$A$ black body,at a temperature of $227\,^{\circ}C$,radiates heat at a rate of $7\,cal\,cm^{-2}\,s^{-1}$. At a temperature of $727\,^{\circ}C$,the rate of heat radiated in the same units will be:

Two bodies $A$ and $B$ at temperatures $T_1 \ K$ and $T_2 \ K$ respectively have the same dimensions. Their emissivities are in the ratio $1: 3$. If they radiate the same amount of heat per unit area per unit time,then the ratio of their temperatures $(T_1: T_2)$ is

Two spheres made of the same material have radii in the ratio $1:2$. Both are at the same temperature. The ratio of heat radiation energy emitted per second by them 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 $2767^{\circ} C$?

An object is at a temperature of $400^{\circ}C$. At what temperature would it radiate energy twice as fast? The temperature of the surroundings may be assumed to be negligible.

The temperature of a body is $400^{\circ}C$. Assume the temperature of the surroundings is negligible. At what temperature will the body emit double the energy?