$A$ black body radiates energy at the rate of $1 \times 10^5 \ J/s \cdot m^2$ at a temperature of $227^\circ C$. The temperature to which it must be heated so that it radiates energy at a rate of $1 \times 10^9 \ J/s \cdot m^2$ 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:

Solar constant $(S)$ depends upon the temperature of the Sun $(T)$ as ........

Suppose the Sun is a spherical body of radius $r$ with a surface temperature of $t \, ^\circ C$. It radiates energy like a black body. The power received per unit area at a distance $R$ from the center of the Sun will be: ($\sigma$ is the Stefan-Boltzmann constant)

$A$ metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated $(P)$ by the metal. The sensor has a scale that displays $\log_{2}(P / P_0)$,where $P_0$ is a constant. When the metal surface is at a temperature of $487^{\circ} C$,the sensor shows a value of $1$. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to $2767^{\circ} C$?

$A$ 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