Two identical metal rods are welded end-to-end as shown in figure $(1)$. It takes $4 \ min$ for $20 \ cal$ of heat to flow through them. If these rods are now welded side-by-side as shown in figure $(2)$,the time taken for the same amount of heat to flow through them is .......... $\min$.

Four rods of identical cross-sectional area and made from the same metal form the sides of a square. The temperatures of two diagonally opposite points are $\theta$ and $\sqrt{2}\theta$ respectively in the steady state. Assuming that only heat conduction takes place,what will be the temperature difference between the other two points?

Why do people prefer to give a layer of sand or foam insulation on ceilings made of concrete?

Four identical rods of the same material are joined end to end to form a square. If the temperature difference between the ends of a diagonal is $100^{\circ}C$,then the temperature difference between the ends of the other diagonal will be ........ $^{\circ}C$.

Two plates of equal area are placed in contact with each other. Their thicknesses are $2.0 \, cm$ and $5.0 \, cm$. The temperature of the outer surface of the first plate is $-20^{\circ}C$ and the temperature of the outer surface of the second plate is $20^{\circ}C$. If the plates are made of the same material,find the temperature of the contact surface in $^{\circ}C$.

For the shown figure,calculate the equivalent thermal resistance if the bricks are made of the same material of thermal conductivity $K$.