Which of the following cylindrical rods will conduct the most heat when their ends are maintained at the same steady temperature difference?

Two metal rods $1$ and $2$ have the same length and the same temperature difference at their ends. Their thermal conductivities are $K_1$ and $K_2$ and their cross-sectional areas are $A_1$ and $A_2$ respectively. The condition for the same rate of heat flow in them is ........

Two plates of equal area are placed in contact. Their thicknesses are $2$ and $3$ units respectively. The temperature of the outer surface of the first plate is $-25^{\circ}C$ and the temperature of the outer surface of the second plate is $25^{\circ}C$. Find the temperature of the contact surface if: $(a)$ they are made of the same material,$(b)$ their thermal conductivities are in the ratio $2:3$.

$A$ 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 ................... $^{\circ}C$.

According to the experiment of Ingen Hausz, the relation between the thermal conductivity $K$ of a metal rod and the length $l$ of the rod up to which the wax melts 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