The total energy radiated from a black body source is collected for one minute and is used to heat a quantity of water. The temperature of water is found to increase from $20^{\circ}C$ to $20.5^{\circ}C$. If the absolute temperature of the black body is doubled and the experiment is repeated with the same quantity of water at $20^{\circ}C$,the temperature of water will be....... $^{\circ}C$

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 $.....$

$A$ body radiates energy at a rate of $5 \ W$ at a temperature of $127^{\circ}C$. If the temperature is increased to $927^{\circ}C$,then it radiates energy at the rate of ...... $W$.

The energy emitted 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 rate of energy emission per second will be ...... $J$.

$A$ sphere of surface area $4 \ m^2$ at temperature $400 \ K$ and having emissivity $0.5$ is located in an environment of temperature $200 \ K$. The net rate of energy exchange of the sphere is (Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$) (in $W$)

Two spherical black bodies of radii $r_1$ and $r_2$ at temperatures $T_1$ and $T_2$ respectively radiate power in the ratio $1:2$. Then $r_1:r_2$ is: