Question

Two identical conducting rods are first connected independently to two vessels, one containing water at $100^{\circ }C$ and the other containing ice at $0^{\circ }C$. In the second case, the rods are joined end to end and connected to the same vessels. Let $q_1$ and $q_{2}g/s$ be the rate of melting of ice in two cases, respectively. The ratio of $q_1/q_2$ is

• A. $\frac{1}{2}$
• B. $\frac{2}{1}$
• C. $\frac{4}{1}$
• D. $\frac{1}{4}$

Answer 1

Answer: (C)

Initially the rods are placed in vessels as shown below.


$\frac{Q}{t}=\frac{\left({\theta }_1-{\theta }_2\right)}{R}$
$\Rightarrow {\left(\frac{Q}{t}\right)}_1=\frac{mL}{t}$
$=q_{1}L=\frac{(100-0)}{\frac{R}{2}}$... (i)
Finally when rods are joined end to end as shown,

$\Rightarrow {\left(\frac{Q}{t}\right)}_2=\frac{mL}{t}$
$=q_{2}L=\frac{(100-0)}{2R}$ ....(ii)
From equations (i) and (ii), $\frac{q_1}{q_2}=\frac{4}{1}$