Two rods of same length and material transfer a given amount of heat in12 seconds,when they are joined end to end. But when they are joined lengthwise,then they will transfer the heat in same condition in

Solution:
As per the question, if two rods are attached end to end to each other then it takes 12 sec. Now when they are attached parallel then its length halves and area will be doubled. Heat flow is given as: 



$$\begin{gathered} Q =\frac{KA\Delta T}{L} \\ so, T \propto L/A \\ T\text{'} \propto (L/2)/\left(2A\right) \\ T\text{'} \propto (L/4A) \\ T\text{'} /T = (L/4A)/(L/A) = 4 \\ T\text{'} = 1/4T =\frac{1}{4} \times 12 = 3 sec \end{gathered}$$