Two bodies $A$ and $B$ at temperatures $T_1 \ K$ and $T_2 \ K$ respectively have the same dimensions. Their emissivities are in the ratio $1: 3$. If they radiate the same amount of heat per unit area per unit time,then the ratio of their temperatures $(T_1: T_2)$ is

Two spherical bodies of same materials having radii $0.2 \ m$ and $0.8 \ m$ are placed in the same atmosphere. The temperature of the smaller body is $800 \ K$ and the temperature of the bigger body is $400 \ K$. If the energy radiated from the smaller body is $E$,the energy radiated from the bigger body is (assume the effect of the surrounding to be negligible).