$A$ composite slab consists of two materials having coefficients of thermal conductivity $K$ and $2K$,thickness $x$ and $4x$ respectively. The temperatures of two outer surfaces of the composite slab are $T_2$ and $T_1$ respectively $(T_2 > T_1)$. 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:

The ratio of thermal conductivities of two materials is $1 : 2$. If the ratio of the lengths of the rods of these materials is $1 : 2$ and the ratio of their cross-sectional areas is $2 : 1$,then the ratio of their thermal resistances is:

$A$ 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 ... .

Find the temperature difference between $B$ and $C$. (All rods are identical)

Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of each plate. If the coefficients of thermal conductivity of each plate are $2$ and $3$ respectively,then the thermal conductivity of the composite plate will be:

As per the given figure,two plates $A$ and $B$ of thermal conductivity $K$ and $2K$ are joined together to form a compound plate. The thickness of the plates are $4.0 \,cm$ and $2.5 \,cm$ respectively,and the area of cross-section is $120 \,cm^{2}$ for each plate. If the equivalent thermal conductivity of the compound plate is $\left(1+\frac{5}{\alpha}\right) K$,then the value of $\alpha$ will be . . . . . .