$A$ 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.

Six identical conducting rods are joined as shown. The ends $A$ and $D$ are maintained at $200\,^{\circ}C$ and $20\,^{\circ}C$ respectively. No heat is lost to the surroundings. The temperature of the junction $C$ will be ........ $^{\circ}C$.

Two cylinders $P$ and $Q$ have the same length and diameter and are made of different materials having thermal conductivities in the ratio $2 : 3$. These two cylinders are combined to make a single cylinder. One end of $P$ is kept at $100^{\circ}C$ and the other end of $Q$ is kept at $0^{\circ}C$. The temperature at the interface of $P$ and $Q$ is ...... $^{\circ}C$.

Two plates of thermal conductivities $k_1$ and $k_2$,cross-sectional areas $A_1$ and $A_2$,and the same thickness $l$ are joined as shown in the figure. The equivalent thermal conductivity $k$ of the combination is:

Two cylindrical rods $A$ and $B$ made of different materials are joined in a straight line. The ratios of lengths,radii,and thermal conductivities of these rods are $\frac{L_A}{L_B} = \frac{1}{2}$,$\frac{r_A}{r_B} = 2$,and $\frac{K_A}{K_B} = \frac{1}{2}$. The free ends of rods $A$ and $B$ are maintained at $400 \ K$ and $200 \ K$,respectively. The temperature of the rods' interface is . . . . . . $K$,when equilibrium is established.

Two rods of the same length and material transfer a given amount of heat in $12 \, s$ when they are joined in parallel. But when they are joined in series,then they will transfer the same amount of heat under the same conditions in ........ $s$.