If the temperature of the sun (black body) is doubled,the rate of energy received on earth will be increased by a factor of

$A$ 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 $2767^{\circ} C$?

If the temperature of a perfectly black body is increased by $10\%$,the intensity of radiation emitted by its surface will increase by ......$\%$.

If a black body emits $0.5 \ J$ of energy per second when it is at $27^{\circ} C$,then the amount of energy emitted by it when it is at $627^{\circ} C$ will be (in $J$)

If the temperature of the $Sun = 6000 \, K$,the radius of the Sun is $7.2 \times 10^{5} \, km$,the radius of the Earth is $6000 \, km$,and the distance between the Earth and the Sun is $15 \times 10^{7} \, km$,find the intensity of light on Earth.

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.