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 $f$.

Two identical square rods of metal are welded end to end as shown in figure $(i)$,$20 \text{ calories}$ of heat flows through them in $4 \text{ minutes}$. If the rods are welded as shown in figure $(ii)$,the same amount of heat will flow through the rods in ....... $\text{min}$.

The ratio of thermal conductivity of two rods of different materials is $5 : 4$. If the two rods have the same area of cross-section and the same thermal resistance,what is the ratio of their lengths?

Three rods of identical dimensions are connected as shown in the figure. Points $P$ and $Q$ are maintained at different temperatures. If the rate of heat flow through $PRQ$ and $PQ$ is the same,then...

Two slabs $A$ and $B$ of equal surface area are placed one over the other such that their surfaces are completely in contact. The thickness of slab $A$ is twice that of $B$. The coefficient of thermal conductivity of slab $A$ is twice that of $B$. The first surface of slab $A$ is maintained at $100^{\circ} C$, while the second surface of slab $B$ is maintained at $25^{\circ} C$. The temperature at the contact of their surfaces is (in $^{\circ} C$)

The dimensions of thermal resistance are