$A$ slab of stone of area $0.36\, m^2$ and thickness $0.1\, m$ 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 slab is .......... $J/m/s/^{\circ} C$ (Given latent heat of fusion of ice $= 3.36 \times 10^5\, J/kg$)

For a spherical shell with inner and outer radii $r_1$ and $r_2$ respectively,the formula for the heat flow rate is = ......... where $T_1$ and $T_2$ are the temperatures of the inner and outer surfaces of the shell $(T_1 > T_2)$. The thermal conductivity of the material of the shell is $k$.

Two plates of equal area are placed in contact. Their thicknesses are $2$ and $3$ units respectively. The temperature of the outer surface of the first plate is $-25^{\circ}C$ and the temperature of the outer surface of the second plate is $25^{\circ}C$. Find the temperature of the contact surface if: $(a)$ they are made of the same material,$(b)$ their thermal conductivities are in the ratio $2:3$.

Which of the following cylindrical rods will conduct the most heat when their ends are maintained at the same steady temperature difference?

An ice box is used to keep food cool,having a surface area of $1 \, m^2$ and a thickness of $5.0 \, cm$. The thermal conductivity of the ice box material is $K = 0.01 \, J/(m \cdot s \cdot ^\circ C)$. The inside temperature is maintained at $0 \, ^\circ C$ and the outside temperature is $30 \, ^\circ C$. If the latent heat of fusion of ice is $334 \times 10^3 \, J/kg$,calculate the mass of ice that melts in one day.

$A$ metal cooking pot has a base area of $0.2 \,m^2$ and a thickness of $2.0 \,cm$. It boils water at a rate of $3.0 \,kg/min$ when placed on a hot plate. What is the temperature of the part of the hot plate in contact with the pot (in $^{\circ} C$)? [Thermal conductivity of metal is $120 \,J s^{-1} m^{-1} K^{-1}$,latent heat of vaporisation of water is $2 \times 10^6 \,J/kg$]