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

Which of the following factors affect the thermal conductivity of a rod?

The water in a lake starts freezing at a temperature of $0^{\circ}C$. If it takes $7$ hours to form $1 \ cm$ of ice when the atmospheric temperature is $-10^{\circ}C$, how much additional time will it take to increase the thickness of the ice from $1 \ cm$ to $2 \ cm$ (in $hours$)?

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 ........

Three rods of the 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 their junction is

If $K_{1}$ and $K_{2}$ are the thermal conductivities,$L_{1}$ and $L_{2}$ are the lengths,and $A_{1}$ and $A_{2}$ are the cross-sectional areas of steel and copper rods respectively,such that $\frac{K_{2}}{K_{1}}=9$,$\frac{A_{1}}{A_{2}}=2$,and $\frac{L_{1}}{L_{2}}=2$. For the arrangement shown in the figure,the value of the temperature $T$ of the steel-copper junction in the steady state will be ........... $^{\circ}C$.