$A$ wall has two layers $A$ and $B,$ each made of different material. Both the layers have the same thickness. The thermal conductivity for $A$ is twice that of $B$ and under steady condition,the temperature difference across the wall is $36\,^{\circ}C.$ The temperature difference across the layer $A$ is....... $^{\circ}C$

Three rods $AB, BC$ and $AC$ having thermal resistances of $10 \text{ units}, 10 \text{ units}$ and $20 \text{ units}$ respectively,are connected as shown in the figure. Ends $A$ and $C$ are maintained at constant temperatures of $100^{\circ}C$ and $0^{\circ}C$ respectively. The rate at which the heat is crossing junction $B$ is . . . . . . $units$.

In a composite rod,when two rods of different lengths and of the same area are joined end to end,then if $K$ is the effective coefficient of thermal conductivity,$\frac{{\ell _1} + {\ell _2}}{K}$ is equal to

$A$ large box is connected to an ice cube at $100^{\circ}C$ by two identical metal rods as shown in the figure. The ice melts at a rate of $Q_1 \, g/s$. When the rods are connected in series between the box and the ice cube,the new melting rate is $Q_2 \, g/s$. Then $Q_2/Q_1$ is:

$A$ cylinder of radius $R$ made of a material of thermal conductivity $k_1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of a material of thermal conductivity $k_2$. The two ends of the combined system are maintained at different temperatures. There is no loss of heat from the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in the figure. Temperatures of end points $A$ and $F$ are maintained at $100^{\circ}C$ and $40^{\circ}C$ respectively. Given the thermal conductivity of rod $x$ is three times that of rod $y$,the temperatures at junction points $B$ and $E$ are (close to):