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

$A$ composite metal bar of uniform cross-section is made up of a length of $25 \ cm$ of copper,$10 \ cm$ of nickel,and $15 \ cm$ of aluminium. Each part is in perfect thermal contact with the adjoining part. The copper end of the composite rod is maintained at $100^{\circ}C$ and the aluminium end at $0^{\circ}C$. The whole rod is covered with an insulating belt so that no heat loss occurs at the sides. If $K_{\text{Cu}} = 2K_{\text{Al}}$ and $K_{\text{Al}} = 3K_{\text{Ni}}$,what will be the temperatures of the $\text{Cu-Ni}$ and $\text{Ni-Al}$ junctions,respectively?

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:

$A$ copper rod $2 \ m$ long has a circular cross-section of radius $1 \ cm$. One end is kept at $100^{\circ}C$ and the other at $0^{\circ}C$,and the surface is covered by non-conducting material to prevent heat losses through the surface. The thermal resistance of the bar in Kelvin per Watt is (Take thermal conductivity $K = 401 \ W/m-K$ of copper):- (in $.9$)

$A$ copper rod of length $18 \ cm$ and a steel rod of length $6 \ cm$ are joined together to form a composite rod of uniform cross-section. The temperature of the free end of the copper rod is $100 \ ^\circ C$ and the temperature of the free end of the steel rod is $0 \ ^\circ C$. What is the temperature at the junction in $^\circ C$? (Thermal conductivity of copper is $9$ times that of steel. The rod is in a steady state.)

Three rods of same dimensions are arranged as shown in the figure. They have thermal conductivities ${K_1}, {K_2}$ and ${K_3}$. The points $P$ and $Q$ are maintained at different temperatures. For the heat to flow at the same rate along the path $PRQ$ and the path $PQ$,which of the following options is correct?