The unit of thermal conductivity is

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 temperature of the water of a pond is $0^{\circ} C$ while that of the surrounding atmosphere is $-20^{\circ} C$. If the density of ice is $\rho$,the coefficient of thermal conductivity is $k$,and the latent heat of melting is $L$,then the thickness $Z$ of the ice layer formed increases as a function of time $t$ as:

Two spheres of different materials,one with double the radius and one-fourth wall thickness of the other,are filled with ice. If the time taken for complete melting of ice in the large radius sphere is $25 \ minutes$ and that for the smaller one is $16 \ minutes$,the ratio of thermal conductivities of the materials of the larger sphere to the smaller sphere is:

The rate of heat flow through the cross-section of the rod shown in the figure is ($T_2 > T_1$ and the thermal conductivity of the material of the rod is $K$).

Two metallic blocks $M_{1}$ and $M_{2}$ of the same cross-sectional area are connected to each other as shown in the figure. If the thermal conductivity of $M_{2}$ is $K$,then the thermal conductivity of $M_{1}$ will be $xK$. Find the value of $x$. [Assume steady-state heat conduction]