Two identical square rods of metal are welded end to end as shown in figure $(a)$. Assume that $10 \, cal$ of heat flows through the rods in $2 \, min$. Now the rods are welded as shown in figure $(b)$. The time it would take for $10 \, cal$ to flow through the rods now,is ........ $\min$.

$A$ metallic prong consists of $4$ rods made of the same material,with the same cross-sections and the same lengths as shown below. The three forked ends are kept at $100^{\circ} C$ and the handle end is at $0^{\circ} C$. The temperature of the junction is ............. $^{\circ} C$.

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 ........ $^{\circ}C$.

Three rods of same dimensions are arranged as shown in the figure. They have thermal conductivities ${K_1}, {K_2}$ and ${K_3}$. The points $P$ and $Q$ are maintained at different temperatures. For the heat to flow at the same rate along the path $PRQ$ and the path $PQ$,which of the following options is correct?

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 $^{\circ}C$.

$A$ wall has two layers $A$ and $B,$ each made of different material. Both the layers have the same thickness. The thermal conductivity for $A$ is twice that of $B$ and under steady condition,the temperature difference across the wall is $36\,^{\circ}C.$ The temperature difference across the layer $A$ is....... $^{\circ}C$