$A$ spherical black body with a radius of $12 \ cm$ radiates $450 \ W$ power at $500 \ K$. If the radius were halved and the temperature doubled,the power radiated in watt would be

$A$ black body at $227^o C$ radiates heat at the rate of $7 \; cal/cm^2 s$. At a temperature of $727^o C$,the rate of heat radiated in the same units will be:

Two black bodies $A$ and $B$ have equal surface areas and are maintained at temperatures $27^{\circ} C$ and $177^{\circ} C$ respectively. What will be the ratio of the thermal energy radiated per second by $A$ to that by $B$?

Calculate the surface temperature of the planet,if the energy radiated by unit area in unit time is $5.67 \times 10^4 \, W$. (Assume the planet to be a black body).

Find the radiant energy emitted per second in $Js^{-1}$ by a lamp filament at $2000 K$. The surface area is $5.0 \times 10^{-5} m^{2}$,the relative emissivity is $0.85$,and $\sigma = 5.7 \times 10^{-8} W m^{-2} K^{-4}$.

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 $d_2/d_1$?