question_answer

Two rods of same length and material transfer a given amount of heat in 12 seconds, when they are joined end to end. But when they are joined lengthwise, then they will transfer same heat in same conditions in [BHU 1998; UPSEAT 2002]

A)            24 s                                          

B)            3 s

C)            1.5 s                                         

D)            48s

Correct Answer: D

Solution :

                   Let the heat transferred be Q.  When rods are joined end to end. Heat transferred by each rod\[=Q=\frac{KA\Delta \theta }{l}\times 12\]                                ?..(i) When rods are joined lengthwise, \[Q=\frac{KA\Delta \theta }{2l}t\]      ?..(ii) From equation (i) and (ii) we get \[t=48\ s\]