$A$ cylindrical rod has temperatures $T_1$ and $T_2$ at its ends. The rate of flow of heat is $Q_1 \text{ cal s}^{-1}$. If the length and radius of the rod are doubled while keeping the temperatures constant,then the new rate of flow of heat $Q_2$ will be:

The ratio of thermal conductivity of two rods of different materials is $4:3$. The two rods have same area of cross-section and same thermal resistance. The lengths of rods are in the ratio

$A$ cylindrical rod with one end in a steam chamber and the other end in ice results in melting of $0.1 \ gm$ of ice per second. If the rod is replaced by another with half the length and double the radius of the first,and if the thermal conductivity of the material of the second rod is $\frac{1}{4}$ that of the first,the rate at which ice melts in $gm/sec$ will be:

In the Arctic region,hemispherical houses called Igloos are made of ice. It is possible to maintain a temperature inside an Igloo as high as $20^{\circ} C$ because

If the radius and length of a copper rod are both doubled,the rate of flow of heat along the rod increases ....... times.

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