$A$ partition wall has two layers $A$ and $B$ in contact,each made of a different material. They have the same thickness but the thermal conductivity of layer $A$ is twice that of layer $B$. If the steady state temperature difference across the wall is $60 \ K$,then the corresponding difference across the layer $A$ is ....... $K$.

In a composite rod,when two rods of different lengths and of the same area are joined end to end,then if $K$ is the effective coefficient of thermal conductivity,$\frac{{\ell _1} + {\ell _2}}{K}$ is equal to

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 $^{\circ} C$)

Two conducting rods $A$ and $B$ of same length and cross-sectional area are connected $(i)$ In series $(ii)$ In parallel as shown. In both combinations,a temperature difference of $100^{\circ}C$ is maintained. If the thermal conductivity of $A$ is $3K$ and that of $B$ is $K$,then the ratio of heat current flowing in the parallel combination to that flowing in the series combination is:

Three identical rods have been joined at a junction to make a $Y$-shaped structure. If two free ends are maintained at $90\,^{\circ}C$ and the third end is at $30\,^{\circ}C$,what is the junction temperature $\theta$ in $^{\circ}C$?

Six wires,each of cross-sectional area $A$ and length $l$,are combined as shown in the figure. The thermal conductivities of copper and iron are $K_1$ and $K_2$ respectively. The equivalent thermal resistance between points $A$ and $C$ is: