First slide

Conduction

Question

Two identical conducting rods are first connected independently to two vessels, one containing water at 100⁰C and the other containing ice at 0⁰C. In the second case, the rods are joined end-to-end and connected to the same vessels. Let q₁ and q₂ gs^-1 be the rate of melting of ice in two cases, respectively. The ratio of $\frac{q_{1}}{q_{2}}$ is

Moderate

A

$\frac{1}{2}$
B

$\frac{2}{1}$
C

$\frac{4}{1}$
D

$\frac{1}{4}$

Solution

Initially the rods are in parallel, $\frac{Q}{t} = \frac{(θ_{1} - θ_{2})}{R}$
$\Rightarrow {(\frac{Q}{t})}_{1} = \frac{m L}{t} = q_{1} L = \frac{(100 - 0)}{R / 2}$ …(i)
Finally when rods are in series,
$\Rightarrow {(\frac{Q}{t})}_{2} = \frac{m L}{t} = q_{2} L = \frac{(100 - 0)}{2 R}$ …(ii)
From Eqs. (i) and (ii), we get
$\frac{q_{1}}{q_{2}} = \frac{4}{1}$

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