$A$ rod $CD$ of thermal resistance $10.0 \; K/W$ is joined at the middle of an identical rod $AB$ as shown in the figure. The ends $A$,$B$,and $D$ are maintained at $200^{\circ}C$,$100^{\circ}C$,and $125^{\circ}C$ respectively. The heat current in $CD$ is $P$ watt. The value of $P$ is ... .

Two rods having the same cross-sectional area are used to connect two reservoirs at temperatures $100\,^{\circ}C$ and $0\,^{\circ}C$ as shown. The temperature of the junction is $70\,^{\circ}C$. If the rods are now interchanged,the temperature of the junction will be ......... $^{\circ}C$.

Three rods $AB$, $BC$, and $BD$ made of the same material and having the same cross-section have been joined as shown in the figure. The ends $A$, $C$, and $D$ are held at temperatures of $20^{\circ} C$, $80^{\circ} C$, and $80^{\circ} C$ respectively. If each rod is of the same length, then the temperature at the junction $B$ of the three rods is: (in $^{\circ} C$)

$A$ composite rod is made of three rods of equal length and cross-section as shown in the figure. The thermal conductivities of the materials of the rods are $K/2, 5K$ and $K$ respectively. The ends $A$ and $B$ are at constant temperatures. All heat entering the face $A$ goes out of the end $B$,with no loss of heat from the sides of the bar. The effective thermal conductivity of the bar is:

$A$ slab consists of two parallel layers of copper and brass of equal thickness. The ratio of their thermal conductivities is $1:4$. If the temperature of the free side of the brass is $100^{\circ}C$ and that of the copper is $0^{\circ}C$,find the temperature of the interface in $^{\circ}C$.

Assertion: The equivalent thermal conductivity of two plates of the same thickness in contact is less than the smaller value of thermal conductivity.
Reason: For two plates of equal thickness in contact,the equivalent thermal conductivity is given by: $\frac{2}{K} = \frac{1}{K_1} + \frac{1}{K_2}$