In the following figure,two insulating sheets with thermal resistances $R$ and $3R$ are shown. The temperature $\theta$ at the interface is ...... $^oC$.

$A$ 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 ... .

Five wires each of cross-sectional area $A$ and length $l$ are combined as shown. The thermal conductivity of copper and steel are $k_1$ and $k_2$ respectively. The equivalent thermal resistance between $A$ and $C$ is

$A$ cylinder of radius $R$ made of a material of thermal conductivity $k_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of a material of thermal conductivity $k_2$. The two ends of the combined system are maintained at different temperatures. There is no loss of heat from the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

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: $\frac{2}{K} = \frac{1}{K_1} + \frac{1}{K_2}$

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