Three rods of the same dimensions have thermal conductivities $3K, 2K$, and $K$. They are arranged as shown in the figure. The temperature of the junction in the steady state is:

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ kept at temperatures $T_1$ and $T_2$,respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

$A$ wall is made of equally thick layers $P$ and $Q$ of different materials. The thermal conductivity of $Q$ is half of that of $P$. In the steady state,if the temperature difference across the wall is $24^{\circ} C$,then the temperature difference across the layer $P$ is ............... . (in $^{\circ} C$)

Two layers of a wall,$A$ and $B$,are made of different materials. Both layers have the same thickness. For layer $A$,the thermal conductivity is $K_A = 3 K_B$. The total temperature difference across the wall is $20^{\circ}C$. Find the temperature difference across layer $A$ in $^{\circ}C$.

Which of the following cylindrical rods will conduct the most heat when their ends are maintained at the same steady temperature difference?

There are two identical vessels filled with equal amounts of ice. The vessels are made of different metals. If the ice melts in the two vessels in $20$ and $35$ minutes respectively,the ratio of the coefficients of thermal conductivity of the two metals is: