question_answer

Five identical rods are connected between two large reservoirs of temperatures \[100{}^\circ C\] and \[0{}^\circ C\]. Each rod has thermal conductivity k, length l, and area A.

There is no heat transfer through sides of rods.

Heat flow rate from reservoir A to B is

A) \[\frac{100kA}{l}\]                    

B)  \[\frac{100kA}{7l}\]

C) \[\frac{100kA}{3l}\]                  

D) \[\frac{100kA}{13l}\]

Correct Answer: A

Solution :

Rods are connected as,

Following electrical analogy no heat current flows through rod 2.

So, equivalent thermal resistance of network is

\[{{\operatorname{R}}_{eq}}=\frac{2R\times 2R}{2R+2R}=R=\frac{l}{kA}\]

So, heat flow rate through network is

\[H=\frac{\Delta T}{{{\operatorname{R}}_{eq}}}=\frac{100kA}{l}\]