In a composite rod,when two rods of different lengths $l_1$ and $l_2$ and of the same cross-sectional area are joined end to end,if $K$ is the effective coefficient of thermal conductivity,then the value of $(l_1 + l_2)/K$ is

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 figure shows three different arrangements of materials $1, 2$,and $3$ to form a wall. The thermal conductivities are $k_1 > k_2 > k_3$. The left side of the wall is $20\,^{\circ}\text{C}$ higher than the right side. The temperature difference $\Delta T$ across material $1$ has the following relation in the three cases:

Two rods of the same length and material transfer a given amount of heat in $12 \text{ s}$ when they are joined end-to-end. If they are joined lengthwise, in how many seconds will they transfer the same amount of heat under the same conditions (in $\text{ s}$)?

Two cylinders $P$ and $Q$ have the same length and diameter and are made of different materials having thermal conductivities in the ratio $2 : 3$. These two cylinders are combined to make a single cylinder. One end of $P$ is kept at $100^{\circ}C$ and the other end of $Q$ is kept at $0^{\circ}C$. The temperature at the interface of $P$ and $Q$ is ...... $^{\circ}C$.

Six identical rods are arranged as shown in the figure. The temperature of the junction $B$ will be......... $^oC$