Three very large plates of same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. First and third plates are maintained at absolute temperatures $2 T$ and $3 T$ respectively. Temperature of the middle plate in steady state 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 $2767^{\circ} C$?

$A$ 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 of radii $8 \ cm$ and $2 \ cm$ are cooling. Their temperatures are $127^{\circ} C$ and $527^{\circ} C$ respectively. Find the ratio of energy radiated by them in the same time.

$A$ black rectangular surface of area '$A$' emits energy '$E$' per second at $27^{\circ} C$. If length and breadth are reduced to $\frac{1}{3}$ of their initial values and the temperature is raised to $327^{\circ} C$,then the energy emitted per second becomes:

$A$ 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 .....