Three metal rods of the same material and identical in all respects are joined as shown in the figure. The temperatures at the ends of these rods are maintained as indicated. Assuming no heat energy loss occurs through the curved surfaces of the rods,the temperature at the junction $X$ is (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: $\frac{2}{K} = \frac{1}{K_1} + \frac{1}{K_2}$

Four rods of the same material and having the same cross-section and length have been joined as shown in the figure. The temperature of the junction of the four rods will be ............... $^{\circ}C$.

Two cylindrical rods $A$ and $B$ made of different materials are joined in a straight line. The ratios of lengths,radii,and thermal conductivities of these rods are $\frac{L_A}{L_B} = \frac{1}{2}$,$\frac{r_A}{r_B} = 2$,and $\frac{K_A}{K_B} = \frac{1}{2}$. The free ends of rods $A$ and $B$ are maintained at $400 \ K$ and $200 \ K$,respectively. The temperature of the rods' interface is . . . . . . $K$,when equilibrium is established.

For the figure shown,when arcs $ACD$ and $ADB$ are made of the same material,the total heat current carried between $A$ and $B$ is $H$. If $ADB$ is replaced with another material,the total heat current becomes $2H$. If the temperatures at $A$ and $B$ are fixed at $T_1$ and $T_2$,what is the ratio of the new thermal conductivity to the old thermal conductivity of the arc $ADB$?

The dimensional formula for thermal resistance is