The thermal conductivity of a rod is $2$. What is its thermal resistivity?

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity $K_{1}, K_{2},$ and $K_{3}$,respectively. They are joined together at their ends to make a long rod. One end of the long rod is maintained at $100^{\circ} C$ and the other at $0^{\circ} C$. If the joints of the rod are at $70^{\circ} C$ and $20^{\circ} C$ in steady state and there is no loss of energy from the surface of the rod,the correct relationship between $K_{1}, K_{2}$ and $K_{3}$ is:

Two thin metallic spherical shells of radii $20 \text{ cm}$ and $30 \text{ cm}$,respectively,are placed with their centers coinciding. $A$ material of thermal conductivity $\alpha$ is filled in the space between the shells. The inner shell is maintained at $300 \text{ K}$ and the outer shell at $310 \text{ K}$. If the rate at which heat flows radially through the material is $40 \text{ W}$,find the value of $\alpha$ (in units of $\text{J s}^{-1} \text{ m}^{-1} \text{ K}^{-1}$).

$A$ rod of length $L$ with sides fully insulated is made of a material whose thermal conductivity varies with temperature $T$ as $K = \frac{\alpha}{T}$,where $\alpha$ is a constant. The ends of the rod are kept at temperatures $T_1$ and $T_2$. The temperature $T$ at a distance $x$ from the end kept at $T_1$ 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 $K$).

Which of the following circular rods (given radius $r$ and length $l$),each made of the same material and whose ends are maintained at the same temperature difference,will conduct the most heat?