If two metallic plates of equal thicknesses and thermal conductivities $K_1$ and $K_2$ are put together face to face and a common plate is constructed,then the equivalent thermal conductivity of this plate will be

$A$ wall consists of two layers $A$ and $B$. The two layers have the same thickness but are made of different materials. The thermal conductivity of $A$ is twice that of $B$. Under steady-state conditions,the temperature difference between the two ends is $36 ^\circ C$. The temperature difference across the two surfaces of $A$ is .......... $^\circ C$.

Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20$ minutes and $40$ minutes respectively. The ratio of thermal conductivities of the materials is

$A$ metallic rod of cross-sectional area $9.0 \, cm^2$ and length $0.54 \, m$,with the surface insulated to prevent heat loss,has one end immersed in boiling water and the other in an ice-water mixture. The heat conducted through the rod melts the ice at the rate of $1 \, g$ for every $33 \, s$. The thermal conductivity of the rod is ....... $W m^{-1} K^{-1}$.

In the Arctic region,hemispherical houses called Igloos are made of ice. It is possible to maintain a temperature inside an Igloo as high as $20^{\circ} C$ because

Which of the following cylindrical rods will conduct the most heat when their ends are maintained at the same steady temperature difference?