$A$ composite slab is made of two different materials of equal thickness,having thermal conductivities $K$ and $2K$ respectively. The equivalent thermal conductivity of the slab is ........

Three conductors of the same length having thermal conductivities $k_1, k_2$ and $k_3$ are connected as shown in the figure. The areas of cross-section of the $1^{\text{st}}$ and $2^{\text{nd}}$ conductors are the same,and for the $3^{\text{rd}}$ conductor,it is double that of the $1^{\text{st}}$ conductor. The temperatures are given in the figure. In the steady-state condition,the value of $\theta$ is . . . . . . $^{\circ}C$. (Given: $k_1 = 60 \ J s^{-1} m^{-1} K^{-1}, k_2 = 120 \ J s^{-1} m^{-1} K^{-1}, k_3 = 135 \ J s^{-1} m^{-1} K^{-1}$)

The temperatures of the two outer surfaces of a composite slab,consisting of two materials having coefficients of thermal conductivity $K$ and $2K$ and thicknesses $x$ and $4x$ respectively,are $T_2$ and $T_1$ $(T_2 > T_1)$. The rate of heat transfer through the slab in a steady state is $\left( \frac{A(T_2 - T_1)K}{x} \right)f$,where $f$ is equal to:

Three metal rods of the same material and identical in all respects are joined as shown in the figure. The temperatures at the ends of these rods are maintained as indicated. Assuming no heat energy loss occurs through the curved surfaces of the rods,the temperature at the junction $X$ is (in $^{\circ} C$)

Four rods of identical cross-sectional area and made from the same metal form the sides of a square. The temperatures of two diagonally opposite points are $\theta$ and $\sqrt{2}\theta$ respectively in the steady state. Assuming that only heat conduction takes place,what will be the temperature difference between the other two points?

$A$ wall consists of two layers $A$ and $B$ of equal thickness. Their thermal resistances are $R_1$ and $R_2$. Find the temperature of the interface.