The three rods shown in the figure have identical dimensions. Heat flows from the hot end at a rate of $40 \, W$ in the arrangement $(a)$. Find the rate of heat flow when the rods are joined as in arrangement $(b)$ (Assume $K_{Al} = 200 \, W/m^{\circ}C$ and $K_{Cu} = 400 \, W/m^{\circ}C$). (in $, W$)

Two identical square rods of metal are welded end to end as shown in figure $(i)$,$20 \text{ calories}$ of heat flows through them in $4 \text{ minutes}$. If the rods are welded as shown in figure $(ii)$,the same amount of heat will flow through the rods in ....... $\text{min}$.

$A$ cylinder of radius $R$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$. The thermal conductivity of the material of the inner cylinder is $K_1$ and that of the outer cylinder is $K_2$. Assuming no loss of heat,the effective thermal conductivity of the system for heat flowing along the length of the cylinder is

Six identical conducting rods are joined as shown in the figure. Points $A$ and $D$ are maintained at $100^{\circ} C$ and $10^{\circ} C$ respectively. The temperature of junction $C$ will be $.... ^{\circ} C$.

Two slabs $A$ and $B$ of equal surface area are placed one over the other such that their surfaces are completely in contact. The thickness of slab $A$ is twice that of $B$. The coefficient of thermal conductivity of slab $A$ is twice that of $B$. The first surface of slab $A$ is maintained at $100^{\circ} C$,while the second surface of slab $B$ is maintained at $25^{\circ} C$. The temperature at the contact of their surfaces is (in $^{\circ} C$)

Four identical conducting rods are joined as shown in the figure. Points $A$ and $D$ are maintained at temperatures of $200^{\circ}C$ and $20^{\circ}C$ respectively. The temperature of junction $B$ will be ....... $^{\circ}C$.