$A$ slab consists of two identical plates of copper and brass. The free face of the brass is at $0^{\circ} C$ and that of copper at $100^{\circ} C$. If the thermal conductivities of brass and copper are in the ratio $1: 4$,then the temperature of the interface is (in $^{\circ} C$)

If $K_{1}$ and $K_{2}$ are the thermal conductivities,$L_{1}$ and $L_{2}$ are the lengths,and $A_{1}$ and $A_{2}$ are the cross-sectional areas of steel and copper rods respectively,such that $\frac{K_{2}}{K_{1}}=9$,$\frac{A_{1}}{A_{2}}=2$,and $\frac{L_{1}}{L_{2}}=2$. For the arrangement shown in the figure,the value of the temperature $T$ of the steel-copper junction in the steady state will be ........... $^{\circ}C$.

Two different rods $A$ and $B$ are kept in series as shown in the figure. The variation of temperature across different cross-sections is plotted in the graph. The ratio of thermal conductivities of $A$ and $B$ is

Four identical conducting rods are joined to form a square $ABCD$. The temperatures of junctions $A, B,$ and $C$ are maintained at $100^{\circ}C, 40^{\circ}C,$ and $0^{\circ}C$ respectively. Choose the $\text{INCORRECT}$ statement for this arrangement in a steady state. (The value of $\frac{KA}{L} = 1 \text{ J}/(s \cdot ^{\circ}C)$).

$A$ wall has two layers $A$ and $B$ each made of different materials,both layers have the same thickness. The thermal conductivity of material $A$ is twice that of $B$. Under thermal equilibrium,the temperature difference across wall $B$ is $36^{\circ}C$. The temperature difference across wall $A$ is ....... $^{\circ}C$.

If the ratio of the coefficient of thermal conductivity of silver and copper is $10 : 9$,then the ratio of the lengths up to which wax will melt in the Ingen Hausz experiment will be: