$A$ black body is at $727^\circ C$. It emits energy at a rate which is proportional to

$A$ 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 temperature of a black body is increased by $50 \%$. The percentage increase in the rate of radiation by the body is approximately: (in $\%$)

$A$ black body radiates heat energy at the rate of $2 \times 10^5 \, J/s \cdot m^2$ at a temperature of $127 \, ^\circ C$. The temperature of the black body at which the rate becomes $32 \times 10^5 \, J/s \cdot m^2$ is ....... $^\circ C$.

$A$ black body radiates energy at the rate of $E \text{ W/m}^2$ at a high temperature $T \text{ K}$. When the temperature is reduced to $\left(\frac{T}{2}\right) \text{ K}$,the radiant energy is

$A$ black body surface with an area of $8 \ cm \times 4 \ cm$ emits energy at a rate of $E$ per second at a temperature of $127^{\circ}C$. If the length and width are halved and the temperature is increased to $327^{\circ}C$,find the new rate of energy emission.