Two concentric spheres of radii $r_1$ and $r_2$ are maintained at temperatures $T_1$ and $T_2$ respectively. The rate of radial heat flow between the two concentric spheres is proportional to:

Heat is conducted across a composite block of two slabs of thickness $d$ and $2d$. Their thermal conductivities are $2k$ and $k$ respectively. All the heat entering the face $AB$ leaves from the face $CD$. The temperature in $^oC$ of the junction $EF$ of the two slabs is:

Same quantity of ice is filled in each of the two metal containers $P$ and $Q$ having the same size, shape, and wall thickness but made of different materials. The containers are kept in identical surroundings. The ice in $P$ melts completely in time $t_{1}$ whereas in $Q$ it takes a time $t_{2}$. The ratio of thermal conductivities of the materials of $P$ and $Q$ is

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 $2:3$.

The outer faces of a rectangular slab made of equal thickness of iron and brass are maintained at $100^{\circ} C$ and $0^{\circ} C$ respectively. The temperature at the interface is ........... $^{\circ} C$ (Thermal conductivity of iron and brass are $0.2$ and $0.3$ respectively.)

$A$ 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 $= 3.36 \times 10^5\, J/kg$)