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.)

$A$ cylindrical rod has temperatures $T_1$ and $T_2$ at its ends. The rate of flow of heat is $Q_1 \text{ cal s}^{-1}$. If the length and radius of the rod are doubled while keeping the temperatures constant,then the new rate of flow of heat $Q_2$ will be:

Three metal rods made of copper, brass, and steel, each with a cross-sectional area of $4 \,cm^2$, are joined as shown in the figure. Their lengths are $46 \,cm, 13 \,cm$, and $12 \,cm$ respectively. Their coefficients of thermal conductivity are $0.92, 0.26$, and $0.12$ respectively, all in $CGS$ units. The rods are thermally insulated from the surroundings except at the ends. The rate of flow of heat through the copper rod, in $cal \,s^{-1}$, is:

Three rods of same dimensions have thermal conductivities $3K, 2K$ and $K$. They are arranged as shown with their ends at $100^{\circ}C, 50^{\circ}C$ and $0^{\circ}C$. The temperature of the junction is

Ice formed over lakes has

One end of a metal rod of length $1.0 \ m$ and area of cross-section $100 \ cm^2$ is maintained at $100^{\circ}C$. If the other end of the rod is maintained at $0^{\circ}C$,the quantity of heat transmitted through the rod per minute is (Coefficient of thermal conductivity of the material of the rod = $100 \ W/m-K$).