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

Spheres $P$ and $Q$ are uniformly constructed from the same material,which is a good conductor of heat,and the radius of $Q$ is thrice the radius of $P$. The rate of fall of temperature of $P$ is $x$ times that of $Q$ when both are at the same surface temperature. The value of $x$ is:

$A$ perfectly black body emits radiation at a temperature $T_1 \ K$. If it is to radiate at $16$ times this power,its temperature $T_2 \ K$ should be: (in $T_1$)

$A$ black body emits energy at the rate of $1 \ cal/cm^2 \cdot s$ at a temperature of $127^{\circ}C$. Find the rate of energy emission at a temperature of $527^{\circ}C$ in $cal/cm^2 \cdot s$.

$A$ 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 rate of radiation of a black body at $0^{\circ}C$ is $E \ J/s$. The rate of radiation of this black body at $273^{\circ}C$ will be: