$A$ black body at a temperature of $127^{\circ}C$ radiates heat at the rate of $1 \ cal/cm^2 \cdot s$. At a temperature of $527^{\circ}C$,the rate of heat radiation from the body in $cal/cm^2 \cdot s$ will be:

$A$ solid copper sphere of density $\rho$,specific heat capacity $C$ and radius $r$ is initially at $200 \ K$. It is suspended inside a chamber whose walls are at $0 \ K$. The time required (in $\mu s$) for the temperature of the sphere to drop to $100 \ K$ is ( $\sigma$ is Stefan's constant and all the quantities are in $SI$ units.)

Energy is being emitted from the surface of a black body at $127\,^{\circ}C$ temperature at the rate of $1.0 \times 10^6\,J/s\cdot m^2$. The temperature of the black body at which the rate of energy emission is $16.0 \times 10^6\,J/s\cdot m^2$ will be ......... $^{\circ}C$.

$A$ solid copper sphere (density $\rho$ and specific heat capacity $c$) of radius $r$ at an initial temperature $200 \, K$ is suspended inside a chamber whose walls are at almost $0 \, K$. The time required (in $\mu s$) for the temperature of the sphere to drop to $100 \, K$ is:

Two spheres $P$ and $Q$,of the same color,having radii $8 \; cm$ and $2 \; cm$ are maintained at temperatures $127^{\circ}C$ and $527^{\circ}C$ respectively. The ratio of energy radiated by $P$ and $Q$ is:

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