$A$ star $(P)$ behaves like a perfectly black body emitting radiant energy at temperature $T$. Another star $(Q)$ also behaves like a perfectly black body emitting radiant energy at temperature $T/4$ and has a radius eight times the radius of star $(P)$. The ratio of radiant energy emitted by $(P)$ to that by $(Q)$ is

An object is at a temperature of $400^{\circ}C$. At what temperature would it radiate energy twice as fast? The temperature of the surroundings may be assumed to be negligible.

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 spheres $P$ and $Q$,of the same color,having radii $8 \; cm$ and $2 \; cm$ are maintained at temperatures $127^{\circ}C$ and $527^{\circ}C$ respectively. The ratio of energy radiated by $P$ and $Q$ 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).

Radiation from a black body at the thermodynamic temperature $T_1$ is measured by a small detector at distance $d_1$ from it. When the temperature is increased to $T_2$ and the distance to $d_2$,the power received by the detector is unchanged. What is the ratio $d_2/d_1$?