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 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,one made of copper and the other made of steel,of the same length and same cross-sectional area,are joined together. The thermal conductivities of copper and steel are $385 \, W \, m^{-1} \, K^{-1}$ and $50 \, W \, m^{-1} \, K^{-1}$ respectively. The free ends of copper and steel are held at $100^{\circ} \, C$ and $0^{\circ} \, C$ respectively. The temperature at the junction is nearly $.......^{\circ} \, C$.

Heat current is maximum in which of the following (rods are of identical dimension)?

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

Two plates of the same area are placed in contact. Their thicknesses as well as their thermal conductivities are in the ratio $2:3$. The outer surface of one plate is maintained at $10^{\circ} C$ and that of the other at $0^{\circ} C$. The temperature at the common surface is (in $^{\circ} C$)