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:

As per the given figure,two plates $A$ and $B$ of thermal conductivity $K$ and $2K$ are joined together to form a compound plate. The thickness of the plates are $4.0 \,cm$ and $2.5 \,cm$ respectively,and the area of cross-section is $120 \,cm^{2}$ for each plate. If the equivalent thermal conductivity of the compound plate is $\left(1+\frac{5}{\alpha}\right) K$,then the value of $\alpha$ will be . . . . . .

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 .......... $\min$.

Two rods of equal length and diameter have thermal conductivities $3$ and $4$ units respectively. If they are joined in series, the thermal conductivity of the combination would be

The three rods shown in the figure have identical dimensions. Heat flows from the hot end at a rate of $40 \, W$ in the arrangement $(a)$. Find the rate of heat flow when the rods are joined as in arrangement $(b)$ (Assume $K_{Al} = 200 \, W/m^{\circ}C$ and $K_{Cu} = 400 \, W/m^{\circ}C$). (in $, W$)

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: