$A$ cylindrical rod has temperatures $T_1$ and $T_2$ at its ends. The rate of flow of heat is $Q_1 \text{ cal s}^{-1}$. If the length and radius of the rod are doubled while keeping the temperatures constant,then the new rate of flow of heat $Q_2$ will be:

Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20$ minutes and $40$ minutes respectively. The ratio of thermal conductivities of the materials is

$A$ wall has two layers $A$ and $B$,each made of a different material. Both the layers have the same thickness. The thermal conductivity of the material of $A$ is twice that of $B$. Under thermal equilibrium,the temperature difference across the wall is $36\,^{\circ}C$. The temperature difference across the layer $A$ is ......... $^{\circ}C$

Two plates $A$ and $B$ have thermal conductivities $84 \, W m^{-1} K^{-1}$ and $126 \, W m^{-1} K^{-1}$ respectively. They have the same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of $A$ and $B$ are kept at $100^{\circ} C$ and $0^{\circ} C$ respectively,then the temperature of the surface of contact in steady state is $.......... \, ^{\circ} C$.

$A$ slab consists of two identical plates of copper and brass. The free face of the brass is at $0^{\circ} C$ and that of copper at $100^{\circ} C$. If the thermal conductivities of brass and copper are in the ratio $1: 4$,then the temperature of the interface is (in $^{\circ} C$)

One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two sections of lengths $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two sections is