Transmission Of Heat Question 108
Question: 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]
Options:
A) $ \frac{1}{2} $
B) $ \frac{2}{1} $
C) $ \frac{4}{1} $
D) $ \frac{1}{4} $
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Answer:
Correct Answer: C
Solution:
Initially the rods are placed in vessels as shown below $ \frac{Q}{t}=\frac{({\theta _{1}}-{\theta _{2}})}{R} $
Therefore $ {{( \frac{Q}{t} )} _{1}}=\frac{mL}{t}=q _{1}L=\frac{(100-0)}{\frac{R}{2}} $ … (i) Finally when rods are joined end to end as shown
Therefore $ {{( \frac{Q}{t} )} _{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} $
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