The thermal conductivity of a material in $CGS$ system is $0.4$. In steady state,the rate of flow of heat is $10 \ cal/sec-cm^2$. Then the thermal gradient will be ....... $^oC/cm$.

The temperature drop through each layer of a two-layer furnace wall is shown in the figure. Assume that the external temperatures $T_1$ and $T_3$ are maintained constant and $T_1 > T_3$. If the thicknesses of the layers $x_1$ and $x_2$ are the same,which of the following statements is correct?

The temperature difference across two cylindrical rods $A$ and $B$ of the same material and same mass are $40^{\circ} C$ and $60^{\circ} C$ respectively. In steady state,if the rates of flow of heat through the rods $A$ and $B$ are in the ratio $3: 8$,the ratio of the lengths of the rods $A$ and $B$ is (in $: 3$)

In which case does the thermal conductivity increase from left to right?

$A$ rod of length $10 \, cm$ has a cross-sectional area of $100 \, cm^2$ and a thermal conductivity of $400 \, W/m^\circ C$. If the heat flow through the rod is $4000 \, J/s$,find the temperature difference between the two ends in $^\circ C$.

The thickness of a uniform rectangular metal plate is $5 \ mm$ and the area of each surface is $5 \ cm^2$. In steady state, the temperature difference between the two surfaces of the plate is $14^{\circ} C$. If the heat flowing through the plate in one second from one surface to the other surface is $42 \ J$, then the thermal conductivity of the metal is