The heat is flowing through two cylindrical rods of 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 rate of flow of heat through them will be

A thin paper cup filled with water does not catch fire when placed over a flame. This is because

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

The ends $\mathrm{Q}$ and $\mathrm{R}$ of two thin wires, $\mathrm{PQ}$ and $RS$, are soldered (joined) togetker. Initially each of the wires has a length of $1 \mathrm{~m}$ at $10^{\circ} \mathrm{C}$. Now the end $\mathrm{P}$ is maintained at $10^{\circ} \mathrm{C}$, while the end $\mathrm{S}$ is heated and maintained at $400^{\circ} \mathrm{C}$. The system is thermally insulated from its surroundings. If the thermal conductivity of wire $\mathrm{PQ}$ is twice that of the wire $RS$ and the coefficient of linear thermal expansion of $P Q$ is $1.2 \times 10^{-5} \mathrm{~K}^{-1}$, the change in length of the wire $\mathrm{PQ}$ is

Two thin blankets keep more hotness than one blanket of thickness equal to these two. The reason is

The thermal conductivity of a material in $CGS$ system is $0.4$ . In steady state, the rate of flow of heat $10 cal/sec-cm2$ , then the thermal gradient will be ....... $^oC/cm$