$A$ 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 ....... $K$.

Two identical conducting rods are first connected independently in parallel to two vessels,one containing water at $100^oC$ and the other containing ice at $0^oC$. In the second case,the rods are joined end to end (in series) 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 of $q_1/q_2$ is

Two rods of cross-sectional area $A$ and $2A$ and equal length having thermal conductivities $2K$ and $3K$ are joined in parallel. The equivalent thermal conductivity of their combination will be:

$A$ metallic prong consists of $4$ rods made of the same material,with the same cross-sections and the same lengths as shown below. The three forked ends are kept at $100^{\circ} C$ and the handle end is at $0^{\circ} C$. The temperature of the junction is ............. $^{\circ} C$.

Five rods of identical dimensions are arranged as shown in the figure. Their thermal conductivities are $k_1, k_2, k_5, k_4$ and $k_3$. When $A$ and $B$ are maintained at different temperatures,no heat flows through the central rod if:

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