Question

A one litre glass flask contain some mercury. It is found that at different temperatures the volume of air inside the flask remains the same. What is the volume of mercury in this flask if coefficient of linear expansion of glass is $9\times {10}^{-6}{/}^{o}C$ while of volume expansion of mercury is $1.8\times {10}^{-4}{/}^{o}C$.

• A. $50cc$
• B. $100cc$
• C. $150cc$
• D. $200cc$

Answer 1

Answer: (C)

$150cc$

Solution:- (C) $150cc$

Let $V_G$ and $V_L$ be the volume of glass flask and liquid mercury respectively.

Given that the volume of air in the flask remains the same. This means that the expansion in volume of the vessel is exactly equal to the volume expansion of the mercury.

$\therefore \Delta V_G=\Delta V_L$

As we know that,

$\Delta V=V\gamma \Delta \theta$

whereas,

$\gamma$ is the coefficient of linear expansion.

$\Delta \theta =$ Change in temperature

$\therefore V_G{\gamma }_G\Delta \theta =V_L{\gamma }_L\Delta \theta$

$\Rightarrow V_L=\frac{V_G{\gamma }_G}{{\gamma }_L}$

$\Rightarrow V_L=\frac{1000\times (3\times 9\times {10}^{-6})}{1.8\times {10}^{-4}}=150cc$

Hence the volume of mercury in the flask is $150cc$.