$A$ composite slab is made of two different metals of the same thickness,having thermal conductivities $K$ and $2K$. The equivalent thermal conductivity of the composite slab is:

$A$ wall has two layers $A$ and $B,$ each made of different material. Both the layers have the same thickness. The thermal conductivity for $A$ is twice that of $B$ and under steady condition,the temperature difference across the wall is $36\,^{\circ}C.$ The temperature difference across the layer $A$ is....... $^{\circ}C$

$A$ cylinder of thermal conductivity $k_1$ and radius $r$ is surrounded by a cylindrical shell of inner radius $r$,outer radius $2r$,and thermal conductivity $k_2$. Both cylinders have the same length and the temperature difference across their ends is the same. The equivalent thermal conductivity of the system is:

Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod is of the same length. The left and right ends are kept at $0^{\circ}C$ and $90^{\circ}C$ respectively. The temperature of the junction of the three rods will be ...... $^{\circ}C$.

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: $k_1 = 60 \ J s^{-1} m^{-1} K^{-1}, k_2 = 120 \ J s^{-1} m^{-1} K^{-1}, k_3 = 135 \ J s^{-1} m^{-1} K^{-1}$)

Three rods $A, B$ and $C$ of thermal conductivities $K, 2K$ and $4K$,cross-sectional areas $A, 2A$ and $2A$ and lengths $2l, l$ and $l$ respectively are connected as shown in the figure. If the ends of the rods are maintained at temperatures $100^{\circ}C, 50^{\circ}C$,and $0^{\circ}C$ respectively,then the temperature $\theta$ of the junction is ......... $^{\circ}C$