$A$ slab of stone of area $3600 \, cm^2$ and thickness $10 \, cm$ is exposed on the lower surface to steam at $100^{\circ} C$. $A$ block of ice at $0^{\circ} C$ rests on the upper surface of the slab. In one hour, $4.8 \, kg$ of ice is melted. The thermal conductivity of the stone in $J \, s^{-1} \, m^{-1} \, K^{-1}$ is (Latent heat of ice $= 3.36 \times 10^5 \, J/kg$)

Which of the following circular rods (given radius $r$ and length $l$),each made of the same material and whose ends are maintained at the same temperature difference,will conduct the most heat?

$A$ rod of length $L$ with sides fully insulated is made of a material whose thermal conductivity varies with temperature $T$ as $K = \frac{\alpha}{T}$,where $\alpha$ is a constant. The ends of the rod are kept at temperatures $T_1$ and $T_2$. The temperature $T$ at a distance $x$ from the end kept at $T_1$ is:

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity $2K$ while that in the middle has thermal conductivity $K$. The left end of the combination is maintained at temperature $3T$ and the right end at $T$. The rods are thermally insulated from outside. In steady state,the temperature at the left junction is $T_1$ and that at the right junction is $T_2$. The ratio $T_1 / T_2$ is

$A$ cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat $Q$ in time $t$. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod,when placed in thermal contact with the two reservoirs in time $t$?

$A$ 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).