$A$ certain stellar body has radius $50 \,R_{s}$ and temperature $2 \,T_{s}$ and is at a distance of $2 \times 10^{10} \,AU$ from the earth. Here,$AU$ refers to the earth-sun distance and $R_{s}$ and $T_{s}$ refer to the sun's radius and temperature,respectively. Take both the star and the sun to be ideal black bodies. The ratio of the power received on earth from the stellar body as compared to that received from the sun is close to

Two spherical black bodies of radii $R_1$ and $R_2$ having surface temperatures $T_1$ and $T_2$ respectively, radiate the same power. The ratio of $R_1$ to $R_2$ will be

$A$ black body radiates energy at the rate of $E \text{ W/m}^2$ at a high temperature $T \text{ K}$. When the temperature is reduced to $\left(\frac{T}{2}\right) \text{ K}$, the radiant energy is

If the temperature of the Sun gets doubled, the rate of energy received on the Earth will increase by a factor of

$A$ black rectangular surface of area $A$ emits energy $E$ per unit time at $27^{\circ}C$. If length and breadth are reduced to $(1/4)^{th}$ of their initial values and the temperature is raised to $327^{\circ}C$, then the energy emitted per unit time becomes:

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 $.....$