Question

A one-litre flask contains 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 the flask? Given the coefficient of linear expansion of glass is $9\times {10}^{-6}{}^{\circ }{C}^{-1}$ and the coefficient of volume expansion of mercury is $1.8\times {10}^{-4}{}^{\circ }{C}^{-1}$

• A. $50c{m}^3$
• B. $100c{m}^3$
• C. $150c{m}^3$
• D. $200c{m}^3$

Answer 1

The correct option is C

$150c{m}^3$

Let x be the volume of mercury in the flask. Since the volume of air in the flask remains constant, the volume expansion of the flask must be exactly equal to the expansion of mercury in the flask.
$\therefore V{\gamma }_g\Delta t=x{\gamma }_m\Delta t\Rightarrow x=\frac{V{\gamma }_g}{{\gamma }_m}=\frac{V\times 3{\alpha }_g}{{\gamma }_m}=\frac{1000\times 3\times 9\times {10}^{-6}}{18\times {10}^{-5}}=150c{m}^3$
Hence, the correct choice is (c).