Two containers have the same shape and wall thickness but are made of different materials. They are filled with the same amount of ice at $0^{\circ}C$. If the ice melts completely in $10$ minutes and $25$ minutes respectively,what is the ratio of the thermal conductivities of the materials of the containers?

The two ends of a metal rod are maintained at temperatures $100 ^\circ C$ and $110 ^\circ C$. The rate of heat flow in the rod is found to be $4.0 \ J/s$. If the ends are maintained at temperatures $200 ^\circ C$ and $210 ^\circ C$,the rate of heat flow will be.... $J/s$

The heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio $1:2$ and their lengths are in the ratio $2:1$. If the temperature difference between their ends is the same,the ratio of the rate of flow of heat through them will be:

Two materials having coefficients of thermal conductivity $3K$ and $K$ and thickness $d$ and $3d$,respectively,are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are $\theta_2$ and $\theta_1$ respectively $(\theta_2 > \theta_1)$. The temperature at the interface is

$A$ 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 $80 \text{ cal g}^{-1}$.)

In an $Ingen-Hauz$ experiment,the wax melts on two rods up to lengths of $10 \ cm$ and $25 \ cm$ respectively. If the two rods are made of different materials,what is the ratio of their thermal conductivities?