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 ....... $^oC/cm$.

Two different rods $A$ and $B$ are kept as shown in the figure. The ratio of thermal conductivities of $A$ and $B$ is

$A$ slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio $1 : 4$. If the free face of brass is at $100^\circ C$ and that of copper at $0^\circ C$,the temperature of the interface is ........ $^\circ C$.

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 $hours$)?

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 $: 3$)

Two rods are connected as shown. The rods are of the same length and same cross-sectional area. In the steady state,the temperature $(\theta)$ of the interface will be........ $^oC$