Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in 20 minutes and 40 minutes respectively. The ratio of thermal conductivities of the materials is

5 : 6

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6 : 5

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3 : 1

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2 : 1

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Solution

The correct option is B 2 : 1
$\frac{Q}{t} = \frac{K A (θ_{1} - θ_{2})}{l} \Rightarrow \frac{m L}{t} = \frac{K A (θ_{1} - θ_{2})}{l}$
$\Rightarrow K \propto \frac{1}{t}$ $(∵ r e m a i n i n g q u a n t i t i e s a r e s a m e)$
$\Rightarrow \frac{K_{1}}{K_{2}} = \frac{t_{2}}{t_{1}} = \frac{40}{20} = \frac{2}{1} .$

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