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 $20 \ cm$.

$A$ slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio $1 : 4$. If the free face of brass is at $100^\circ C$ and that of copper at $0^\circ C$,the temperature of the interface is ........ $^\circ C$.

$A$ slab consists of two identical plates of copper and brass. The free face of the brass is at $0^{\circ} C$ and that of copper at $100^{\circ} C$. If the thermal conductivities of brass and copper are in the ratio $1: 4$,then the temperature of the interface is (in $^{\circ} C$)

The area of the glass of a window of a room is $10\;m^2$ and thickness is $2\;mm$. The outer and inner temperatures are $40^{\circ}C$ and $20^{\circ}C$ respectively. The thermal conductivity of glass in the $MKS$ system is $0.2\;W/(m\cdot K)$. The heat flowing into the room per second will be:

$Assertion :$ $A$ 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.

$A$ cylindrical rod has temperatures $T_1$ and $T_2$ at its ends. The rate of flow of heat is $Q_1 \ cal/sec$. If all the linear dimensions are doubled while keeping the temperatures constant,then the new rate of flow of heat $Q_2$ will be: