$A$ wall has two layers $A$ and $B$,each made of different materials. Both layers are of the same thickness. The thermal conductivity of material $A$ is twice that of $B$. If in the steady state,the temperature difference across the wall is $24^{\circ} C$,then the temperature difference across the layer $B$ is (in $^{\circ} C$)

Six identical conducting rods are joined as shown in the figure. Points $A$ and $D$ are maintained at temperatures of $200^oC$ and $20^oC$ respectively. The temperature of junction $B$ will be ....... $^oC$.

Three rods of the same material and same cross-sectional area,but different lengths $10 \, cm$,$20 \, cm$,and $30 \, cm$,are connected at a junction $O$ as shown in the figure. What is the temperature of the junction $O$ in $^{\circ} C$?

$A$ slab consists of two parallel layers of copper and brass of equal thickness. The ratio of their thermal conductivities is $1:4$. If the temperature of the free side of the brass is $100^{\circ}C$ and that of the copper is $0^{\circ}C$,find the temperature of the interface in $^{\circ}C$.

Two walls have thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$,respectively. In the steady state,the temperatures of the outer surfaces are $T_1$ and $T_2$. What is the temperature at the interface of the two walls?

Two rectangular blocks,having identical dimensions,can be arranged either in configuration $I$ or in configuration $II$ as shown in the figure. One of the blocks has thermal conductivity $k$ and the other $2k$. The temperature difference between the ends along the $x$-axis is the same in both the configurations. It takes $9 \ s$ to transport a certain amount of heat from the hot end to the cold end in the configuration $I$. The time to transport the same amount of heat in the configuration $II$ is: (in $s$)