The lengths and radii of two rods made of the same material are in the ratios $1:2$ and $2:3$ respectively. If the temperature difference between the ends for the two rods is the same,then in the steady state,the amount of heat flowing per second through them will be in the ratio:

Rate of flow of heat through a cylindrical rod is $H_1$. The temperatures at the ends of the rod are $T_1$ and $T_2$. If all the dimensions of the rod become double and the temperature difference remains the same,the rate of flow of heat becomes $H_2$. Then:

Three rods of the same dimensions have thermal conductivities $3K, 2K$,and $K$. They are arranged as shown in the figure. The temperature of the junction in the steady state is:

These days,people use steel utensils with copper bottoms. This is considered good for uniform heating of food. Explain this effect using the fact that copper is a better conductor of heat.

$A$ 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 length of a metal rod is $20 \ cm$ and its area of cross-section is $4 \ cm^2$. If one end of the rod is kept at a temperature of $100^{\circ} C$ and the other end is kept in ice at $0^{\circ} C$,then the mass of the ice melted in $7 \ minutes$ is (Thermal conductivity of the metal $= 90 \ W \ m^{-1} \ K^{-1}$ and latent heat of fusion of ice $= 336 \times 10^3 \ J \ kg^{-1}$) (in $g$)