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

Two metal rods $P$ and $Q$ have the same length and the same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$,and their cross-sectional areas are $A_1$ and $A_2$ respectively. If the rate of flow of heat through rod $Q$ is three times that in rod $P$,then:

Which of the following cylindrical rods will conduct the most heat when their ends are maintained at the same steady temperature difference?

$A$ metal rod of length $10 \text{ cm}$ and area of cross-section $2.8 \times 10^{-4} \text{ m}^2$ is covered with a non-conducting substance. One end of it is maintained at $80^{\circ} \text{C}$,while the other end is put in ice at $0^{\circ} \text{C}$. It is found that $20 \text{ g}$ of ice melts in $5 \text{ min}$. The thermal conductivity of the metal in $\text{J s}^{-1} \text{ m}^{-1} \text{ K}^{-1}$ is (Latent heat of ice is $80 \text{ cal g}^{-1}$.)

$A$ 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 coefficients of thermal conductivity of copper,mercury,and glass are respectively $K_c, K_m$,and $K_g$ such that $K_c > K_m > K_g$. If the same quantity of heat is to flow per second per unit area of each and corresponding temperature gradients are $X_c, X_m$,and $X_g$,then: