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 10J 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 :

[C]

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

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

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