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 the thermal conductivities of rods $A$ and $B$ are $3K$ and $K$ respectively,and $T_A$ and $T_B$ are the temperature drops across rods $A$ and $B$,then:

$A$ metal cooking pot has a base area of $0.2 \,m^2$ and a thickness of $2.0 \,cm$. It boils water at a rate of $3.0 \,kg/min$ when placed on a hot plate. What is the temperature of the part of the hot plate in contact with the pot (in $^{\circ} C$)? [Thermal conductivity of metal is $120 \,J s^{-1} m^{-1} K^{-1}$, latent heat of vaporisation of water is $2 \times 10^6 \,J/kg$]

The thermal conductivity of a wire is $1.7 \ W \ m^{-1} \ K^{-1}$ and that of cement is $2.9 \ W \ m^{-1} \ K^{-1}$. The thickness of the cement insulation is $..... \ cm$. Here,the thickness of the wire is $20 \ cm$.

In steady state heat conduction,the equations that determine the heat current $j(r)$ [heat flowing per unit time per unit area] and temperature $T(r)$ in space are exactly the same as those governing the electric field $E(r)$ and electrostatic potential $V(r)$ with the equivalence given in the table below.

Heat flow	Electrostatics
$T(r)$	$V(r)$
$j(r)$	$E(r)$

We exploit this equivalence to predict the rate $\dot{Q}$ of total heat flowing by conduction from the surfaces of spheres of varying radii,all maintained at the same temperature. If $\dot{Q} \propto R^{n}$,where $R$ is the radius,then the value of $n$ is

The unit of thermal conductivity is

$A$ heat flux of $4000 \, J/s$ passes through a rod of length $10 \, cm$ and cross-sectional area $100 \, cm^2$. The thermal conductivity of copper is $400 \, W/m^{\circ}C$. The ends of the rod must be maintained at a temperature difference of ....... $^{\circ}C$.