$A$ slab consists of two parallel layers of copper and brass of equal thickness. The ratio of their thermal conductivities is $1:4$. If the temperature of the free side of the brass is $100^{\circ}C$ and that of the copper is $0^{\circ}C$,find the temperature of the interface in $^{\circ}C$.

Four identical conducting rods are joined as shown in the figure. Points $A$ and $D$ are maintained at temperatures of $200^{\circ}C$ and $20^{\circ}C$ respectively. The temperature of junction $B$ will be ....... $^{\circ}C$.

The ratio of thermal conductivity of two rods $A$ and $B$ with the same area of cross-section is $3: 2$. If the thermal resistance of two rods is the same,then the ratio of length of rod $A$ to length of rod $B$ is

Three identical rods $A, B$ and $C$ are placed end to end. $A$ temperature difference is maintained between the free ends of $A$ and $C$. The thermal conductivity of $B$ is thrice that of $C$ and half of that of $A$. The effective thermal conductivity of the system will be ($K_{A}$ is the thermal conductivity of rod $A$).

Consider the situation as shown in the figure. Find the amount of heat flowing per second through a cross-section of the bent part,if the total heat taken out per second from the end at $200^{\circ} C$ is $150 \ J/s$.

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