$A$ 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 ..... units.

The surface area of a person is $1.9 \, m^2$,their body temperature is $37 \, ^oC$,and the room temperature is $22 \, ^oC$. If the temperature of the skin is $28 \, ^oC$,find the rate of heat emission. The emissivity of the skin is $0.97$.

$A$ black coloured solid sphere of radius $R$ and mass $M$ is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature $T_0$. The initial temperature of the sphere is $3T_0$. If the specific heat of the material of the sphere varies as $\alpha T^3$ per unit mass with the temperature $T$ of the sphere,where $\alpha$ is a constant,then the time taken for the sphere to cool down to temperature $2T_0$ will be ($\sigma$ is Stefan-Boltzmann constant).

At temperature $T$,the power radiated by a body is $Q$ watts. At the temperature $3T$,the power radiated by it will be (in $Q$)

Assuming the sun to have a spherical outer surface of radius $r$,radiating like a black body at temperature $t^{\circ} C$,the power received by a unit surface (normal to the incident rays) at a distance $R$ from the centre of the sun is,where $\sigma$ is the Stefan's constant.

$A$ planet of radius $R_{p}$ is revolving around a star of radius $R^{*}$ which is at temperature $T^{*}$. The distance between the star and the planet is $d$. If the planet's temperature is $f T^{*}$, then $f$ is proportional to