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How much mercury must be placed inside a glass flask, having an internal volume 300 cc so that the volume of the remaining space inside the flask remains constant at all temperatures ? $(γ_{Hg} = 1 .8 \times {10^{- 4}}^{0} C^{- 1}, α_{g} = 1 \times {10^{- 5}}^{0} C^{- 1})$

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25 cc

50 cc

100 cc

150 cc

answer is B.

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Detailed Solution

To keep empty space constant, change in volume of container will be equal to the change in volume of the liquid.
$\Rightarrow V_{c} \times γ_{c} = V_{l} \times γ_{l} (γ_{c} = 3 \times 10^{- 5} /^{\circ} C)$

$\Rightarrow V_{l} = \frac{V_{c} \times γ_{c}}{γ_{l}} = \frac{300 \times 3 \times 10^{- 5}}{1.8 \times 10^{- 4}} = 50 cc$

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