$A$ large cylindrical rod of length $L$ is made by joining two identical rods of copper and steel of length $(\frac{L}{2})$ each. The rods are completely insulated from the surroundings. If the free end of the copper rod is maintained at $100\,^oC$ and that of the steel rod at $0\,^oC$,then the temperature of the junction is........$^oC$ (Thermal conductivity of copper is $9$ times that of steel).

The thermal conductivity of a wire is $1.7 \ W \ m^{-1} \ K^{-1}$ and that of cement is $2.9 \ W \ m^{-1} \ K^{-1}$. The thickness of the cement insulation is $..... \ cm$. Here,the thickness of the wire is $20 \ cm$.

Two walls of thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$ are in contact. In the steady state,if the temperatures at the outer surfaces are $T_1$ and $T_2$,the temperature at the common wall is

What properties should a material used for making a cooking pot possess? ($K =$ thermal conductivity,$S =$ specific heat capacity)

Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20$ minutes and $40$ minutes respectively. The ratio of thermal conductivities of the materials is

Two thin metallic spherical shells of radii $20 \text{ cm}$ and $30 \text{ cm}$,respectively,are placed with their centers coinciding. $A$ material of thermal conductivity $\alpha$ is filled in the space between the shells. The inner shell is maintained at $300 \text{ K}$ and the outer shell at $310 \text{ K}$. If the rate at which heat flows radially through the material is $40 \text{ W}$,find the value of $\alpha$ (in units of $\text{J s}^{-1} \text{ m}^{-1} \text{ K}^{-1}$).