The lengths and radii of two rods made of the same material are in the ratios $1:2$ and $2:3$ respectively. If the temperature difference between the ends for the two rods is the same,then in the steady state,the amount of heat flowing per second through them will be in the ratio:

In the Ingen-Hauz's experiment,the wax melts up to lengths $10 \ cm$ and $25 \ cm$ on two identical rods of different materials. The ratio of thermal conductivities of the two materials is:

Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20$ minutes and $40$ minutes respectively. The ratio of thermal conductivities of the materials is

$A$ cylindrical rod has temperatures $\theta_1$ and $\theta_2$ at its ends. The rate of heat flow is $Q$. All the linear dimensions of the rod are doubled while keeping the temperatures constant. The new rate of flow of heat is

$A$ 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 two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_1$ and $T_2$ $(T_1 > T_2)$. The rate of heat transfer,$\frac{dQ}{dt}$,through the rod in a steady state is given by: