If the thermal conductivity of copper is $9$ times that of steel,what will be the temperature of the junction in $^oC$?

The rate of heat conduction through a cylindrical rod is $Q_1$. The temperatures at the ends of the rod are $T_1$ and $T_2$. If all the dimensions of the rod are doubled while keeping the temperatures the same,the new rate of heat conduction is $Q_2$. Then:

Two concentric spheres of radii $r_1$ and $r_2$ are maintained at temperatures $T_1$ and $T_2$ respectively. The rate of radial heat flow between the two concentric spheres is proportional to:

The temperature difference between the ends of two cylindrical rods $A$ and $B$ of the same material is $2: 3$. In steady state, the ratio of the rates of flow of heat through the rods $A$ and $B$ is $5: 9$. If the radii of the rods $A$ and $B$ are in the ratio $1: 2$, then the ratio of lengths of the rods $A$ and $B$ is

$A$ cylindrical steel rod of length $0.10 \,m$ and thermal conductivity $50 \,Wm^{-1}K^{-1}$ is welded end to end to a copper rod of thermal conductivity $400 \,Wm^{-1}K^{-1}$ and of the same area of cross-section but $0.20 \,m$ long. The free end of the steel rod is maintained at $100^{\circ}C$ and that of the copper rod at $0^{\circ}C$. Assuming that the rods are perfectly insulated from the surroundings,the temperature at the junction of the two rods is ................... $^{\circ}C$.

The ratio of the thermal conductivity of two rods of different materials is $6:5$. The two rods of same area of cross section and same thermal resistance will have the lengths in the ratio: