The heat is flowing through two cylindrical rods of the same material. The diameters of the rods are in the ratio $1:2$ and their lengths are in the ratio $2:1$. If the temperature difference between their ends is the same,the ratio of the rate of flow of heat through them will be:

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 closed containers of same dimensions made of different materials are completely filled with ice. The ice in the first container takes $20 \ min$ and that in the second container takes $10 \ min$,respectively,for complete melting. The ratio of the thermal conductivities of the materials of the two containers is . . . . . . .

$A$ cylindrical rod has temperatures $T_1$ and $T_2$ at its ends. The rate of flow of heat is $Q_1 \ cal/sec$. If all the linear dimensions are doubled while keeping the temperatures constant,then the new rate of flow of heat $Q_2$ will be:

Which of the following factors affect the thermal conductivity of a rod?

Two metal cubes $A$ and $B$ of the same size are arranged as shown in the figure. The extreme ends of the combination are maintained at the indicated temperatures. The arrangement is thermally insulated. The coefficients of thermal conductivity of $A$ and $B$ are $300 \; W/m^{\circ}C$ and $200 \; W/m^{\circ}C$,respectively. After steady state is reached,the temperature of the interface will be ...... $^{\circ}C$.