question_answer

Two identical conducting rods are first connected independently to two vessels, one containing water at 100o C and the other containing ice at 0oC. In the second case, the rods are joined end to end and connected to the same vessels. Let q1 and q2  g / s be the rate of melting of ice in two cases respectively. The ratio of \[{{q}_{1}}/{{q}_{2}}\] is  [IIT-JEE (Screening) 2004]

A)            \[\frac{1}{2}\]                      

B)            \[\frac{2}{1}\]

C)            \[\frac{4}{1}\]                      

D)            \[\frac{1}{4}\]

Correct Answer: C

Solution :

                   Initially the rods are placed in vessels as shown below \[\frac{Q}{t}=\frac{({{\theta }_{1}}-{{\theta }_{2}})}{R}\]Þ\[{{\left( \frac{Q}{t} \right)}_{1}}=\frac{mL}{t}={{q}_{1}}L=\frac{(100-0)}{\frac{R}{2}}\]   ... (i) Finally when rods are joined end to end as shown Þ \[{{\left( \frac{Q}{t} \right)}_{2}}=\frac{mL}{t}={{q}_{2}}L=\frac{(100-0)}{2R}\]                   ... (ii) From equation (i) and (ii),  \[\frac{{{q}_{1}}}{{{q}_{2}}}=\frac{4}{1}\]