The Sun emits electromagnetic energy at a rate of $3.9 \times 10^{25} \ W$. Its radius is $6.96 \times 10^8 \ m$. The intensity of sunlight at the solar surface in $W \ m^{-2}$ is:

Two identical plates $P$ and $Q$,radiating as perfect black bodies,are kept in vacuum at constant absolute temperatures $T_P$ and $T_Q$,respectively,with $T_Q < T_P$,as shown in Fig. $1$. The radiated power transferred per unit area from $P$ to $Q$ is $W_0$. Subsequently,two more plates,identical to $P$ and $Q$,are introduced between $P$ and $Q$,as shown in Fig. $2$. Assume that heat transfer takes place only between adjacent plates. If the power transferred per unit area in the direction from $P$ to $Q$ (Fig. $2$) in the steady state is $W_S$,then the ratio $\frac{W_0}{W_S}$ is $.....$

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:

Two spheres of radii $8 \ cm$ and $2 \ cm$ are cooling. Their temperatures are $127^{\circ} C$ and $527^{\circ} C$ respectively. Find the ratio of energy radiated by them in the same time.

When the temperature of a black body increases,it is observed that the wavelength corresponding to maximum energy changes from $0.26 \mu m$ to $0.13 \mu m$. The ratio of the emissive powers of the body at the respective temperatures is

$A$ black body radiates heat energy at the rate of $2 \times 10^5 \, J/s \cdot m^2$ at a temperature of $127 \, ^\circ C$. The temperature of the black body at which the rate becomes $32 \times 10^5 \, J/s \cdot m^2$ is ....... $^\circ C$.