What properties should a material used for making a cooking pot possess? ($K =$ thermal conductivity,$S =$ specific heat capacity)

$A$ 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

$A$ rod of length $L$ with sides fully insulated is made of a material whose thermal conductivity varies with temperature $T$ as $K = \frac{\alpha}{T}$,where $\alpha$ is a constant. The ends of the rod are kept at temperatures $T_1$ and $T_2$. The temperature $T$ at a distance $x$ from the end kept at $T_1$ is:

For cooking the food,which of the following type of utensil is most suitable?

Copper and iron rods of identical dimensions are coated with wax. The ratio of thermal conductivity of copper to iron is $10:9$. If one end of each rod is placed in hot water,the wax melts. Find the ratio of the lengths of the rods for which the wax melts at the same rate.

One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two sections of lengths $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two sections is