$Assertion :$ $A$ brass tumbler feels much colder than a wooden tray on a chilly day.
$Reason :$ The thermal conductivity of brass is more than the thermal conductivity of wood.

$A$ metal rod of length $2\, m$ has cross-sectional areas $2A$ and $A$ as shown in the figure. The two ends are maintained at temperatures $100\,^{\circ}C$ and $70\,^{\circ}C$. The temperature of the junction point $C$ is ........ $^{\circ}C$.

Define thermal conductivity. Also,provide its $SI$ unit and dimensional formula.

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

$A$ cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat $Q$ in time $t$. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod,when placed in thermal contact with the same two reservoirs in time $t$?

$A$ room is maintained at $20^{\circ}C$ by a heater of resistance $20 \ \Omega$ connected to $200 \ V$ mains. The temperature is uniform throughout the room and heat is transmitted through a glass window of area $1 \ m^2$ and thickness $0.2 \ cm$. What will be the temperature outside in $^{\circ}C$? Given that thermal conductivity $K = 0.2 \ J/(s \cdot m \cdot K)$ for glass and $J = 4.2 \ J/cal$.