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

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 $^{\circ} C$)

$A$ copper rod of length $75 \ cm$ and an iron rod of length $125 \ cm$ are joined together end to end. Both are of circular cross-section with diameter $2 \ cm$. The free ends of the copper and iron are maintained at $100^{\circ} C$ and $0^{\circ} C$ respectively. The surfaces of the bars are insulated thermally. The temperature of the copper-iron junction is (Thermal conductivity of copper is $386.4 \ W/m-K$ and thermal conductivity of iron is $48.46 \ W/m-K$) (in $^{\circ} C$)

Two plates of thermal conductivities $k_1$ and $k_2$,cross-sectional areas $A_1$ and $A_2$,and the same thickness $l$ are joined as shown in the figure. The equivalent thermal conductivity $k$ of the combination is:

$A$ wall is made of two layers of thickness $1\ cm$ and $4\ cm$ and thermal conductivities $K$ and $3K$ respectively. If the temperature difference across the wall is $50\ ^oC$,then the temperature difference across the thin layer will be

Five rods of identical dimensions are arranged as shown in the figure. Their thermal conductivities are $k_1, k_2, k_5, k_4$ and $k_3$. When $A$ and $B$ are maintained at different temperatures,no heat flows through the central rod if: