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

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ kept at temperatures $T_1$ and $T_2$,respectively. The radial rate of flow of heat in a substance between the two concentric spheres is proportional to

Two rods $A$ and $B$ of the same cross-sectional area $A$ and length $l$ are connected in series between a source $(T_1 = 100^{\circ}C)$ and a sink $(T_2 = 0^{\circ}C)$ as shown in the figure. The rods are laterally insulated. If $G_A$ and $G_B$ are the temperature gradients across rod $A$ (thermal conductivity $3K$) and rod $B$ (thermal conductivity $K$),then:

$A$ copper rod of length $10 \ cm$ and cross-sectional area $100 \ cm^2$ is to conduct $4000 \ J/s$ of heat. The thermal conductivity of copper is $400 \ W/m \cdot ^\circ C$. The temperature difference between the two ends of the rod must be maintained at ............. $^\circ C$.

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $T_1=300 \ K$ and $T_2=100 \ K$,as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are $K_1$ and $K_2$ respectively. If the temperature at the junction of the two cylinders in the steady state is $200 \ K$,then $K_1 / K_2 = . . . . . .$

Heat is conducted across a composite block of two slabs of thickness $d$ and $2d$. Their thermal conductivities are $2k$ and $k$ respectively. All the heat entering the face $AB$ leaves from the face $CD$. The temperature in $^oC$ of the junction $EF$ of the two slabs is: