The rate of heat conduction through a cylindrical rod is $Q_1$. The temperatures at the ends of the rod are $T_1$ and $T_2$. If all the dimensions of the rod are doubled while keeping the temperatures the same,the new rate of heat conduction is $Q_2$. Then:

$A$ 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 ....... $^{\circ}C$.

The rate of heat flow through the cross-section of the rod shown in the figure is ($T_2 > T_1$ and the thermal conductivity of the material of the rod is $K$).

$A$ slab of stone of area $3600 \, cm^2$ and thickness $10 \, cm$ 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 stone in $J \, s^{-1} \, m^{-1} \, K^{-1}$ is (Latent heat of ice $= 3.36 \times 10^5 \, J/kg$)

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 ........... $^{\circ}C$.

The two ends of a metal rod are maintained at temperatures $100 ^\circ C$ and $110 ^\circ C$. The rate of heat flow in the rod is found to be $4.0 \ J/s$. If the ends are maintained at temperatures $200 ^\circ C$ and $210 ^\circ C$,the rate of heat flow will be.... $J/s$