Question

A one litre flask contains certain quantity of mercury. If the volume of air inside the flask remains the same at all temperatures then the volume of mercury in the flask is (volume expansion coefficient of mercury is 20 times that of flask)

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

Answer 1

Answer: (B)

Let $V$ and $V_{\text {mercury }}$ be the volume of flask and volume of mercury inside it. Respectively as the volume of air inside the flask remains the same at all temperatures, this is possible only if the volume expansion of flask will be equal to that of mercury.
i.e. $\Delta V=\Delta V_{\text {mercury }}$ or
$V \gamma_{\text {flask }} \Delta T=V_{\text {mercury }} \gamma_{\text {mercury }} \Delta T$
or $V_{\text {mercury }}=\frac{V \gamma_{\text {flask }}}{\gamma_{\text {mercury }}}$
Here, $V=1\, L =1000 \,cc , \frac{\gamma_{\text {flask }}}{\gamma_{\text {mercury }}}=\frac{1}{20}$
$\therefore V_{\text {mercury }}=(1000\, cc )\left(\frac{1}{20}\right)=50\, cc$