In Searle's method for finding the thermal conductivity of metals,the temperature gradient along the bar:

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 $\text{J s}^{-1} \text{ m}^{-1} \text{ K}^{-1}$).

Why does a metal bar appear hotter than a wooden bar at the same temperature? Equivalently,it also appears cooler than a wooden bar if they are both colder than room temperature.

$A$ copper rod and a steel rod of equal cross-sections and lengths $L$ are joined side by side and connected between two heat baths as shown in the figure. If heat flows through them from $x = 0$ to $x = 2L$ at a steady rate and thermal conductivities of the metals are $K_{Cu}$ and $K_{Steel}$ $(K_{Cu} > K_{Steel})$,then the temperature varies as (convection and radiation are negligible):

Find the equivalent thermal conductivity of the system.

Two metal rods $1$ and $2$ have the same length and the same temperature difference at their ends. Their thermal conductivities are $K_1$ and $K_2$ and their cross-sectional areas are $A_1$ and $A_2$ respectively. The condition for the same rate of heat flow in them is ........