Question

A $1L$ glass 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 this flask ? If coefficient of linear expansion of glass is $9\times 10^{-6}/{}^{0}C$ while of volume expansion of mercury is $1.8\times 10^{-4}/{}^{0}C$

• A. $\text{50 cc}$
• B. $\text{100 cc}$
• C. $\text{150 cc}$
• D. $\text{200 cc}$

Answer 1

Answer: (C)

It is given that the volume of air in the flask remains the same. This means that the expansion in the volume of the vessel is exactly equal to the volume expansion of mercury.
i.e., $\Delta {\text{V}}_{\text{G}}=\Delta {\text{V}}_{\text{L}}$
or ${\text{V}}_{\text{G}}{\gamma }_{\text{G}}\Delta \theta ={\text{V}}_{\text{L}}{\gamma }_{\text{L}}\Delta \theta$
$\therefore V_L=\frac{V_G{\gamma }_G}{{\gamma }_L}=\frac{1000\times \left(3\times 9\times 10^{-6}\right)}{1.8\times 10^{-4}}=150cc$