Write the value and dimensional formula of the Stefan-Boltzmann constant.

The emissivity (power radiated per unit area) of a perfect black body is increased to $16$ times by increasing its temperature. If the initial temperature is $T$, then the final temperature of that black body is: (in $\,T$)

Radiation from a black body at the thermodynamic temperature $T_1$ is measured by a small detector at distance $d_1$ from it. When the temperature is increased to $T_2$ and the distance to $d_2$,the power received by the detector is unchanged. What is the ratio $d_2/d_1$?

$A$ black body is at a temperature of $500 \; K$. It emits energy at a rate which is proportional to:

$A$ sphere at temperature $600\,K$ is placed in an environment of temperature $200\,K$. Its cooling rate is $H$. If its temperature is reduced to $400\,K$,then the cooling rate in the same environment will become:

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