$A$ wall consists of two layers $A$ and $B$ of equal thickness. Their thermal resistances are $R_1$ and $R_2$. Find the temperature of the interface.

Two rods of same material have same length and area. The heat $\Delta Q$ flows through them for $12 \, \text{minutes}$ when they are joined in series. If now both the rods are joined in parallel,then the same amount of heat $\Delta Q$ will flow in ........ $\text{minutes}$.

Three metal rods of the same material and identical in all respects are joined as shown in the figure. The temperatures at the ends of these rods are maintained as indicated. Assuming no heat energy loss occurs through the curved surfaces of the rods,the temperature at the junction $X$ is (in $^{\circ} C$)

Two rods $A$ and $B$ of different materials but same cross-section are joined as shown in the figure. The free end of $A$ is maintained at $100^{\circ}C$ and the free end of $B$ is maintained at $0^{\circ}C$. If $l_2 = 2l_1$,$K_1 = 2K_2$ and the rods are thermally insulated from the sides to prevent heat losses,then the temperature $\theta$ of the junction of the two rods is ........ $^{\circ}C$.

Consider a compound slab consisting of two different materials having equal thickness and thermal conductivities $K$ and $2K$ respectively. The equivalent thermal conductivity of the slab is

The dimensional formula for thermal resistance is