$A$ black sphere has radius $R$ whose rate of radiation is $E$ at temperature $T$. If the radius is made $R/3$ and the temperature $3T$,the rate of radiation will be:

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

The 'Kangri' is an earthen pot used to stay warm in Kashmir during the winter months. Assume that the 'Kangri' is spherical and of surface area $7 \times 10^{-2} \,m^{2}$. It contains $300 \,g$ of a mixture of coal,wood,and leaves with a calorific value of $30 \,kJ/g$ (and provides heat with $10 \%$ efficiency). The surface temperature of the 'Kangri' is $60^{\circ}C$ and the room temperature is $0^{\circ}C$. Then,a reasonable estimate for the duration $t$ (in $h$) that the 'Kangri' heat will last is (take the 'Kangri' to be a black body).

$A$ black body,at a temperature of $227\,^{\circ}C$,radiates heat at a rate of $7\,cal\,cm^{-2}\,s^{-1}$. At a temperature of $727\,^{\circ}C$,the rate of heat radiated in the same units will be:

Three large identical plates are kept parallel to each other. The outer two plates are maintained at temperatures $T$ and $2T$, respectively. The temperature of the middle plate in steady state will be close to ........... $T$.

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