$ABCDE$ is a regular pentagon made of uniform wire. Heat enters at $A$ and leaves at $C$. $T_B$ and $T_D$ are the temperatures of points $B$ and $D$ respectively. Find the temperature $T_C$.

In a composite rod,two rods of different lengths and the same cross-sectional area are joined end to end. If $K$ is the equivalent coefficient of thermal conductivity of the composite rod,then $\left( \frac{\ell_1 + \ell_2}{K} \right)$ is equal to:

Two diagonally opposite corners of a square made of four thin rods of the same material and same dimensions are at temperatures $40^{\circ} C$ and $10^{\circ} C$. If only heat conduction takes place,then the temperature difference between the other two corners will be .......... $^{\circ} C$.

$A$ slab consists of two parallel layers of two different materials of same thickness having thermal conductivities $K_1$ and $K_2$. The equivalent conductivity of the combination is

Consider two insulating sheets with thermal resistances $R_1$ and $R_2$ as shown in the figure. The temperature $\theta$ at the junction is:

Two rods of same length, radius and material transfer a given amount of heat in '$t$' seconds when they are joined as shown in fig $(1)$. But when they are joined as shown in fig $(2)$, then they will transfer the same amount of heat under the same conditions in time: (in $t$)