$A$ wall consists of two layers $A$ and $B$. The two layers have the same thickness but are made of different materials. The thermal conductivity of $A$ is twice that of $B$. Under steady-state conditions,the temperature difference between the two ends is $36 ^\circ C$. The temperature difference across the two surfaces of $A$ is .......... $^\circ C$.

$A$ $5 \ cm$ thick ice block is present on the surface of water in a lake. The temperature of the air is $-10^{\circ}C$. How much time will it take to double the thickness of the block? (Given: $L = 80 \ cal/g$,$K_{ice} = 0.004 \ cal/s \cdot cm \cdot ^{\circ}C$,$\rho_{ice} = 0.92 \ g/cm^3$)

Two layers of a wall,$A$ and $B$,are made of different materials. Both layers have the same thickness. For layer $A$,the thermal conductivity is $K_A = 3 K_B$. The total temperature difference across the wall is $20^{\circ}C$. Find the temperature difference across layer $A$ in $^{\circ}C$.

Two thin metallic spherical shells of radii $r_{1}$ and $r_{2}$ $(r_{1} < r_{2})$ are placed with their centres coinciding. $A$ material of thermal conductivity $K$ is filled in the space between the shells. The inner shell is maintained at temperature $\theta_{1}$ and the outer shell at temperature $\theta_{2}$ $(\theta_{1} < \theta_{2})$. The rate at which heat flows radially through the material is:

Three rods each of length $l$ and cross-sectional area $A$ are joined in series between two heat reservoirs as shown in the figure. Their thermal conductivities are $2K$,$K$,and $\frac{K}{2}$,respectively. Assuming that the conductors are insulated from the surroundings,the temperatures $T_1$ and $T_2$ of the junctions in the steady-state condition are,respectively:

$A$ brass rod of length $2 \ m$ and radius $1 \ cm$ has one end maintained at $250 \ ^oC$. When steady state is reached, the rate of heat flow through any cross-section is $0.5 \ cal \ s^{-1}$. Find the temperature of the other end in $^oC$. (Thermal conductivity of brass $K = 0.26 \text{ cal s}^{-1} \text{ cm}^{-1} \text{ } ^\circ\text{C}^{-1}$)