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?

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:

The temperature $\theta$ at the junction of two insulating sheets,having thermal resistances $R_{1}$ and $R_{2}$ as well as top and bottom temperatures $\theta_{1}$ and $\theta_{2}$ (as shown in figure) is given by

$A$ 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....... $^{\circ}C$

Two identical conducting rods are first connected independently to two vessels,one containing water at $100^{\circ}C$ and the other containing ice at $0^{\circ}C$. In the second case,the rods are joined end to end and connected to the same vessels. Let $q_1$ and $q_2$ $g/s$ be the rate of melting of ice in the two cases respectively. The ratio $q_2/q_1$ is

$A$ 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: