Find the rate of energy radiated per minute by an incandescent lamp at $2000 \ K$. The surface area is $5 \times 10^{-5} \ m^{2}$,the emissivity is $0.85$,and $\sigma = 5.7 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$. (in $J$)

$A$ 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

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 $B$?

If the temperature of the sun is decreased by $1 \%$,then the value of the solar constant will change by ........... $\%$

$A$ black metal foil is warmed by radiation from a small sphere at temperature $T$ and at a distance $d$. It is found that the power received by the foil is $P$. If both the temperature and distance are doubled,the power received by the foil will be:

$A$ black body radiates maximum energy at wavelength $\lambda$ and its emissive power is $E$. Now,due to a change in temperature of that body,it radiates maximum energy at wavelength $\frac{\lambda}{3}$. At that new temperature,the emissive power is: (in $E$)