Question

A two litre glass flask contains some mercury. It is found that at all temperatures the volume of the air inside the flask remains the same. The volume of the mercury inside the flask is ( $\alpha$ for glass $=9\times {{10}^{-6}}/C,\gamma$ for mercury $=\text{ }1.8\times {{10}^{-4}}/{}^\circ C$ )

• A. 1500 cc
• B. 150 cc
• C. 3000 cc
• D. 300 cc

Answer 1

Answer: (D)

300 cc

Answer 2

It is 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 mercury, ie, $\Delta {{V}_{v}}=\Delta {{V}_{m}}$ or ${{V}_{v}}{{\gamma }_{v}}\Delta T={{V}_{m}}{{\gamma }_{m}}\Delta T$ $\therefore$ ${{V}_{m}}=\frac{{{V}_{v}}{{\gamma }_{v}}}{{{\gamma }_{m}}}=\frac{{{V}_{v}}\times 3\alpha }{{{\gamma }_{m}}}$ $(\because \,{{\gamma }_{v}}=3\alpha )$ $\Rightarrow$ ${{V}_{m}}=\frac{2000\times 3\times 9\times {{10}^{-6}}}{1.8\times {{10}^{-4}}}$ $=300\,cc$