Which of the following material properties is most suitable for a cooking utensil?

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 $g$)

$A$ copper pipe of length $10 \,m$ carries steam at temperature $110^{\circ} C$. The outer surface of the pipe is maintained at a temperature $10^{\circ} C$. The inner and outer radii of the pipe are $2 \,cm$ and $4 \,cm$,respectively. The thermal conductivity of copper is $0.38 \,kW / m /^{\circ} C$. In the steady state,the rate at which heat flows radially outward through the pipe is closest to ............. $\,kW$.

An ice box used for keeping eatables cold has a total wall area of $1\;m^2$ and a wall thickness of $5.0\;cm$. The thermal conductivity of the ice box material is $K = 0.01\;J/(m\cdot s\cdot ^\circ C)$. It is filled with ice at $0^\circ C$ along with eatables on a day when the temperature is $30^\circ C$. The latent heat of fusion of ice is $334 \times 10^3\;J/kg$. The amount of ice melted in one day is ........ $g$ $(1\;day = 86,400\;s)$.

The thermal conductivity of a rod is $2$. What is its thermal resistivity?

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $T_1 = 300 \ K$ and $T_2 = 100 \ K$,as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are $K_1$ and $K_2$ respectively. If the temperature at the junction of the two cylinders in the steady state is $200 \ K$,then $K_1 / K_2 = \dots$