The ratio of the coefficient of thermal conductivity of two different materials is $5 : 3$. If the thermal resistance of the rods and the cross-sectional area of these materials are the same,then the ratio of the lengths of these rods will be

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 ....... $^oC$.

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 ........ $^{\circ}C$.

For the figure shown,when arcs $ACD$ and $ADB$ are made of the same material,the total heat current carried between $A$ and $B$ is $H$. If $ADB$ is replaced with another material,the total heat current becomes $2H$. If the temperatures at $A$ and $B$ are fixed at $T_1$ and $T_2$,what is the ratio of the new thermal conductivity to the old thermal conductivity of the arc $ADB$?

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 ....... $\text{min}$.

In a composite rod,when two rods of different lengths and of the same area are joined end to end,then if $K$ is the effective coefficient of thermal conductivity,$\frac{{\ell _1} + {\ell _2}}{K}$ is equal to