Two different rods $A$ and $B$ are kept as shown in figure. The variation of temperature of different cross sections is plotted in a graph shown in figure. The ratio of thermal conductivities of $A$ and $B$ is

Two rectangular blocks, having identical dimensions, can be arranged either in configuration $I$ or in configuration $II$ as shown in the figure. One of the blocks has thermal conductivity $k$ and the other $2k$. The temperature difference between the ends along the $x-$ axis is the same in both the configurations. It takes $9s$ to transport a certain amount of heat from the hot end to the cold end in the configuration $I$. The time to transport the same amount of heat in the configuration $II$ is .......... $\sec$

A rod of length $L$ with sides fully insulated is of a material whose thermal conductivity varies with $\alpha$ temperature as $ K= \frac{\alpha }{T}$, where $\alpha$ is a constant. The ends of the rod are kept at temperature $T_1$ and $T_2$. The temperature $T$ at $x,$ where $x$ is the distance from the end whose temperature is $T_1$ is 

The ratio of the diameters of two metallic rods of the same material is $2 : 1$ and their lengths are in the ratio $1 : 4$ . If the temperature difference between their ends are equal, the rate of flow of heat in them will be in the ratio

Bottom of a lake is at $0^{\circ} C$ and atmospheric temperature is $-20^{\circ} C$. If $1 cm$ ice is formed on the surface in $24 \,h$, then time taken to form next $1 \,cm$ of ice is ......... $h$

The thickness of a metallic plate is $0.4 cm$ . The temperature between its two surfaces is ${20^o}C$. The quantity of heat flowing per second is $50$ calories from $5c{m^2}$ area. In $CGS$ system, the coefficient of thermal conductivity will be