$A$ black sphere has radius $R$ whose rate of radiation is $E$ at temperature $T$. If the radius is made $R/3$ and the temperature $3T$,the rate of radiation will be:

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 $.....$

The emissivity (power radiated per unit area) of a perfect black body is increased to $16$ times by increasing its temperature. If the initial temperature is $T$, then the final temperature of that black body is: (in $\,T$)

If the temperature of the sun (black body) is doubled,the rate of energy received on earth will be increased by a factor of

The energy emitted per second by a black body at $27^{\circ}C$ is $10\;J$. If the temperature of the black body is increased to $327^{\circ}C$,the energy emitted per second will be ......... $J$.

Obtain the equation for the rate of emission of heat for a perfect black body by using the Stefan-Boltzmann law.