Heat is conducted across a composite block of two slabs of thickness $d$ and $2d$. Their thermal conductivities are $2k$ and $k$ respectively. All the heat entering the face $AB$ leaves from the face $CD$. The temperature in $^o C$ of the junction $EF$ of the two slabs is :

Six wires each of cross-sectional area $A$ and length $l$ are combined as shown in the figure. The thermal conductivities of copper and iron are $K_1$ and $K_2$ respectively. The equivalent thermal resistance between points $A$ and $C$ is

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ and 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

In a composite rod, when two rods of different lengths and of the same area are joined end to end, then if $K$ is the effective coefficient of thermal conductivity ; $\frac{{{\ell _1} + {\ell _2}}}{K}$ is equal to

Three metal rods of the same material an identical in all respects are joined as shown in the figure. The temperatures at the ends are maintained as indicated. Assuming no loss of heat from the curved surfaces of the rods, the temperature at the junction $X$ would be ....... $^oC$

Two sheets of thickness $d$ and $2 d$ and same area are touching each other on their face. Temperature $T_A$, $T_B$, $T_C$ shown are in geometric progression with common ratio $r = 2$. Then ratio of thermal conductivity of thinner and thicker sheet are