Two identical metal wires of thermal conductivities $K_{1}$ and $K_{2}$ respectively are connected in series. The effective thermal conductivity of the combination is

The dimensional formula for thermal resistance is

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:

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 . . . . . .

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 $^{\circ} C$)

Three rods $AB, BC$ and $AC$ having thermal resistances of $10 \text{ units}, 10 \text{ units}$ and $20 \text{ units}$ respectively,are connected as shown in the figure. Ends $A$ and $C$ are maintained at constant temperatures of $100^{\circ}C$ and $0^{\circ}C$ respectively. The rate at which the heat is crossing junction $B$ is . . . . . . $units$.