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

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:

If the thermal conductivity of copper is $9$ times that of steel,what will be the temperature of the junction in $^oC$?

$A$ rod of length $10 \, cm$ has a cross-sectional area of $100 \, cm^2$ and a thermal conductivity of $400 \, W/m^\circ C$. If the heat flow through the rod is $4000 \, J/s$,find the temperature difference between the two ends in $^\circ C$.

Two different rods $A$ and $B$ are kept as shown in the figure. The ratio of thermal conductivities of $A$ and $B$ 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 two reservoirs in time $t$?