$A$ 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?

Two rods $A$ and $B$ of the same cross-sectional area $A$ and length $l$ are connected in series between a source $(T_1 = 100^{\circ}C)$ and a sink $(T_2 = 0^{\circ}C)$ as shown in the figure. The rods are laterally insulated. If the thermal conductivities of rods $A$ and $B$ are $3K$ and $K$ respectively,and $T_A$ and $T_B$ are the temperature drops across rods $A$ and $B$,then:

According to the experiment of Ingen Hausz, the relation between the thermal conductivity $K$ of a metal rod and the length $l$ of the rod up to which the wax melts is:

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 ........ $g$ $(1\;day = 86,400\;s)$.

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: