Two rods one made of copper and other made of steel of the same length and same cross sectional area are joined together. The thermal conductivity of copper and steel are $385\,J\,s ^{-1}\,K ^{-1}\,m ^{-1}$ and $50\,J\,s ^{-1}\,K ^{-1}\,m ^{-1}$ respectively. The free ends of copper and steel are held at $100^{\circ}\,C$ and $0^{\circ}\,C$ respectively. The temperature at the junction is, nearly $.......^{\circ}\,C$

The outer faces of a rectangular slab made of equal thickness of iron and brass are maintained at $100^{\circ} C$ and $0^{\circ} C$ respectively. The temperature at the interface is ........... $^{\circ} C$ (Thermal conductivity of iron and brass are $0.2$ and $0.3$ respectively.)

$ABCDE$ is a regular pentagon of uniform wire. The rate of heat entering at $A$ and leaving at $C$ is equal. $T_B$ and $T_D$ are temperature of $B$ and $D$ . Find the temperature $T_C$

Twelve conducting rods form the riders of a uniform cube of side $'l'.$ If in steady state, $B$ and $H$ ends of the rod are at $100^o C$ and $0^o C$. Find the temperature of the junction $'A'$  ....... $^oC$ 

$A$ cylinder of radius $R$ made of a material of thermal conductivity ${K_1}$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of material of thermal conductivity ${K_2}$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

The dimensional formula for thermal resistance is