$A$ rod $CD$ of thermal resistance $10.0 \; K/W$ is joined at the middle of an identical rod $AB$ as shown in the figure. The ends $A$,$B$,and $D$ are maintained at $200^{\circ}C$,$100^{\circ}C$,and $125^{\circ}C$ respectively. The heat current in $CD$ is $P$ watt. The value of $P$ is ... .

Four identical conducting rods are joined as shown in the figure. Points $A$ and $D$ are maintained at temperatures of $200^{\circ}C$ and $20^{\circ}C$ respectively. The temperature of junction $B$ will be ....... $^{\circ}C$.

$A$ wall consists of alternating blocks of length $d$ and coefficients of thermal conductivity $K_{1}$ and $K_{2}$ respectively,as shown in the figure. The cross-sectional areas of the blocks are the same. The equivalent coefficient of thermal conductivity of the wall between the left and right sides is

The temperatures of the two outer surfaces of a composite slab are $T_2$ and $T_1$ $(T_2 > T_1)$. The thermal conductivities of the materials are $K$ and $2K$,and their thicknesses are $x$ and $4x$,respectively. In the steady state,the rate of heat flow through the slab is given by $f \left( \frac{A(T_2 - T_1)K}{x} \right)$. Find the value of $f$.

$A$ slab consists of two parallel layers of copper and brass of equal thickness. The ratio of their thermal conductivities is $1:4$. If the temperature of the free side of the brass is $100^{\circ}C$ and that of the copper is $0^{\circ}C$,find the temperature of the interface in $^{\circ}C$.

$A$ 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: