Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of each plate. If the coefficients of thermal conductivity of each plate are $2$ and $3$ respectively,then the thermal conductivity of the composite plate will be:

Two rods whose lengths are $l_1$ and $l_2$ with thermal conductivity coefficients $k_1$ and $k_2$ are placed end to end. The thermal conductivity coefficient of a uniform rod of length $l_1+l_2$ whose thermal resistance is the same as that of the system of these two rods is

Find the effective thermal resistance between $A$ and $B$ of a cube made up of $12$ rods of the same dimensions,with the given thermal conductivities as shown in the figure. [ $l =$ length of rod,$a =$ cross-sectional area of rod ]

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 $150 \ J/s$.

$A$,$B$ and $C$ are three identical conductors but made from different materials. They are kept in contact as shown. Their thermal conductivities are $K$,$2K$ and $K/2$. The free end of $A$ is at $100^{\circ} C$ and the free end of $C$ is at $0^{\circ} C$. During steady state,the temperature of the junction of $A$ and $B$ is nearly (in $^{\circ} C$)

Four rods of the same material and having the same cross-section and length have been joined as shown in the figure. The temperature of the junction of the four rods will be ............... $^{\circ}C$.