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 $\,T$)

The energy spectrum of a black body exhibits a maximum of wavelength $\lambda_0$. The temperature of the black body is now changed such that the energy is maximum at wavelength $\frac{3\lambda_0}{2}$. The ratio of power radiated by the black body will be

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

The total radiative power emitted by a spherical black body with radius $R$ and temperature $T$ is $P$. If the radius is doubled and the temperature is halved,then the radiative power will be

The temperature of a spherical black body is inversely proportional to its radius. If its radius is doubled,then the power radiating from it will be

$A$ black body radiates energy at a rate of $E \, W/m^2$ at a temperature of $T \, K$. When the temperature is reduced to $T/2 \, K$,the radiated energy will be .....