The rate of flow of heat through a metal rod with a temperature difference of $40^{\circ} C$ is $1600 cal/s$. The thermal resistance of the metal rod in $^{\circ} C s/cal$ is

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

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:

Two identical square rods of metal are welded end to end as shown in figure $(a)$. Assume that $10 \, cal$ of heat flows through the rods in $2 \, min$. Now the rods are welded as shown in figure $(b)$. The time it would take for $10 \, cal$ to flow through the rods now,is ........ $\min$.

Two rectangular blocks,having identical dimensions,can be arranged either in configuration $I$ or in configuration $II$ as shown in the figure. One of the blocks has thermal conductivity $k$ and the other $2k$. The temperature difference between the ends along the $x$-axis is the same in both the configurations. It takes $9 \ s$ to transport a certain amount of heat from the hot end to the cold end in the configuration $I$. The time to transport the same amount of heat in the configuration $II$ is: (in $s$)

Three conducting rods $AB, BC$ and $BD$ made of the same material and same cross-section are arranged as shown in the figure. Temperatures at the points $A, D$ and $C$ are maintained at $20^{\circ} C, 90^{\circ} C$ and $0^{\circ} C$ respectively. The ratio of lengths of $BD$ to $BC$ when there is no heat flow in $AB$ is: