The operating temperature and emissivity of a tungsten filament are $2000 \ K$ and $0.3$,respectively. The surface area of the filament is $A \ cm^2$. If the power of the lamp is $25 \ W$,find $A$. (Given: $\sigma = 5.67 \times 10^{-8} \ W/m^2K^4$)

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 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....... $^{\circ}C$

Find the emissive power from the $0.3 \, cm^2$ surface of a tungsten filament bulb at $3000 \, K$ temperature. Take emissivity $e = 0.4$ for the tungsten bulb. (in $, W$)

$A$ container has a small hole. At what temperature (in $K$) should it be maintained so that it emits $1 \ cal$ of energy per second per $m^2$?

The adjoining diagram shows the spectral energy density distribution $E_\lambda$ of a black body at two different temperatures. If the areas under the curves are in the ratio $16 : 1$,the value of temperature $T$ is ......... $K$. (in $,000$)