For the figure shown, when arc $ACD$ and $ADB$ are made of same material, the heat carried between $A$ and $B$ is $H$ . If $ADB$ is replaced with another material, the heat carried becomes $2H$ . If the temperatures at $A$ and $B$ are fixed at $T_1$ and $T_2$ , what is the ratio of the new conductivity to the old one of $ADB$

$A$ 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 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

Ice formed over lakes has

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 $30$ minutes. The ratio of their thermal conductivities will be

The temperature of hot and cold end of a $20cm$ long rod in thermal steady state are at ${100^o}C$ and ${20^o}C$ respectively. Temperature at the centre of the rod is…… $^oC$