Four rods with different radii $r$ and length $l$ are used to connect two heat reservoirs at different temperatures. Which one will conduct the most heat?

If $4 \, kg$ of ice is inside a closed cubical thermocol box of side length $20 \, cm$ and wall thickness $4 \, cm$, then the mass of the ice remaining after $10 \, hours$ is nearly. (Given: Outside temperature $= 50^{\circ}C$, Thermal conductivity of thermocol $K = 0.01 \, Js^{-1}m^{-1\circ}C^{-1}$, Latent heat of fusion of ice $L = 335 \times 10^3 \, Jkg^{-1}$) (in $ \, kg$)

There is a layer of snow $x \ cm$ thick on water,when the temperature of the air is $-\theta ^\circ C$ (less than the freezing point). If the thickness of the layer increases from $x$ to $y$ in time $t$,then the value of $t$ is given by:

In the figure shown,$AB$ is a rod of length $30 \ cm$,area of cross-section $1 \ cm^2$ and thermal conductivity $336 \ SI$ units. The ends $A$ and $B$ are at constant temperatures $20^{\circ} C$ and $40^{\circ} C$ respectively. $A$ point $C$ of the rod is connected to ice at $0^{\circ} C$ in a thermally insulated box $D$ through a highly conducting wire of negligible heat capacity. The rate at which ice melts in the box is $\left(L_{ice}=80 \ cal \ g^{-1}\right)$.

$A$ 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 same two reservoirs in time $t$?

The temperature drop through each layer of a two-layer furnace wall is shown in the figure. Assume that the external temperatures $T_1$ and $T_3$ are maintained constant and $T_1 > T_3$. If the thicknesses of the layers $x_1$ and $x_2$ are the same,which of the following statements is correct?