$A$ metal utensil is generally preferred for cooking because ......

Two plates $A$ and $B$ have thermal conductivities $84 \, W m^{-1} K^{-1}$ and $126 \, W m^{-1} K^{-1}$ respectively. They have the same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of $A$ and $B$ are kept at $100^{\circ} C$ and $0^{\circ} C$ respectively,then the temperature of the surface of contact in steady state is $.......... \, ^{\circ} C$.

$A$ 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:

$A$ slab of stone of area $3600 \, cm^2$ and thickness $10 \, cm$ is exposed on the lower surface to steam at $100^{\circ} C$. $A$ block of ice at $0^{\circ} C$ rests on the upper surface of the slab. In one hour, $4.8 \, kg$ of ice is melted. The thermal conductivity of the stone in $J \, s^{-1} \, m^{-1} \, K^{-1}$ is (Latent heat of ice $= 3.36 \times 10^5 \, J/kg$)

The area of a glass window is $10 \ m^2$ and its thickness is $2 \ mm$. The outside and inside temperatures are $40^{\circ}C$ and $20^{\circ}C$ respectively. The thermal conductivity in $MKS$ units is $0.2$. The heat conducted per second into the room is ......

$A$ solid cylinder of radius $R$ made of a material of thermal conductivity $K_{1}$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of a material of thermal conductivity $K_{2}$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is