Two spheres of the same material have radii $1 \; m$ and $4 \; m$ and temperatures $4000 \; K$ and $2000 \; K$ respectively. The ratio of the energy radiated per second by the first sphere to that by the second is

The temperature of a perfect black body is $727^{\circ}C$ and its surface area is $0.1\, m^{2}$. If the Stefan-Boltzmann constant is $\sigma = 5.67 \times 10^{-8} \, W/m^{2} \cdot K^{4}$,then the heat radiated in $1\, min$ is ........ $cal$.

Two spherical black bodies have radii $R_1$ and $R_2$. Their surface temperatures are $T_1 \ K$ and $T_2 \ K$ respectively. If they radiate the same power,the ratio $\frac{R_1}{R_2}$ is

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.

If the ambient temperature is $300 \ K$,the rate of cooling at $600 \ K$ is $H$. In the same surroundings,the rate of cooling at $900 \ K$ is:

$A$ 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: