Three conducting rods of the same material and cross-section are shown in the figure. The temperatures of $A$,$D$,and $C$ are maintained at $20^{\circ} C$,$90^{\circ} C$,and $0^{\circ} C$ respectively. If there is no heat flow in rod $AB$,the ratio of the lengths of $BD$ and $BC$ is:

The unit of thermal conductivity is

These days,people use steel utensils with copper bottoms. This is considered good for uniform heating of food. Explain this effect using the fact that copper is a better conductor of heat.

Two rods of same length and cross-section are joined along their length. The thermal conductivities of the first and second rods are $K_1$ and $K_2$,respectively. The temperatures of the free ends of the first and second rods are maintained at $\theta_1$ and $\theta_2$,respectively. The temperature of the common junction is:

In an $Ingen-Hauz$ experiment,the wax melts on two rods up to lengths of $10 \ cm$ and $25 \ cm$ respectively. If the two rods are made of different materials,what is the ratio of their thermal conductivities?

$A$ wall is made up of two layers $A$ and $B$. The thickness of the two layers is the same,but materials are different. The thermal conductivity of $A$ is double that of $B$. In thermal equilibrium,the temperature difference between the two ends is $36^{\circ}C$. Then the difference of temperature at the two surfaces of $A$ will be ....... $^{\circ}C$