Heat is conducted across a composite block of two slabs of thickness $d$ and $2d$. Their thermal conductivities are $2k$ and $k$ respectively. All the heat entering the face $AB$ leaves from the face $CD$. The temperature in $^oC$ of the junction $EF$ of the two slabs is:

The coefficient of thermal conductivity of copper is $9$ times that of steel. In the composite cylindrical bar shown in the figure,what will be the temperature at the junction of copper and steel (in $^{\circ} C$)?

The walls of a closed cubical box of edge $60 \text{ cm}$ are made of material of thickness $1 \text{ mm}$ and thermal conductivity $4 \times 10^{-4} \text{ cal s}^{-1} \text{ cm}^{-1} {}^{\circ}\text{C}^{-1}$. The interior of the box is maintained $1000^{\circ}\text{C}$ above the outside temperature by a heater placed inside the box and connected across a $400 \text{ V}$ $DC$ supply. The resistance of the heater is: (in $\Omega$)

$A$ 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 ......... $^{\circ}C$

Same quantity of ice is filled in each of the two metal containers $P$ and $Q$ having the same size, shape, and wall thickness but made of different materials. The containers are kept in identical surroundings. The ice in $P$ melts completely in time $t_{1}$ whereas in $Q$ it takes a time $t_{2}$. The ratio of thermal conductivities of the materials of $P$ and $Q$ is

The ratio of thermal conductivity of two rods of different materials is $4:3$. The two rods have same area of cross-section and same thermal resistance. The lengths of rods are in the ratio