question_answer

Two identical rectangular rods of metal are welded end to end in series between temperature \[0{}^\circ C\] and \[100{}^\circ C\] and 10 J of heat is conducted (in steady state process) through the rod in 2.00 min. If 5 such rods are taken and joined as shown in figure maintaining the same temperature difference between A and B, then the. time in which 20 J heat will flow through the rods is:

A) 30 sec.

B) 2 min.

C) 1 min.

D) 20 sec.

Correct Answer: C

Solution :

\[\frac{dQ}{dt}=\frac{KA\,\Delta \,T}{2\ell }=\frac{\Delta \,T}{\frac{2\ell }{KA}}=\frac{10}{120}J/sec.\]

New rate \[\frac{dQ}{dt}=\frac{\Delta \,T}{\frac{\ell }{2\,KA}}=\frac{40}{120}J/sec.\,\,;\]

So time taken is \[t=\frac{20}{40}\times 120\,\sec .=60sec.\]