Five identical rods are joined as shown in the figure. Points $A$ and $C$ are maintained at temperatures $120^\circ C$ and $20^\circ C$ respectively. The temperature of junction $B$ will be....... $^\circ C$

Two identical metal rods are welded end-to-end as shown in figure $(1)$. It takes $4 \ min$ for $20 \ cal$ of heat to flow through them. If these rods are now welded side-by-side as shown in figure $(2)$,the time taken for the same amount of heat to flow through them is .......... $\min$.

An iron bar $(L_{1}=0.1 \; m, A_{1}=0.02 \; m^{2}, K_{1}=79 \; W m^{-1} K^{-1})$ and a brass bar $(L_{2}=0.1 \; m, A_{2}=0.02 \; m^{2}, K_{2}=109 \; W m^{-1} K^{-1})$ are soldered end to end as shown in the figure. The free ends of the iron bar and brass bar are maintained at $373 \; K$ and $273 \; K$ respectively. Obtain expressions for and hence compute:
$(i)$ the temperature of the junction of the two bars,
$(ii)$ the equivalent thermal conductivity of the compound bar,and
$(iii)$ the heat current through the compound bar.

Two rods of same length, radius and material transfer a given amount of heat in '$t$' seconds when they are joined as shown in fig $(1)$. But when they are joined as shown in fig $(2)$, then they will transfer the same amount of heat under the same conditions in time: (in $t$)

Five metal rods of the same cross-sectional area $A$ and same length $l$ are connected as shown in the figure. If the thermal conductivities of copper and steel are $K_1$ and $K_2$ respectively,then the resultant thermal resistance between $A$ and $C$ is:

Consider a compound slab consisting of two different materials having equal thickness and thermal conductivities $K$ and $2K$ respectively. The equivalent thermal conductivity of the slab is