Question

A flask of volume $V$ contains some mercury. It is found that at different temperatures, the volume of air inside the flask remains the same. If ${\gamma }_g$ and ${\gamma }_m$ are the coefficients of cubical expansion of glass and mercury respectively, the volume of mercury in the flask is

• A. $\frac{{\gamma }_{g}V}{{\gamma }_m}$
• B. $\frac{{\gamma }_{m}V}{{\gamma }_g}$
• C. $(1-\frac{{\gamma }_g}{{\gamma }_m})V$
• D. $(1-\frac{{\gamma }_m}{{\gamma }_g})V$

Answer 1

The correct option is A

$\frac{{\gamma }_{g}V}{{\gamma }_m}$

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.
$\therefore V{\gamma }_g\Delta t=x{\gamma }_m\Delta t\Rightarrow x=\frac{{\gamma }_{g}V}{{\gamma }_m}$
Hence, the correct choice is (a).