$A$ 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:

$A$ sphere is at temperature $600 \text{ K}$. In an external environment of $200 \text{ K}$, its cooling rate is $R$. When the temperature of the sphere falls to $400 \text{ K}$, then the cooling rate $R'$ will become:

$A$ solid cylinder of radius $r_1=2.5 \ cm$, length $l_1=5.0 \ cm$ and temperature $40^{\circ}C$ is suspended in an environment of temperature $60^{\circ}C$. The thermal radiation transfer rate for the cylinder is $1.0 \ W$. If the cylinder is stretched until its radius becomes $r_2=0.50 \ cm$, the thermal radiation transfer rate is changed to (in $W$)

When the temperature of a black body increases, it is observed that the wavelength corresponding to maximum energy changes from $0.26 \mu m$ to $0.13 \mu m$. The ratio of the emissive powers of the body at the respective temperatures is

For two identical cylindrical emitters,the ratio of their radii is $1:4$ and the ratio of their temperatures is $2:1$. The ratio of the amount of heat emitted by them is ....... (Assume length is proportional to radius for the cylinders).

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